The practice and study of water hydraulics / Hidraulicki proracuni

Water Hydraulics

Beginning students of water hydraulics and its principlesoften come to the subject matter with certain misgivings.For example, water/wastewater operators quickly learn onthe job that their primary operational/maintenance con-cerns involves a daily routine of monitoring, sampling,laboratory testing, operation and process maintenance.How does water hydraulics relate to daily operations? Thehydraulic functions of the treatment process have alreadybeen designed into the plant. Why learn water hydraulicsat all?

Simply put, while having hydraulic control of the plant isobviously essential to the treatment process, maintainingand ensuring continued hydraulic control is also essential.No water/wastewater facility (and/or distribution collec-tion system) can operate without proper hydraulic control.The operator must know what hydraulic control is andwhat it entails to know how to ensure proper hydrauliccontrol. Moreover, in order to understand the basics ofpiping and pumping systems, water/wastewater mainte-nance operators must have a fundamental knowledge ofbasic water hydraulics.1

Note: The practice and study of water hydraulics isnot new. Even in medieval times, water hydrau-lics was not new. “Medieval Europe had inher-ited a highly developed range of Romanhydraulic components.”2 The basic conveyancetechnology, based on low-pressure systems ofpipe and channels, was already established. Instudying modern water hydraulics, it is impor-tant to remember that the science of waterhydraulics is the direct result of two immediateand enduring problems: “The acquisition offresh water and access to continuous strip ofland with a suitable gradient between the sourceand the destination.”3

5.1 WHAT IS WATER HYDRAULICS?

The word hydraulic is derived from the Greek words hydro(meaning water) and aulis (meaning pipe). Originally, theterm hydraulics referred only to the study of water at restand in motion (flow of water in pipes or channels). Todayit is taken to mean the flow of any liquid in a system.

What is a liquid? In terms of hydraulics, a liquid canbe either oil or water. In fluid power systems used inmodern industrial equipment, the hydraulic liquid of

choice is oil. Some common examples of hydraulic fluidpower systems include automobile braking and powersteering systems, hydraulic elevators, and hydraulic jacksor lifts. Probably the most familiar hydraulic fluid powersystems in water and wastewater operations are used ondump trucks, front-end loaders, graders, and earth-movingand excavation equipment. In this text, we are concernedwith liquid water.

Many find the study of water hydraulics difficult andpuzzling (especially those related questions on the licen-sure examinations), but we know it is not mysterious ordifficult. It is the function or output of practical applica-tions of the basic principles of water physics.

Because water and wastewater treatment is based onthe principles of water hydraulics, concise, real-worldtraining is necessary for operators who must operate theplant and for those sitting for state licensure/certificationexaminations.

5.2 BASIC CONCEPTS

The relationship shown above is important because ourstudy of hydraulics begins with air. A blanket of air, manymiles thick surrounds the earth. The weight of this blanketon a given square inch of the earth’s surface will varyaccording to the thickness of the atmospheric blanketabove that point. As shown above, at sea level, the pressureexerted is 14.7 pounds per square inch (psi). On a moun-taintop, air pressure decreases because the blanket is notas thick.

1 ft3 H2O = 62.4 lb

The relationship shown above is also important: bothcubic feet and pounds are used to describe a volume ofwater. There is a defined relationship between these twomethods of measurement. The specific weight of water isdefined relative to a cubic foot. One cubic foot of waterweighs 62.4 lb. This relationship is true only at a temper-ature of 4°C and at a pressure of 1 atm (known as standardtemperature and pressure (STP) — 14.7 psi at sea levelcontaining 7.48 gal). The weight varies so little that, forpractical purposes, this weight is used from a temperature

5

Air Pressure @ Sea Level psi( ) = 14 7.

© 2003 by CRC Press LLC

0°C to 100°C. One cubic inch of water weighs 0.0362 lb.Water 1 ft deep will exert a pressure of 0.43 psi on thebottom area (12 in. ¥ 0.0362 lb/in.3). A column of watertwo feet high exerts 0.86 psi, a column 10 ft high exerts4.3 psi, and a column 55 ft high exerts

A column of water 2.31 ft high will exert 1.0 psi. Toproduce a pressure of 50 psi requires a water column

The important points being made here are:

1. 1 ft3 H2O = 62.4 lb (see Figure 4.11)2. A column of water 2.31 ft high will exert

1.0 psi.

Another relationship is also important:

1 gal H2O = 8.34 lb

At STP, 1 ft3 H2O contains 7.48 gal. With these tworelationships, we can determine the weight of 1 gal H2O.This is accomplished by

wt 1 gal H2O =

Thus,

1 gal H2O = 8.34 lb

Note: Further, this information allows cubic feet to beconverted to gallons by simply multiplying thenumber of cubic feet by 7.48 gal/ft.3

EXAMPLE 5.1

Problem:

Find the number of gallons in a reservoir that has a volumeof 855.5 ft.3

Solution:

Note: As mentioned in Chapter 4, the term head isused to designate water pressure in terms of theheight of a column of water in feet. For exam-ple, a 10-ft column of water exerts 4.3 psi. Thiscan be called 4.3-psi pressure or 10 ft of head.

5.2.1 STEVIN’S LAW

Stevin’s law deals with water at rest. Specifically, the lawstates: “The pressure at any point in a fluid at rest dependson the distance measured vertically to the free surface andthe density of the fluid.” Stated as a formula, this becomes

p = w ¥ h (5.1)

wherep = pressure in pounds per square foot (lb/ft2)w = density in pounds per cubic foot (lb/ft3)h = vertical distance in feet

EXAMPLE 5.2

Problem:

What is the pressure at a point 18 ft below the surface ofa reservoir?

Solution:

Note: To calculate this, we must know that the densityof the water (w) is 62.4 lb/ft3.

Water and wastewater operators generally measurepressure in pounds per square inch rather than pounds persquare foot; to convert, divide by 144 in.2/ft2 (12 in. ¥12 in. = 144 in.2):

5.3 PROPERTIES OF WATER

Table 5.1 shows the relationship between temperature,specific weight, and the density of water.

5.3.1 DENSITY AND SPECIFIC GRAVITY

When we say that iron is heavier than aluminum, we saythat iron has greater density than aluminum. In practice,what we are really saying is that a given volume of ironis heavier than the same volume of aluminum.

Note: What is density? Density is the mass per unitvolume of a substance.

Suppose you had a tub of lard and a large box of coldcereal, each having a mass of 600 g. The density of the

55 0 43 23 65ft psi ft psi¥ =. .

50 2 31 115 5psi ft psi ft¥ =. .

62.4 lb7.48 alg

lb gal= 8 34.

855 5 7 48 63993 3. .ft gal ft gal¥ = ( )rounded

p w h

lb ft ft

lb ft

= ¥

= ¥

=

62 4 18

1123

3

2

.

Pft

= = ( )1123 lb ft144 in.

psi rounded2

2 2 7 8.


cereal would be much less than the density of the lardbecause the cereal occupies a much larger volume thanthe lard occupies.

The density of an object can be calculated by usingthe formula:

(5.2)

In water and wastewater treatment, perhaps the mostcommon measures of density are pounds per cubic foot(lb/ft3) and pounds per gallon (lb/gal).

The density of a dry material, such as cereal, lime,soda, and sand, is usually expressed in pounds per cubicfoot. The density of a liquid, such as liquid alum, liquidchlorine, or water, can be expressed either as pounds percubic foot or as pounds per gallon. The density of a gas,such as chlorine gas, methane, carbon dioxide, or air, isusually expressed in pounds per cubic foot.

As shown in Table 5.1, the density of a substance likewater changes slightly as the temperature of the substance

changes. This occurs because substances usually increasein volume (size — they expand) as they become warmer.Because of this expansion with warming, the same weightis spread over a larger volume, so the density is lowerwhen a substance is warm than when it is cold.

Note: What is specific gravity? Specific gravity is theweight (or density) of a substance compared tothe weight (or density) of an equal volume ofwater. [Note: The specific gravity of water is 1].

This relationship is easily seen when 1 ft3 H2O, whichweighs 62.4 lb as shown earlier, is compared to 1 ft3 ofaluminum, which weights 178 lb. Aluminum is 2.7 timesas heavy as water.

It is not that difficult to find the specific gravity (sp gr)of a piece of metal. All you have to do is to weigh themetal in air, then weigh it under water. Its loss of weightis the weight of an equal volume of water. To find thespecific gravity, divide the weight of the metal by its lossof weight in water.

(5.3)

EXAMPLE 5.3

Problem:

Suppose a piece of metal weighs 150 lb in air and 85 lbunderwater. What is the specific gravity?

Solution:

Step 1: Calculate the loss of weight in water:

150 lb – 85 lb = 65 lb loss of weight in H2O

Step 2: Calculate the specific gravity

Note: In a calculation of specific gravity, it is essentialthat the densities be expressed in the same units.

As stated earlier, the specific gravity of water is 1.00.This is the standard — the reference to which all other liquidor solid substances are compared. Specifically, any objectthat has a specific gravity greater than 1.0 will sink in water(rocks, steel, iron, grit, floc, sludge). Substances with aspecific gravity of less than 1.0 will float (wood, scum,gasoline). Considering the total weight and volume of a ship,its specific gravity is less than one; therefore, it can float.

The most common use of specific gravity in water andwastewater treatment operations is in gallons-to-poundsconversions. In many cases, the liquids being handled have

TABLE 5.1 Water Properties (Temperature, Specific Weight, and Density)

Temperature(∞∞∞∞F)

Specific Weight(lb/ft3)

Density(slugs/ft3)

32 62.4 1.9440 62.4 1.9450 62.4 1.9460 62.4 1.9470 62.3 1.9480 62.2 1.9390 62.1 1.93

100 62.0 1.93110 61.9 1.92120 61.7 1.92130 61.5 1.91140 61.4 1.91150 61.2 1.90160 61.0 1.90170 60.8 1.89180 60.6 1.88190 60.4 1.88200 60.1 1.87210 59.8 1.86

Source: From Spellman, F.R. and Drinan, J., WaterHydraulics, Technomic Publ., Lancaster, PA, 2001.

Densityv

= Mass

1 62 4 62 4

1 8 34 8 34

32

3

2

ft H O lb lb ft

gal H O lb lb gal

= =

= =

. .

. .

— Density

— Density

sp grWt of Substance

Wt of Equal Volume of Water=

sp gr150

65 = = 2 3.


a specific gravity of 1.00 or very nearly 1.00 (between0.98 and 1.02), so 1.00 may be used in the calculationswithout introducing significant error. However, in calcu-lations involving a liquid with a specific gravity of lessthan 0.98 or greater than 1.02, the conversions from gallonsto pounds must consider specific gravity. The techniqueis illustrated in the following example.

EXAMPLE 5.4

Problem:

There are 1455 gal of a certain liquid in a basin. If thespecific gravity of the liquid is 0.94, how many poundsof liquid are in the basin?

Solution:

Normally, for a conversion from gallons to pounds, wewould use the factor 8.34 lb/gal (the density of water) if thesubstance’s specific gravity were between 0.98 and 1.02.However, in this instance the substance has a specific gravityoutside this range, so the 8.34 factor must be adjusted.

Step 1: Multiply 8.34 lb/gal by the specific gravity toobtain the adjusted factor:

Step 2: Convert 1455 gal to lb using the corrected factor:

5.4 FORCE AND PRESSURE

Water exerts force and pressure against the walls of itscontainer, whether it is stored in a tank or flowing in apipeline. There is a difference between force and pressure,though they are closely related. Force and pressure aredefined below.

Force is the push or pull influence that causes motion.In the English system, force and weight are often used inthe same way. The weight of 1 ft3 H2O is 62.4 lb. Theforce exerted on the bottom of a 1-ft cube is 62.4 lb (seeFigure 4.11). If we stack two cubes on top of one another,the force on the bottom will be 124.8 lb.

Pressure is a force per unit of area. In equation form,this can be expressed as:

(5.4)

whereP = pressureF = forceA = area over which the force is distributed

Earlier we pointed out that pounds per square inch orpounds per square foot are common expressions of pres-sure. The pressure on the bottom of the cube is 62.4 lb/ft2

(see Figure 4.11). It is normal to express pressure inpounds per square inch. This is easily accomplished bydetermining the weight of 1 in.2 of a cube 1 ft high. If wehave a cube that is 12 inches on each side, the number ofsquare inches on the bottom surface of the cube is 12 in. ¥12 in. = 144 in.2 Dividing the weight by the number ofsquare inches determines the weight on each square inch.

This is the weight of a column of water one-inchsquare and 1 ft tall. If the column of water were 2 ft tall,the pressure would be 2 ft ¥ 0.433 psi/ft = 0.866 psi.

Note: 1 ft H2O = 0.433 psi

With the above information, feet of head can be con-verted to pounds per square inch by multiplying the feetof head times 0.433 psi/ft.

EXAMPLE 5.5

Problem:

A tank is mounted at a height of 90 ft. Find the pressureat the bottom of the tank.

Solution:

Note: To convert pounds per square inch to feet, youwould divide the pounds per square inch by0.433 psi/ft.

EXAMPLE 5.6

Problem:

Find the height of water in a tank if the pressure at thebottom of the tank is 22 psi.

Solution:

Important Point: One of the problems encountered ina hydraulic system is storing the liquid. Unlikeair, which is readily compressible and is capa-ble of being stored in large quantities in rela-tively small containers, a liquid such as watercannot be compressed. Therefore, it is not pos-sible to store a large amount of water in a small

8 34 0 94 7 84. . .lb gal lb gal¥ = ( ) rounded

1455 7 84 11 407gal lb gal lb¥ = ( ). , rounded

P = FA

psiin

= =62.4 lb ft

psi ft144

0 4332..

90 0 433 39ft psi ft psi¥ = ( ). rounded

H ft22 psi

.433 psi ft ft rounded( ) ( )= =

051


tank — 62.4 lb of water occupies a volume of1 ft3, regardless of the pressure applied to it.

5.4.1 HYDROSTATIC PRESSURE

Figure 5.1 shows a number of differently shaped, con-nected, open containers of water. Note that the water levelis the same in each container, regardless of the shape orsize of the container. This occurs because pressure isdeveloped, within water (or any other liquid), by theweight of the water above. If the water level in any onecontainer were to be momentarily higher than that in anyof the other containers, the higher pressure at the bottomof this container would cause some water to flow into thecontainer having the lower liquid level. In addition, thepressure of the water at any level (such as Line T) is thesame in each of the containers. Pressure increases becauseof the weight of the water. The further down from thesurface, the more pressure is created. This illustrates thatthe weight, not the volume, of water contained in a vesseldetermines the pressure at the bottom of the vessel.

Nathanson (1997) points out some very importantprinciples that always apply for hydrostatic pressure.

1. The pressure depends only on the depth ofwater above the point in question (not on thewater surface area).

2. The pressure increases in direct proportion tothe depth.

3. The pressure in a continuous volume of wateris the same at all points that are at the samedepth.

4. The pressure at any point in the water acts inall directions at the same depth.

5.4.2 EFFECTS OF WATER UNDER PRESSURE5

Water under pressure and in motion can exert tremendousforces inside a pipeline. One of these forces, calledhydraulic shock or water hammer, is the momentaryincrease in pressure that occurs when there is a suddenchange of direction or velocity of the water.

When a rapidly closing valve suddenly stops waterflowing in a pipeline, pressure energy is transferred to thevalve and pipe wall. Shockwaves are set up within thesystem. Waves of pressure move in a horizontal yo-yofashion — back and forth — against any solid obstaclesin the system. Neither the water nor the pipe will compressto absorb the shock, which may result in damage to pipes,valves, and shaking of loose fittings.

Another effect of water under pressure is called thrust.Thrust is the force that water exerts on a pipeline as itrounds a bend. As shown in Figure 5.2, thrust usually actsperpendicular (at 90°) to the inside surface its pushesagainst. As stated, it affects bends, but also reducers, deadends, and tees. Uncontrolled, the thrust can cause move-ment in the fitting or pipeline, which will lead to separa-tion of the pipe coupling away from both sections ofpipeline, or at some other nearby coupling upstream ordownstream of the fitting.

There are two types of devices commonly used tocontrol thrust in larger pipelines: thrust blocks and thrustanchors. A thrust block is a mass of concrete cast in placeonto the pipe and around the outside bend of the turn. Anexample is shown in Figure 5.3. These are used for pipeswith tees or elbows that turn left or right or slant upward.The thrust is transferred to the soil through the largerbearing surface of the block.

FIGURE 5.1 Hydrostatic pressure. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

T

Liquidlevel

FIGURE 5.2 Shows direction of thrust in a pipe in a trench(viewed from above). (From Spellman, F.R. and Drinan, J.,Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

Thrust90°

Flow

Flow


A thrust anchor is a massive block of concrete, oftena cube, cast in place below the fitting to be anchored (seeFigure 5.4). As shown in Figure 5.4, imbedded steelshackle rods anchor the fitting to the concrete block, effec-tively resisting upward thrusts.

The size and shape of a thrust control device dependson pipe size, type of fitting, water pressure, water hammer,and soil type.

5.5 HEAD

Head is defined as the vertical distance the water or waste-water must be lifted from the supply tank to the discharge,or as the height a column of water would rise due to thepressure at its base. A perfect vacuum plus atmosphericpressure of 14.7 psi would lift the water 34 ft. If the topof the sealed tube is opened to the atmosphere and thereservoir is enclosed, the pressure in the reservoir isincreased; the water will rise in the tube. Because atmo-spheric pressure is essentially universal, we usually ignorethe first 14.7-psi of actual pressure measurements, andmeasure only the difference between the water pressureand the atmospheric pressure; we call this gauge pressure.For example, water in an open reservoir is subjected to the

14.7 psi of atmospheric pressure, but subtracting this14.7 psi leaves a gauge pressure of 0 psi. This shows thatthe water would rise 0 feet above the reservoir surface. Ifthe gauge pressure in a water main were 120 psi, the waterwould rise in a tube connected to the main:

The total head includes the vertical distance the liquidmust be lifted (static head), the loss to friction (frictionhead), and the energy required to maintain the desiredvelocity (velocity head).

(5.5)

5.5.1 STATIC HEAD

Static head is the actual vertical distance the liquid mustbe lifted.

(5.6)

EXAMPLE 5.7

Problem:

The supply tank is located at elevation 118 ft. The dis-charge point is at elevation 215 ft. What is the static headin feet?

Solution:

Static Head (ft) = 215 ft ¥ 118 ft = 97 ft

5.5.2 FRICTION HEAD

Friction head is the equivalent distance of the energy thatmust be supplied to overcome friction. Engineering refer-ences include tables showing the equivalent vertical dis-tance for various sizes and types of pipes, fittings, andvalves. The total friction head is the sum of the equivalentvertical distances for each component.

(5.7)

5.5.3 VELOCITY HEAD

Velocity head is the equivalent distance of the energyconsumed in achieving and maintaining the desired veloc-ity in the system.

FIGURE 5.3 Thrust block. (From Spellman, F.R. and Drinan,J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

FIGURE 5.4 Thrust anchor. (From Spellman, F.R. and Dri-nan, J., Water Hydraulics, Technomic Publ., Lancaster, PA,2001.)

Thrust

Top view

Thrustdirection

Shacklerods

Couplings

120 2 31 277psi ft psi ft¥ = ( ). rounded

Total Head Static Head Friction Head

Velocity Head

= + +

Static Head Discharge Elevation

Supply Elevation

= ¥

Friction Head ft Energy Losses Due

to Friction

( ) =


(5.8)

5.5.4 TOTAL DYNAMIC HEAD (TOTAL SYSTEM HEAD)

5.5.5 PRESSURE/HEAD

The pressure exerted by water and wastewater is directlyproportional to its depth or head in the pipe, tank, orchannel. If the pressure is known, the equivalent head canbe calculated.

(5.10)

EXAMPLE 5.8

Problem:

The pressure gauge on the discharge line from the influent

pump reads 72.3 psi. What is the equivalent head in feet?

Solution:

5.5.6 HEAD/PRESSURE

If the head is known, the equivalent pressure can be cal-culated using the following equation:

(5.11)

EXAMPLE 5.9

Problem:

The tank is 22 ft deep. What is the pressure in psi at the

bottom of the tank when it is filled with water?

Solution:

5.6 FLOW/DISCHARGE RATE: WATER IN MOTION

The study of fluid flow is much more complicated thanthat of fluids at rest, but it is important to have an under-standing of these principles. This is because the water ina waterworks and distribution system and in a wastewatertreatment plant and collection system is nearly always inmotion.

Discharge (or flow) is the quantity of water passing agiven point in a pipe or channel during a given period.This is stated another way for open channels: the flow ratethrough an open channel is directly related to the velocityof the liquid and the cross-sectional area of the liquid inthe channel.

Q = A ¥ V (5.12)

whereQ = flow (discharge in cubic feet per second

[ft3/sec])

A = cross-sectional area of the pipe or channel (ft2)V = water velocity in feet per second (ft/sec)

EXAMPLE 5.10

Problem:

The channel is 6 ft wide and the water depth is 3 ft. Thevelocity in the channel is 4 ft/sec. What is the dischargeor flow rate in ft3/sec?

Solution:

Discharge or flow can be recorded as gallons per day(gal/d), gallons per minute (gal/min), or cubic feet(ft3/sec). Flows treated by many waterworks or wastewatertreatment plants are large, and often referred to in milliongallons per day (MGD). The discharge or flow rate canbe converted from cubic feet per second to other unitssuch as gallons per minute or million gallons per day byusing appropriate conversion factors.

EXAMPLE 5.11

Problem:

A pipe 12 in. in diameter has water flowing through it at10 ft/sec. What is the discharge in (a) ft3/sec, (b) gal/min,and (c) MGD?

Velocity Head ft Energy Losses to

Maintain Velocity

( ) =

Total Dynamic Head Static Head Friction Head

Velocity Head

= + +

(5.9)

Head ft Pressure psi ft psi( ) = ( ) ¥ 2 31.

Head ft( ) = ¥ =72 3 2 31 167. .psi ft psi ft

Pressure psiHead ft .31 ft psi

( ) = ( )2

Pressure psi22 ft

.31 ft psi

psi rounded

( )

( )

=

=

2

9 52.

Q ft A V

ft ft ft ft

3

36 3 4 72

sec

sec sec

( ) = ¥

= ¥ ¥ =


Solution:

Before we can use the basic formula (Equation 5.13), wemust determine the area of the pipe. The formula for thearea of a circle is

whereD = diameter of the circle in feetr = radius of the circle in feet

p = the constant value 3.14159 (or simply 3.14)

Therefore, the area of the pipe is:

Now we can determine the discharge in ft3/sec (part [a]):

For part (b), we need to know that 1 ft3/sec is 449 gal/min,so 7.85 ft3/sec ¥ 449 gal/min/ft3/sec = 3525 gal/min(rounded).

Finally, for part (c), 1 MGD is 1.55 ft3/sec, so:

Note: Flow may be laminar (streamline — seeFigure 5.5) or turbulent (see Figure 5.6). Lam-inar flow occurs at extremely low velocities.The water moves in straight parallel lines,called streamlines, or laminae, that slide uponeach other as they travel, rather than mixing up.Normal pipe flow is turbulent flow that occursbecause of friction encountered on the inside ofthe pipe. The outside layers of flow are throwninto the inner layers; the result is that all thelayers mix and are moving in different direc-tions and at different velocities. However, thedirection of flow is forward.

Note: Flow may be steady or unsteady. For our pur-poses, we consider steady state flow only; mostof the hydraulic calculations in this manualassume steady state flow.

5.6.1 AREA/VELOCITY

The law of continuity states that the discharge at eachpoint in a pipe or channel is the same as the discharge at

any other point (if water does not leave or enter the pipeor channel). That means that under the assumption ofsteady state flow, the flow that enters the pipe or channelis the same flow that exits the pipe or channel. In equationform, this becomes

Q1 = Q2 or A1 ¥ V1 = A2 ¥ V2 (5.13)

Note: In regards to the area/velocity relationship,Equation 5.13 also makes clear that for a givenflow rate the velocity of the liquid varies indi-rectly with changes in the cross-sectional areaof the channel or pipe. This principle providesthe basis for many of the flow measurementdevices used in open channels (weirs, flumes,and nozzles).

EXAMPLE 5.12

Problem:

A pipe 12 in. in diameter is connected to a 6-in. diameterpipe. The velocity of the water in the 12-in. pipe is 3 ft/sec.What is the velocity in the 6-in. pipe?

Solution:

Using the equation A1 ¥ V1 = A2 ¥ V2, we need to deter-mine the area of each pipe:

AD

r= ¥ = ¥p p2

2

4

Aft

= ¥ = ¥ =( )

pD

0.785 ft

22

43 14

1

4

2

.

Q A V ft ft ft= ¥ = ¥ =0 785 10 7 852 3. sec . sec

7.85 ft

.55 ft GD

3

3

sec

sec.

15 06

MGDM=

FIGURE 5.5 Laminar (streamline) flow. (From Spellman,F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lan-caster, PA, 2001.)

FIGURE 5.6 Turbulent flow. (From Spellman, F.R. and Dri-nan, J., Water Hydraulics, Technomic Publ., Lancaster, PA,2001.)

B

Streamline Turbulent


For 12-in. pipe:

For 6-in. pipe:

The continuity equation now becomes:

0.785 ft2 ¥ 3ft/sec = 0.196 ft2 ¥ V2

Solving for V2:

5.6.2 PRESSURE/VELOCITY

In a closed pipe flowing full (under pressure), the pressureis indirectly related to the velocity of the liquid. This prin-ciple, when combined with the principle discussed in theprevious section, forms the basis for several flow measure-ment devices (venturi meters and rotameters) as well as theinjector used for dissolving chlorine into water, and chlo-rine, sulfur dioxide and/or other chemicals into wastewater.

Velocity1 ¥ Pressure1 = Velocity2 ¥ Pressure2 (5.14)

or

V1 ¥ P1 = V2 ¥ P2

5.7 PIEZOMETRIC SURFACE AND BERNOULLI’S THEOREM

They will take your hand and lead you to the pearls ofthe desert, those secret wells swallowed by oyster cragsof wadi, underground caverns that bubble rusty salt wateryou would sell your own mothers to drink.6

To keep the systems in your plant operating properly andefficiently, you must understand the basics of hydraulics —the laws of force, motion, and others. As stated previously,most applications of hydraulics in water and wastewater

treatment systems involve water in motion — in pipesunder pressure or in open channels under the force ofgravity. The volume of water flowing past any given pointin the pipe or channel per unit time is called the flow rateor discharge, or just flow.

In regards to flow, continuity of flow and the continu-ity equation have been discussed (i.e., Equation 5.15).Along with the continuity of flow principle and continuityequation, the law of conservation of energy, piezometricsurface, and Bernoulli’s theorem (or principle) are alsoimportant to our study of water hydraulics.

5.7.1 LAW OF CONSERVATION OF ENERGY

Many of the principles of physics are important to thestudy of hydraulics. When applied to problems involvingthe flow of water, few of the principles of physical scienceare more important and useful to us than the law of con-servation of energy. Simply, the law of conservation ofenergy states that energy can neither be created nordestroyed, but it can be converted from one form toanother. In a given closed system, the total energy isconstant.

5.7.2 ENERGY HEAD

Two types of energy, kinetic and potential, and three formsof mechanical energy exist in hydraulic systems: potentialenergy due to elevation, potential energy due to pressure,and kinetic energy due to velocity. Energy has the unitsof foot pounds (ft-lb). It is convenient to express hydraulicenergy in terms of energy head, in feet of water. This isequivalent to foot-pounds per pound of water (ft-lb/lbH2O = ft H2O).

5.7.3 PIEZOMETRIC SURFACE7

As mentioned earlier, we have seen that when a verticaltube, open at the top, is installed onto a vessel of water,the water will rise in the tube to the water level in thetank. The water level to which the water rises in a tube isthe piezometric surface. The piezometric surface is animaginary surface that coincides with the level of the waterto which water in a system would rise in a piezometer (aninstrument used to measure pressure).

The surface of water that is in contact with the atmo-sphere is known as free water surface. Many importanthydraulic measurements are based on the difference inheight between the free water surface and some point inthe water system. The piezometric surface is used to locatethis free water surface in a vessel, where it cannot beobserved directly.

To understand how a piezometer actually measurespressure, consider the following example.

If a clear, see-through pipe is connected to the side ofa clear glass or plastic vessel, the water will rise in the

A

ft

= ¥

= ¥( )

pD

= 0.785 ft

2

2

4

3 141

4

2

.

A = ¥3 140 5

4

2

..

= 0.196 ft2

Vft2

2

2

0 785 3

0 196=

¥.

.

ft ft sec

= 12 ft sec


pipe to indicate the level of the water in the vessel. Sucha see-through pipe, the piezometer, allows you to see thelevel of the top of the water in the pipe; this is the piezo-metric surface.

In practice, a piezometer is connected to the side of atank or pipeline. If the water-containing vessel is not underpressure (as is the case in Figure 5.7), the piezometricsurface will be the same as the free water surface in thevessel, just as it would if a drinking straw (the piezometer)were left standing a glass of water.

When pressurized in a tank and pipeline system, asthey often are, the pressure will cause the piezometricsurface to rise above the level of the water in the tank. Thegreater the pressure, the higher the piezometric surface (seeFigure 5.8). An increased pressure in a water pipeline sys-tem is usually obtained by elevating the water tank.

Note: In practice, piezometers are not installed onwater towers, because water towers are hundredsof feet high, or on pipelines. Instead, pressuregauges are used that record pressure in feet ofwater or in pounds per square inch.

Water only rises to the water level of the main bodyof water when it is at rest (static or standing water). The

situation is quite different when water is flowing. Con-sider, for example, an elevated storage tank feeding adistribution system pipeline. When the system is at rest,all valves closed, all the piezometric surfaces are the sameheight as the free water surface in storage. On the otherhand, when the valves are opened and the water begins toflow, the piezometric surface changes. This is an importantpoint because as water continues to flow down a pipeline,less pressure is exerted. This happens because some pres-sure is lost (used up) keeping the water moving over theinterior surface of the pipe (friction). The pressure that islost is called head loss.

5.7.3.1 Head Loss

Head loss is best explained by example. Figure 5.9 showsan elevated storage tank feeding a distribution systempipeline. When the valve is closed (Figure 5.9A), all thepiezometric surfaces are the same height as the free watersurface in storage. When the valve opens and water beginsto flow (Figure 5.9B), the piezometric surfaces drop. The

FIGURE 5.7 A container not under pressure where the pie-zometric surface is the same as the free water surface in thevessel. (From Spellman, F.R. and Drinan, J., Water Hydrau-lics, Technomic Publ., Lancaster, PA, 2001.)

Free watersurface

Open end

Piezometer

Piezometric surface

FIGURE 5.8 A container under pressure where the piezo-metric surface is above the level of the water in the tank.(From Spellman, F.R. and Drinan, J., Water Hydraulics, Tech-nomic Publ., Lancaster, PA, 2001.)

Pressure applied

Piezometric surface

FIGURE 5.9 Shows head loss and piezometric surface changes when water is flowing. (From Spellman, F.R. and Drinan, J.,Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

Piezometric surface Piezometric surface

Closed valve Open valve

HGL

HGL

1 2 3 1 2 3

(A) (B)


further along the pipeline, the lower the piezometric sur-face, because some of the pressure is used up keeping thewater moving over the rough interior surface of the pipe.Thus, pressure is lost and is no longer available to pushwater up in a piezometer; this is the head loss.

5.7.3.2 Hydraulic Grade Line

When the valve is opened as in Figure 5.9, flow beginswith a corresponding energy loss due to friction. Thepressures along the pipeline can measure this loss. InFigure 5.9B, the difference in pressure heads betweensections 1, 2, and 3 can be seen in the piezometer tubesattached to the pipe. A line connecting the water surfacein the tank with the water levels at sections 1, 2, and 3shows the pattern of continuous pressure loss along thepipeline. This is called the hydraulic grade line (HGL) orhydraulic gradient of the system. (It is important to pointout that in a static water system, the HGL is always hor-izontal. The HGL is a very useful graphical aid whenanalyzing pipe flow problems.)

Note: During the early design phase of a treatmentplant, it is important to establish the hydraulicgrade line across the plant because both theproper selection of the plant site elevation andthe suitability of the site depend on this consid-eration. Typically, most conventional watertreatment plants required 16 to 17 ft of headloss across the plant.

Key Point: Changes in the piezometric surface occurwhen water is flowing.

5.7.4 BERNOULLI’S THEOREM8

Swiss physicist and mathematician Samuel Bernoullideveloped the calculation for the total energy relationshipfrom point to point in a steady state fluid system in the1700s. Before discussing Bernoulli’s energy equation, itis important to understand the basic principle behind Ber-noulli’s equation.

Water (and any other hydraulic fluid) in a hydraulicsystem possesses two types of energy — kinetic andpotential. Kinetic energy is present when the water is inmotion. The faster the water moves, the more kineticenergy is used. Potential energy is a result of the waterpressure. The total energy of the water is the sum of thekinetic and potential energy. Bernoulli’s principle statesthat the total energy of the water (fluid) always remainsconstant. Therefore, when the water flow in a systemincreases, the pressure must decrease. When water startsto flow in a hydraulic system, the pressure drops. Whenthe flow stops, the pressure rises again. The pressure gaugesshown in Figure 5.10 indicate this balance more clearly.

Note: The basic principle explained above ignoresfriction losses from point to point in a fluidsystem employing steady state flow.

5.7.4.1 Bernoulli’s Equation

In a hydraulic system, total energy head is equal tothe sum of three individual energy heads. This can beexpressed as

Total Head = Elevation Head + Pressure Head + Velocity Head

whereElevation head = pressure due to the elevation of the

waterPressure head = the height of a column of water that

a given hydrostatic pressure in a system could support

Velocity head = energy present due to the velocity of the water

This can be expressed mathematically as

(5.15)

whereE = total energy headz = height of the water above a reference plane (ft)P = pressure (psi)w = unit weight of water (62.4 lb/ft3)V = flow velocity (ft/sec)g = acceleration due to gravity (32.2 ft/sec2)

Consider the constriction in section of pipe shown inFigure 5.11. We know, based on the law of energy con-servation, that the total energy head at section A, E1, mustequal the total energy head at section B, E2, and usingEquation 5.16, we get Bernoulli’s equation.

(5.16)

FIGURE 5.10 Demonstrates Bernoulli’s principle. (FromSpellman, F.R. and Drinan, J., Water Hydraulics, TechnomicPubl., Lancaster, PA, 2001.)

E zw

Vg

= + +P

2

2

zP

w

Vz

P

w

V

gAA A

BB B= + = + +

2 2

2 2

g


The pipeline system shown in Figure 5.11 is horizon-tal. Therefore, we can simplify Bernoulli’s equationbecause zA = zB.

Because they are equal, the elevation heads cancel outfrom both sides, leaving:

(5.17)

As water passes through the constricted section of thepipe (section B), we know from continuity of flow thatthe velocity at section B must be greater than the velocityat section A, because of the smaller flow area at sectionB. This means that the velocity head in the systemincreases as the water flows into the constricted section.However, the total energy must remain constant. For thisto occur, the pressure head, and therefore the pressure,must drop. In effect, pressure energy is converted intokinetic energy in the constriction.

The fact that the pressure in the narrower pipe section(constriction) is less than the pressure in the bigger sectionseems to defy common sense. However, it does followlogically from continuity of flow and conservation ofenergy. The fact that there is a pressure difference allowsmeasurement of flow rate in the closed pipe.

EXAMPLE 5.13

Problem:

In Figure 5.11, the diameter at Section A is 8 in. and atsection B, it is 4 in. The flow rate through the pipe is 3.0ft3/sec and the pressure at Section A is 100 psi. What isthe pressure in the constriction at Section B?

Solution:

Step 1: Compute the flow area at each section, as follows:

Step 2: From Q = A ¥ V or V = Q/A, we get:

Step 3: Applying Equation 5.18, we get:

Note: The pressures are multiplied by 144 in2/ft2 toconvert from psi to lb/ft2 to be consistent withthe units for w; the energy head terms are infeet of head.

Continuing, we get

231 + 1.15 = 2.3PB + 18.5

and

FIGURE 5.11 Shows the result of the law of conservation. Since the velocity and kinetic energy of the water flowing in theconstricted section must increase, the potential energy may decrease. This is observed as a pressure drop in the constriction.(Adapted from Nathanson, J.A., Basic Environmental Technology: Water Supply, Waste Management, and Pollution Control,2nd ed. Prentice Hall, Upper Saddle River, NJ: 1997. p. 29.)

Reference plane

Constriction

PA

w

2/2gvB

2

2g

PBw

zBzA

E2

Total energy line

QA B

Pressuredrop

vA

1E

P

w

V P

w

V

gA A B B+ = +

2 2

g 2 2

Aft

A=

¥=

( ) ( )p 0 666

4

.

0.349 ft rounded

22

Aft

B=

¥=( )p 0 333

4

.2

2

0.087 ft

VA

= = ( )3 06

. sec.

ft

0.349 ft 8 ft sec rounded

3

2

VB

= = ( )3 034 5

. sec.

ft

0.087 ft ft sec rounded

3

2

100 144

62 4

8 6

2 32 2

144

62 4

34 5

2 32 2

¥+

¥=

¥+

¥.

.

. .

.

.

2 2

PB


5.8 HYDRAULIC MACHINES (PUMPS)

Only the sail can contend with the pump for the title ofthe earliest invention for the conversion of natural energyto useful work, and it is doubtful that the sail takes prece-dence. Since the sail cannot, in any event, be classified asa machine, the pump stands essentially unchallenged asthe earliest form of machine that substituted natural energyfor muscular effort in the fulfillment of man’s needs.9

Conveying water and wastewater to and from processequipment is an integral part of the water and wastewaterindustry that requires energy consumption. The amount ofenergy required depends on the height to which the wateror wastewater is raised, the length and diameter of theconveying conduits, the rate of flow, and the water orwastewater’s physical properties (in particular, viscosityand density). In some applications, external energy fortransferring water or wastewater is not required. For exam-ple, when water or wastewater flows to a lower elevationunder the influence of gravity, a partial transformation ofthe water or wastewater’s potential energy into kineticenergy occurs. However, when conveying water or waste-water through horizontal conduits, especially to higherelevations within a system, mechanical devices such aspumps are employed. Requirements vary from small unitsused to pump only a few gallons per minute to large unitscapable of handling several hundred cubic feet per sec-ond.10 Table 5.2 lists pump applications in water andwastewater treatment operations.

Note: In determining the amount of pressure or forcea pump must provide to move the water orwastewater, the term pump head was estab-lished.

Several methods are available for transporting water,wastewater, and chemicals for treatment between processequipment:

1. Centrifugal force inducing fluid motion2. Volumetric displacement of fluids, either mechan-

ically, or with other fluids3. Transfer of momentum from another fluid4. Mechanical impulse5. Gravity induction

Depending on the facility and unit processes containedwithin, all of the methods above may be important to themaintenance operator.

5.8.1 PUMPING HYDRAULICS12

During operation, water enters a pump on the suction side,where the pressure is lower. Since the function of the pumpis to add pressure to the system, discharge pressure willalways be higher. In pump systems, an important conceptto keep in mind is measurements are taken from the pointof reference to the centerline of the pump (horizontal linedrawn through center of pump).

In order to understand pump operation, or pumpinghydraulics, we need to be familiar with certain basic termsand then relate these terms pictorially (as we do inFigure 5.12) to illustrate how water is pumped from onepoint to another.

1. Static head — The distance between the suctionand discharge water levels when the pump isshut off. We indicate static head conditions withthe letter Z (see Figure 5.12).

2. Suction lift — The distance between the suctionwater level and the center of the pump impeller.This term is only used when the pump is in asuction lift condition; the pump must have theenergy to provide this lift. A pump is said to be

TABLE 5.2Pump Applications in Water and Wastewater Systems11

Application Function Pump Type

Low service To lift water from the source to treatment processes, or from storage to filter-backwashing system

Centrifugal

High service To discharge water under pressure to distribution system; to pump collected or intercepted water/wastewater and pump to treatment facility

Centrifugal

Booster To increase pressure in the distribution/collection system or to supply elevated storage tanks CentrifugalWell To lift water from shallow or deep wells and discharge it to the treatment plant, storage

facility, or distribution systemCentrifugal or jet

Chemical feed To add chemical solutions at desired dosages for treatment processes Positive displacementSampling To pump water/wastewater from sampling points to the laboratory or automatic analyzers Positive displacement or centrifugalSludge/biosolids To pump sludge or biosolids from sedimentation facilities to further treatment or disposal Positive displacement or centrifugal

Source: From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.

PB

=-

= = ( )232 2

2 3

213 7

2 393

.

.

.

.

18.5 psi rounded


in a suction lift condition any time the center(eye) of the impeller is above the water beingpumped (see Figure 5.12).

3. Suction head — A pump is said to be in asuction head condition any time the center (eye)of the impeller is below the water level beingpumped. Specifically, suction head is the dis-tance between the suction water level and thecenter of the pump impeller when the pump isin a suction head condition (see Figure 5.12).

4. Velocity head — The amount of energyrequired to bring water or wastewater fromstandstill to its velocity. For a given quantity offlow, the velocity head will vary indirectly withthe pipe diameter. Velocity head is often shownmathematically as V2/2g (see Figure 5.12).

5. Total dynamic head — The total energy neededto move water from the centerline of a pump(eye of the first impeller of a lineshaft turbine)to some given elevation or to develop somegiven pressure. This includes the static head,velocity head and the head loss due to friction(see Figure 5.12).

5.9 WELL AND WET WELL HYDRAULICS

When the source of water for a water distribution systemis from a groundwater supply, knowledge of well hydraulicsis important to the operator. Basic well hydraulics terms are

presented and defined, and they are related pictorially inFigure 5.13. Also discussed are wet wells, which are impor-tant, both in water and wastewater operations.

5.9.1 WELL HYDRAULICS

1. Static water level — The water level in a wellwhen no water is being taken from the ground-water source (i.e., the water level when thepump is off; see Figure 5.13). Static water levelis normally measured as the distance from theground surface to the water surface. This is animportant parameter because it is used to mea-sure changes in the water table.

2. Pumping water level — The water level whenthe pump is off. When water is pumped out ofa well, the water level usually drops below thelevel in the surrounding aquifer and eventuallystabilizes at a lower level; this is the pumpinglevel (see Figure 5.13).

3. Drawdown — the difference, or the drop,between the static water level and the pumpingwater level, measured in feet. Simply, it is thedistance the water level drops once pumpingbegins (see Figure 5.13).

4. Cone of depression — In unconfined aquifers,there is a flow of water in the aquifer from alldirections toward the well during pumping. Thefree water surface in the aquifer then takes theshape of an inverted cone or curved funnel line.

FIGURE 5.12 Components of total dynamic head. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ.,Lancaster, PA, 2001.)

HeadlossHL = 19 ft

Static HeadZ = 80 ft

Suction Lift

THD = 100 ft

Tot

al D

ynam

ic H

ead

Velocity Head V2/2g = 1 ft


The curve of the line extends from the pumpingwater level to the static water level at the outsideedge of the zone (or radius) of influence (seeFigure 5.13).

Note: The shape and size of the cone of depression isdependent on the relationship between thepumping rate and the rate at which water canmove toward the well. If the rate is high, thecone will be shallow and its growth will stabi-lize. If the rate is low, the cone will be sharpand continue to grow in size.

5. Zone (or radius) of influence — The distancebetween the pump shaft and the outermost areaaffected by drawdown (see Figure 5.13). Thedistance depends on the porosity of the soil andother factors. This parameter becomes impor-tant in well fields with many pumps. If wellsare set too close together, the zones of influencewill overlap, increasing the drawdown in allwells. Obviously, pumps should be spaced apartto prevent this from happening.

Note: Two important parameters not shown inFigure 5.13 are well yield and specific capacity.

1. Well yield is the rate of water withdrawal thata well can supply over a long period. Alterna-tively, this is simply the maximum pumping ratethat can be achieved without increasing thedrawdown. The yield of small wells is usuallymeasured in gallons per minute (liters perminute) or gallons per hour (liters per hour).

For large wells, it may be measured in cubicfeet per second (cubic meters per second).

2. Specific capacity is the pumping rate per footof drawdown (gallon per minute per foot), or

(5.18)

EXAMPLE 5.14

Problem:

If the well yield is 300 gal/min and the drawdown ismeasured to be 20 ft, what is the specific capacity?

Solution:

Specific capacity is one of the most important con-cepts in well operation and testing. The calculation shouldbe made frequently in the monitoring of well operation.A sudden drop in specific capacity indicates problemssuch as pump malfunction, screen plugging, or other prob-lems that can be serious. Such problems should be iden-tified and corrected as soon as possible.

5.9.2 WET WELL HYDRAULICS

Water pumped from a wet well by a pump set above thewater surface exhibits the same phenomena as the ground-water well. In operation, a slight depression of the watersurface forms right at the intake line (drawdown), but in

FIGURE 5.13 Hydraulic characteristics of a well. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ.,Lancaster, PA, 2001.)

Discharge

Ground surface Static water levelPump

Drawdown

Zone of influence

Pump water level

Cone of depression

SpecificWDrawdown

Capacityell Yield=

Specific Capacity

of drawdown

=

=

300

20

15 gal ftmin


this case it is minimal because there is free water at thepump entrance at all times (at least there should be). Themost important consideration in wet well operations is toensure that the suction line is submerged far enough belowthe surface, so that air entrained by the active movementof the water at this section is not able to enter the pump.

Because water or wastewater flow is not always con-stant or at the same level, variable speed pumps are com-monly used in wet well operations, or several pumps areinstalled for single or combined operation. In many cases,pumping is accomplished in an on/off mode. Control ofpump operation is in response to water level in the well.Level control devices, such as mercury switches, are usedto sense a high and low level in the well and transmit thesignal to pumps for action.

5.10 FRICTION HEAD LOSS

Materials or substances capable of flowing cannot flowfreely. Nothing flows without encountering some type ofresistance. Consider electricity, the flow of free electronsin a conductor. Whatever type of conductor used (i.e.,copper, aluminum, silver, etc.) offers some resistance. Inhydraulics, the flow of water or wastewater is analogousto the flow of electricity. Within a pipe or open channel,for instance, flowing water, like electron flow in a con-ductor, encounters resistance. However, resistance to theflow of water is generally termed friction loss (or moreappropriately, head loss).

5.10.1 FLOW IN PIPELINES

The problem of waste and wastewater flow in pipelines —the prediction of flow rate through pipes of given charac-teristics, the calculation of energy conversions therein, andso forth — is encountered in many applications of waterand wastewater operations and practice. Although the sub-ject of pipe flow embraces only those problems in which

pipes flow completely full (as in water lines), we alsoaddress pipes that flow partially full (wastewater lines,normally treated as open channels) in this section.

The solution of practical pipe flow problems resultingfrom application of the energy principle, the equation ofcontinuity, and the principle and equation of water resis-tance are also discussed. Resistance to flow in pipes is notonly the result of long reaches of pipe but is also offeredby pipe fittings, such as bends and valves, that dissipateenergy by producing relatively large-scale turbulence.

5.10.2 PIPE AND OPEN FLOW BASICS

In order to gain understanding of what friction head lossis all about, it is necessary to review a few terms presentedearlier in the text and to introduce some new terms perti-nent to the subject.13

1. Laminar flow — Laminar flow is ideal flow;that is, water particles moving along straight,parallel paths, in layers or streamlines. More-over, in laminar flow there is no turbulence inthe water and no friction loss. This is not typicalof normal pipe flow because the water velocityis too great, but is typical of groundwater flow.

2. Turbulent flow — Characterized as normal fora typical water system, turbulent flow occurswhen water particles move in a haphazard fash-ion and continually cross each other in all direc-tions resulting in pressure losses along a lengthof pipe.

3. Hydraulic grade line (HGL) — Recall that thehydraulic grade line (HGL) (shown inFigure 5.14) is a line connecting two points towhich the liquid would rise at various placesalong any pipe or open channel if piezometerswere inserted in the liquid. It is a measure of thepressure head available at these various points.

FIGURE 5.14 Comparison of pipe flow and open-channel flow. (Adapted from Metcalf & Eddy. Wastewater Engineering:Collection and Pumping of Wastewater, Tchobanoglous, G. (Ed.), McGraw-Hill, New York, 1981, p. 11.)

Water surface

1

2

Pipe flow Open channel flow

Datum

V2g

h

Piezometers

Center line of pipez

y

V2g

VV

z

y

V2g

z

y

Energy grade line

Channel bottom

VV

1 2 1 2

12

1

1

12

z2

22

Hydraulic grade line

Energy grade lineL

V2g

h

22

L

y2

1

1

2

2

12


Note: When water flows in an open channel, the HGLcoincides with the profile of the water surface.

4. Energy grade line — the total energy of flowin any section with reference to some datum(i.e., a reference line, surface or point) is thesum of the elevation head, z, the pressure head,y, and the velocity head, V2/2g. Figure 5.14shows the energy grade line or energy gradient,which represents the energy from section tosection. In the absence of frictional losses, theenergy grade line remains horizontal, althoughthe relative distribution of energy may varybetween the elevation, pressure, and velocityheads. In all real systems, however, losses ofenergy occur because of resistance to flow, andthe resulting energy grade line is sloped (i.e.,the energy grade line is the slope of the specificenergy line).

5. Specific energy (E) — sometimes called spe-cific head, is the sum of the pressure head, y,and the velocity head, V2/2g. The specificenergy concept is especially useful in analyzingflow in open channels.

6. Steady flow — Occurs when the discharge orrate of flow at any cross section is constant.

7. Uniform and nonuniform flow — Uniform flowoccurs when the depth, cross-sectional area, andother elements of flow are substantially con-stant from section to section. Nonuniform flowoccurs when the slope, cross-sectional area, andvelocity change from section to section. Theflow through a venturi section used for measur-ing flow is a good example.

8. Varied flow — Flow in a channel is consideredvaried if the depth of flow changes along thelength of the channel. The flow may be gradu-

ally varied or rapidly varied (i.e., when thedepth of flow changes abruptly) as shown inFigure 5.15.

9. Slope (gradient) — The head loss per foot ofchannel.

5.10.3 MAJOR HEAD LOSS

Major head loss consists of pressure decreases along thelength of pipe caused by friction created as water encoun-ters the surfaces of the pipe. It typically accounts for mostof the pressure drop in a pressurized or dynamic watersystem.

5.10.3.1 Components of Major Head Loss

The components that contribute to major head loss: rough-ness, length, diameter, and velocity.

5.10.3.1.1 Roughness

Even when new, the interior surfaces of pipes are rough.The roughness varies depending on pipe material, corro-sion (tuberculation and pitting), and age. Because normalflow in a water pipe is turbulent, the turbulence increaseswith pipe roughness, which in turn causes pressure to dropover the length of the pipe.

5.10.3.1.2 Pipe Length

With every foot of pipe length, friction losses occur. Thelonger the pipe, the more head loss. Friction loss becauseof pipe length must be factored into head loss calculations.

5.10.3.1.3 Pipe Diameter

Generally, small diameter pipes have more head loss thanlarge diameter pipes. This is the case because in largediameter pipes less of the water actually touches the inte-rior surfaces of the pipe (encountering less friction) thanin a small diameter pipe.

FIGURE 5.15 Varied flow. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

RVF – Rapidly Varied FlowGVF – Gradually Varied Flow

RVF GVF RVF GVF RVF GVF RVF

Flow overa weir

Hydraulicdrop

Hydraulicjump

Sluice gate


5.10.3.1.4 Water VelocityTurbulence in a water pipe is directly proportional to thespeed (or velocity) of the flow. Thus, the velocity headalso contributes to head loss.

Note: For the same diameter pipe, when flowincreases, head loss increases.

5.10.3.2 Calculating Major Head Loss

Henry Darcy, Julies Weisbach, and others developed thefirst practical equation used to determine pipe friction inabout 1850. The equation or formula now known as theDarcy-Weisbach equation for circular pipes is:

(5.19)

In terms of the flow rate Q, the equation becomes:

(5.20)

wherehf = head loss (ft)f = coefficient of friction

L = length of pipe (ft)V = mean velocity (ft/sec)D = diameter of pipe (ft)g = acceleration due to gravity (32.2 ft/sec2)Q = flow rate (ft3/sec)

The Darcy-Weisbach formula as such was meant toapply to the flow of any fluid. Into this friction factor wasincorporated the degree of roughness and an elementcalled the Reynold’s number, which was based on theviscosity of the fluid and the degree of turbulence of flow.

The Darcy-Weisbach formula is used primarily fordetermining head loss calculations in pipes. For makingthis determination in open channels, the Manning equationwas developed during the later part of the 19th century.Later, this equation was used for both open channels andclosed conduits.

In the early 1900s, a more practical equation, theHazen-Williams equation, was developed for use in mak-ing calculations related to water pipes and wastewaterforce mains:

Q = 0.435 ¥ CD2.63 ¥ S0.54 (5.21)

whereQ = flow rate (ft3/sec)C = coefficient of roughness (C decreases with

roughness)D = hydraulic radius r (ft)S = slope of energy grade line (ft/ft)

5.10.3.2.1 C Factor

The C factor, as used in the Hazen-Williams formula,designates the coefficient of roughness. C does not varyappreciably with velocity, and by comparing pipe typesand ages, it includes only the concept of roughness, ignor-ing fluid viscosity and Reynold’s number.

Based on experience (experimentation), acceptedtables of C factors have been established for pipe (seeTable 5.3). Generally, C factor decreases by one with eachyear of pipe age. Flow for a newly designed system isoften calculated with a C factor of 100, based on averagingit over the life of the pipe system.

Note: A high C factor means a smooth pipe. A low Cfactor means a rough pipe.

Note: An alternate to calculating the Hazen-Williamsformula, called an alignment chart, has becomequite popular for fieldwork. The alignmentchart can be used with reasonable accuracy.

5.10.3.2.2 Slope

Slope is defined as the head loss per foot. In open chan-nels, where the water flows by gravity, slope is the amount

h fD gf = LV2

2

hfLQgDf = 8 2

p2 5

TABLE 5.3 C FACTORS15

Type of Pipe C Factor

Asbestos cement 140Brass 140Brick sewer 100Cast iron

10 years old20 years old

11090

Ductile iron (cement lined) 140Concrete or concrete lined

Smooth, steel formsWooden formsRough

140120110

Copper 140Fire hose (rubber lined) 135Galvanized iron 120Glass 140Lead 130Masonry conduit 130Plastic 150Steel

Coal-tar enamel linedNew unlinedRiveted

150140110

Tin 130Vitrified 120Wood stave 120

Source: From Spellman, F.R. and Drinan, J., WaterHydraulics, Technomic Publ., Lancaster, PA, 2001.


of incline of the pipe and is calculated as feet of drop perfoot of pipe length (ft/ft). Slope is designed to be justenough to overcome frictional losses, so that the velocityremains constant, the water keeps flowing, and solids willnot settle in the conduit. In piped systems, where pressureloss for every foot of pipe is experienced, slope is notprovided by slanting the pipe, but instead by pressureadded to overcome friction.

5.10.4 MINOR HEAD LOSS

In addition to the head loss caused by friction betweenthe fluid and the pipe wall, losses also are caused byturbulence created by obstructions (i.e., valves and fittingsof all types) in the line, changes in direction, and changesin flow area.

Note: In practice, if minor head loss is less than 5%of the total head loss, it is usually ignored.

5.11 BASIC PIPING HYDRAULICS

Water, regardless of the source, is conveyed to the water-works for treatment and distributed to the users. Convey-ance from the source to the point of treatment occurs byaqueducts, pipelines, or open channels, but the treatedwater is normally distributed in pressurized closed con-duits. After use, whatever the purpose, the water becomeswastewater, which must be disposed of somehow, butalmost always ends up being conveyed back to a treatmentfacility before being outfalled to some water body, tobegin the cycle again.

We call this an urban water cycle, because it provides ahuman-generated imitation of the natural water cycle.Unlike the natural water cycle, however, without pipes,the cycle would be nonexistent or, at the very least,short-circuited.

For use as water mains in a distribution system, pipes mustbe strong and durable in order to resist applied forces andcorrosion. The pipe is subjected to internal pressure fromthe water and to external pressure from the weight of thebackfill (soil) and vehicles above it. The pipe may also haveto withstand water hammer. Damage due to corrosion orrusting may also occur internally because of the water qual-ity or externally because of the nature of the soil conditions.

Pipes used in a wastewater system must be strong anddurable to resist the abrasive and corrosive properties ofthe wastewater. Like water pipes, wastewater pipes mustalso be able to withstand stresses caused by the soil back-fill material and the effect of vehicles passing above thepipeline.

Joints between wastewater collection/interceptor pipesections should be flexible, but tight enough to preventexcessive leakage, either of sewage out of the pipe orgroundwater into the pipe.

Of course, pipes must be constructed to withstand theexpected conditions of exposure, and pipe configurationsystems for water distribution and/or wastewater collectionand interceptor systems must be properly designed andinstalled in terms of water hydraulics. Because the waterand wastewater operator should have a basic knowledgeof water hydraulics related to commonly used standardpiping configurations, piping basics are briefly discussedin this section.

5.11.1 PIPING NETWORKS

It would be far less costly and make for more efficientoperation if municipal water and wastewater systems werebuilt with separate single pipe networks extending fromtreatment plant to user’s residence, or from user’s sink orbathtub drain to the local wastewater treatment plant.Unfortunately, this ideal single-pipe scenario is not prac-tical for real world applications. Instead of a single pipingsystem, a network of pipes is laid under the streets. Eachof these piping networks is composed of different mate-rials that vary (sometimes considerably) in diameter,length, and age. These networks range in complexity tovarying degrees, and each of these joined-together pipescontribute energy losses to the system.

5.11.1.1 Energy Losses in Pipe Networks

Water and wastewater flow networks may consist of pipesarranged in series, parallel, or some complicated combina-tion. In any case, an evaluation of friction losses for theflows is based on energy conservation principles applied tothe flow junction points. Methods of computation dependon the particular piping configuration. In general, however,they involve establishing a sufficient number of simulta-neous equations or employing a friction loss formula wherethe friction coefficient depends only on the roughness ofthe pipe (e.g., Hazen-Williams equation). (Note: Demon-strating the procedure for making these complex computa-tions is beyond the scope of this text. We only present theoperator “need to know” aspects of complex or compoundpiping systems in this text.)

5.11.1.2 Pipes in Series

When two pipes of different sizes or roughnesses areconnected in series (see Figure 5.16), head loss for a givendischarge, or discharge for a given head loss, may becalculated by applying the appropriate equation betweenthe bonding points, taking into account all losses in theinterval. Thus, head losses are cumulative.

Series pipes may be treated as a single pipe of constantdiameter to simplify the calculation of friction losses. Theapproach involves determining an equivalent length of aconstant diameter pipe that has the same friction loss anddischarge characteristics as the actual series pipe system.


In addition, application of the continuity equation to thesolution allows the head loss to be expressed in terms ofonly one pipe size.

Note: In addition to the head loss caused by frictionbetween the water and the pipe wall, losses alsoare caused by minor losses: obstructions in theline, changes in directions, and changes in flowarea. In practice, the method of equivalentlength is often used to determine these losses.The method of equivalent length uses a table toconvert each valve or fitting into an equivalentlength of straight pipe.

In making calculations involving pipes in series,remember these two important basic operational tenets:

1. The same flow passes through all pipes con-nected in series.

2. The total head loss is the sum of the head lossesof all of the component pipes.

In some operations involving series networks wherethe flow is given and the total head loss is unknown, wecan use the Hazen-Williams equation to solve for the slopeand the head loss of each pipe as if they were separatepipes. Adding up the head losses to get the total head lossis then a simple matter.

Other series network calculations may not be as sim-ple to solve using the Hazen-Williams equation. For exam-ple, one problem we may be faced with is what diameterto use with varying sized pipes connected together in aseries combination. Moreover, head loss is applied to bothpipes (and other multiples), and it is not known how muchloss originates from each one. This makes determiningslope difficult, but not impossible.

In such cases the equivalent pipe theory, as mentionedearlier, can be used. Again, one single equivalent pipe iscreated which will carry the correct flow. This is practicalbecause the head loss through it is the same as that in theactual system. The equivalent pipe can have any C factorand diameter, just as long as those same dimensions aremaintained all the way through to the end. Keep in mindthat the equivalent pipe must have the correct length, sothat it will allow the correct flow through, which yieldsthe correct head loss (the given head loss).16

5.11.1.3 Pipes in Parallel

Two or more pipes connected (as in Figure 5.17) so thatflow is first divided among the pipes and is then rejoinedcomprise a parallel pipe system. A parallel pipe system isa common method for increasing the capacity of an exist-ing line. Determining flows in pipes arranged in parallelare also made by application of energy conservation prin-ciples — specifically, energy losses through all pipes con-necting common junction points must be equal. Each legof the parallel network is treated as a series piping systemand converted to a single equivalent length pipe. The fric-tion losses through the equivalent length parallel pipes arethen considered equal and the respective flows determinedby proportional distribution.

Note: Computations used to determine friction lossesin parallel combinations may be accomplishedusing a simultaneous solution approach for aparallel system that has only two branches.However, if the parallel system has three ormore branches, a modified procedure using theHazen-Williams loss formula is easier.16

5.12 OPEN-CHANNEL FLOW

Water is transported over long distances through aque-ducts to locations where it is to be used and/or treated.Selection of an aqueduct type rests on such factors astopography, head availability, climate, construction prac-tices, economics, and water quality protection. Along withpipes and tunnels, aqueducts may also include or be solelycomposed of open channels.17

In this section, we deal with water passage in open chan-nels, which allow part of the water to be exposed to theatmosphere. This type of channel — an open-flowchannel — includes natural waterways, canals, culverts,flumes, and pipes flowing under the influence of gravity.

FIGURE 5.16 Pipes in series. (From Spellman, F.R. andDrinan, J., Water Hydraulics, Technomic Publ., Lancaster,PA, 2001.)

1 2 3

FIGURE 5.17 Pipe in parallel. (From Spellman, F.R. andDrinan, J., Water Hydraulics, Technomic Publ., Lancaster,PA, 2001.)

2

3


5.12.1 CHARACTERISTICS OF OPEN- CHANNEL FLOW18

Basic hydraulic principles apply in open-channel flow(with water depth constant) although there is no pressureto act as the driving force. Velocity head is the only naturalenergy this water possesses, and at normal water veloci-ties, this is a small value (V2/2g).

Several parameters can be (and often are) used todescribe open-channel flow. However, we begin our dis-cussion with a few characteristics, including laminar orturbulent; uniform or varied; and subcritical, critical, orsupercritical.

5.12.1.1 Laminar and Turbulent Flow

Laminar and turbulent flow in open channels is analogousto that in closed pressurized conduits (i.e., pipes). It isimportant to point out that flow in open channels is usuallyturbulent. In addition, there is no important circumstancein which laminar flow occurs in open channels in eitherwater or wastewater unit processes or structures.

5.12.1.2 Uniform and Varied Flow

Flow can be a function of time and location. If the flowquantity is invariant, it is said to be steady. Uniform flowis flow in which the depth, width, and velocity remainconstant along a channel. This means that if the flow crosssection does not depend on the location along the channel,the flow is said to be uniform. Varied or nonuniform flowinvolves a change in depth, width, and velocity, with achange in one producing a change in the others. Mostcircumstances of open-channel flow in water and waste-water systems involve varied flow. The concept of uniformflow is valuable, however, in that it defines a limit that thevaried flow may be considered to be approaching in manycases.

Note: Uniform channel construction does not ensureuniform flow.

5.12.1.3 Critical Flow

Critical flow (i.e., flow at the critical depth and velocity)defines a state of flow between two flow regimes. Criticalflow coincides with minimum specific energy for a givendischarge and maximum discharge for a given specificenergy. Critical flow occurs in flow measurement devicesat or near free discharges, and establishes controls in open-channel flow. Critical flow occurs frequently in water andwastewater systems and is very important in their opera-tion and design.

Note: Critical flow minimizes the specific energy andmaximizes discharge.

5.12.1.4 Parameters Used in Open-Channel Flow

The three primary parameters used in open-channel floware: hydraulic radius, hydraulic depth, and slope, S.

5.12.1.4.1 Hydraulic Radius

The hydraulic radius is the ratio of area in flow to wettedperimeter.

(5.22)

whererH = hydraulic radius

A = the cross sectional area of the waterP = wetted perimeter

Why is the hydraulic radius important?Probably the best way in which to answer this question

is by illustration. Consider, for example, that in open chan-nels it is of primary importance to maintain the propervelocity. This is the case because if velocity is not main-tained then flow stops (theoretically). In order to maintainvelocity at a constant level, the channel slope must beadequate to overcome friction losses. As with other flows,calculation of head loss at a given flow is necessary, andthe Hazen-Williams equation is useful (Equation 5.22).Keep in mind that the concept of slope has not changed.The difference? We are now measuring, or calculating for,the physical slope of a channel (ft/ft), equivalent to headloss.

The preceding seems logical, but there is a problem.The problem is with the diameter. In conduits that are notcircular (grit chambers, contact basins, streams and riv-ers), or in pipes only partially full (drains, wastewatergravity mains, sewers, etc.) where the cross-sectional areaof the water is not circular, there is no diameter.

If there is no diameter, then what do we do?Because there is no diameter in a situation where the

cross-sectional area of the water is not circular, we mustuse another parameter to designate the size of the crosssection, and the amount of it that contacts the sides of theconduit. This is where the hydraulic radius (rH) comes in.The hydraulic radius is a measure of the efficiency withwhich the conduit can transmit water. Its value dependson pipe size and amount of fullness. Simply, we use thehydraulic radius to measure how much of the water is incontact with the sides of the channel, or how much of thewater is not in contact with the sides (see Figure 5.18).

Note: For a circular channel flowing either full or half-full, the hydraulic radius is D/4. Hydraulic radiiof other channel shapes are easily calculatedfrom the basic definition.

rPH = A


5.12.1.4.2 Hydraulic DepthThe hydraulic depth is the ratio of area in flow to the widthof the channel at the fluid surface. [Note that another namefor hydraulic depth is the hydraulic mean depth or hydrau-lic radius].

(5.23)

wheredH = hydraulic depthA = area in floww = width of the channel at the fluid surface

5.12.1.4.3 SlopeThe slope, S, in open channel equations is the slope ofthe energy line. If the flow is uniform, the slope of theenergy line will parallel the water surface and channelbottom. In general, the slope can be calculated from Ber-noulli’s equation as the energy loss per unit length ofchannel.

(5.24)

5.12.2 OPEN-CHANNEL FLOW CALCULATIONS

As mentioned, the calculation for head loss at a given flowis typically accomplished by using Hazen-Williams equa-tion. In addition, in open-channel flow problems wherealthough the concept of slope has not changed, the prob-lem arises with the diameter. Again, in pipes only partiallyfull where the cross-sectional area of the water is notcircular, there is no diameter. Thus, the hydraulic radiusis used for these noncircular areas.

In the original version of the Hazen-Williams Equa-tion, the hydraulic radius was incorporated. Moreover,similar versions developed by Antoine Chezy (pronounced“Shay-zee”) and Robert Manning, and others incorporated

the hydraulic radius. For use in open channels, Manning’sformula has become most commonly used:

(5.25)

where

Q = channel discharge capacity (ft3/sec)

1.5 = constant

n = channel roughness coefficient

A = cross-sectional flow area (ft2)

r = hydraulic radius of the channel (ft)

S = slope of the channel bottom, dimensionless

The hydraulic radius of a channel is defined as the ratioof the flow area to the wetted perimeter P. In formula form,r = A/P. The new component is n (the roughness coefficient)and depends on the material and age for a pipe or linedchannel and on topographic features for a natural stream-bed. It approximates roughness in open channels and canrange from a value of 0.01 for a smooth clay pipe to 0.1for a small natural stream. The value of n commonlyassumed for concrete pipes or lined channels is 0.013. Asthe channels get smoother, n values decrease (see Table 5.4).

The following example illustrates the application ofManning’s formula for a channel with a rectangular crosssection.

EXAMPLE 5.15

Problem:

A rectangular drainage channel is 3 ft wide and is linedwith concrete, as illustrated in Figure 5.19. The bottomof the channel drops in elevation at a rate of 0.5/100 ft.What is the discharge in the channel when the depth ofwater is 2 ft?

Solution:

Assume n = 0.013

Referring to Figure 5.19, we see that the cross-sectionalflow area A = 3 ft ¥ 2 ft = 6 ft2, and the wetted perimeterP = 2 ft + 3 ft + 2 ft = 7 ft. The hydraulic radius R =A/P = 6 ft2/7 ft = 0.86 ft. The slope, S = 0.5/100 = 0.005.

Applying Manning’s formula, we get:

FIGURE 5.18 Hydraulic radius. (From Spellman, F.R. andDrinan, J., Water Hydraulics, Technomic Publ., Lancaster,PA, 2001.)

Wetted perimeter Wetted area

dH = Aw

S = DhDl

Q A r S= ¥ ¥ ¥1.5n

. .66 5

Q

Q ft

= ¥ ¥ ¥

=

2.0

0.0136 0 86 0 005

59

66 5

3

. .

sec

. .


5.12.3 OPEN-CHANNEL FLOW: THE BOTTOM LINE

To this point, we have set the stage for explaining (in thesimplest possible way) what open-channel flow is andwhat it is all about. Now that we have explained thenecessary foundational material and important concepts,we are ready to explain open-channel flow in a mannerwhereby it will be easily understood.

We stated that when water flows in a pipe or channelwith a free surface exposed to the atmosphere, it is calledopen-channel flow. We also know that gravity providesthe motive force, the constant push, while friction resiststhe motion and causes energy expenditure. River andstream flow is open-channel flow. Flow in sanitary sewersand storm water drains are open-channel flow, except inforce mains where the water is pumped under pressure.

The key to solving storm water and/or sanitary sewerroutine problems is a condition known as steady uniformflow; that is, we assume steady uniform flow. Steady flowmeans that the discharge is constant with time. Uniformflow means that the slope of the water surface and thecross-sectional flow area are also constant. It is commonpractice to call a length of channel, pipeline, or stream thathas a relatively constant slope and cross section a reach.19

The slope of the water surface, under steady uniformflow conditions, is the same as the slope of the channelbottom. The HGL lies along the water surface and, as inpressure flow in pipes, the HGL slopes downward in thedirection of flow. Energy loss is evident as the water sur-face elevation drops. Figure 5.20 illustrates a typical

TABLE 5.4Manning Roughness Coefficient (n)

Type of Conduit n Type of Conduit n

PipeCast iron, coated 0.012–0.014 Cast iron, uncoated 0.013–0.015Wrought iron, galvanized 0.015–0.017 Wrought iron, black 0.012–0.015Steel, riveted and spiral 0.015–0.017 Corrugated 0.021–0.026Wood stave 0.012–0.013 Cement surface 0.010–0.013Concrete 0.012–0.017 Vitrified 0.013–0.015Clay, drainage tile 0.012–0.014

Lined ChannelsMetal, smooth semicircular 0.011–0.015 Metal, corrugated 0.023–0.025Wood, planed 0.010–0.015 Wood, unplaned 0.011–0.015Cement lined 0.010–0.013 Concrete 0.014–0.016Cement rubble 0.017–0.030 Grass N/R–0.020a

Unlined ChannelsEarth: straight and uniform 0.017–0.025 Earth: dredged 0.025–0.033Earth: winding 0.023–0.030 Earth: stony 0.025–0.040Rock: smooth and uniform 0.025–0.035 Rock: jagged and irregular 0.035–0.045

a N/R = No result

Source: From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster,PA, 2001.

FIGURE 5.19 For Example 5.15. (From Spellman, F.R. and Dri-nan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

2.0 ft

Free water surface

Wetted perimeter

3.0 ft

FIGURE 5.20 Steady uniform open-channel flow — wherethe slope of the water surface (or HGL) is equal to the slopeof the channel bottom. (From Spellman, F.R. and Drinan, J.,Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

hL

Slope = hL/L

Water surface = HGL

Channel bottom

Q

L


profile view of uniform steady flow. The slope of the watersurface represents the rate of energy loss.

Note: Rate of energy loss (see Figure 5.20) may beexpressed as the ratio of the drop in elevationof the surface in the reach to the length of thereach.

Figure 5.21 shows typical cross sections of open-chan-nel flow. In Figure 5.21A, the pipe is only partially filledwith water and there is a free surface at atmospheric pres-sure. This is still open-channel flow, although the pipe isa closed underground conduit. Remember, the importantpoint is that gravity — not a pump — is moving the water.

5.13 FLOW MEASUREMENT

While it is clear that maintaining water/wastewater flowis at the heart of any treatment process, clearly, it is themeasurement of flow that is essential to ensuring theproper operation of a water/wastewater treatment system.Few knowledgeable operators would argue with this state-ment. Hauser (1996) asks: “Why measure flow?” Thenshe explains: “The most vital activities in the operationof water and wastewater treatment plants are dependenton a knowledge of how much water is being processed.”20

In the statement above, Hauser makes clear that flow mea-surement is not only important, but also routine, in waterand wastewater operations. Routine, yes, but also the mostimportant variable measured in a treatment plant. Hauseralso pointed out that there are several reasons to measureflow in a treatment plant. The American Water WorksAssociation21 lists several additional reasons to measureflow:

1. The flow rate through the treatment processesneeds to be controlled so that it matches distri-bution system use.

2. It is important to determine the proper feed rateof chemicals added in the processes.

3. The detention times through the treatment pro-cesses must be calculated. This is particularlyapplicable to surface water plants that mustmeet contact ¥ time (C ¥ T) values required bythe Surface Water Treatment Rule.

4. Flow measurement allows operators to maintaina record of water furnished to the distributionsystem for periodic comparison with the totalwater metered to customers. This provides ameasure of “water accounted for,” or conversely(as pointed out earlier by Hauser), the amountof water wasted, leaked, or otherwise not paidfor (i.e., lost water).

5. Flow measurement allows operators to deter-mine the efficiency of pumps. (Note: Pumps arecovered in detail in Chapter 7). Pumps that arenot delivering their designed flow rate are prob-ably not operating at maximum efficiency, andso power is being wasted.

6. For well systems, it is very important to main-tain records of the volume of water pumped andthe hours of operation for each well. The peri-odic computation of well pumping rates canidentify problems such as worn pump impellersand blocked well screens.

7. Reports that must be furnished to the state bymost water systems must include records of rawand finished water pumpage.

8. Wastewater generated by a treatment systemmust also be measured and recorded.

9. Individual meters are often required for theproper operation of individual pieces of equip-ment. For example, the makeup water to a flu-oride saturator is always metered to assist intracking the fluoride feed rate.

Note: Simply put, measurement of flow is essentialfor operation, process control, and recordkeep-ing of water and wastewater treatment plants.

FIGURE 5.21 Shows open-channel flow, whether in a surface stream or in an underground pipe. (From Spellman, F.R. andDrinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

Stream

(A) (B)

Buried pipepartial flow

Pipe crown

Air

Pipe invert

Ground surface


All of the uses addressed create the need for a numberof flow-measuring devices, often with different capabili-ties. In this section, we discuss many of the major flowmeasuring devices currently used in water and wastewateroperations.

5.13.1 FLOW MEASUREMENT: THE OLD-FASHIONED WAY

An approximate but very simple method to determineopen-channel flow has been used for many years. Theprocedure involves measuring the velocity of a floatingobject moving in a straight uniform reach of the channelor stream. If the cross-sectional dimensions of the channelare known and the depth of flow is measured, then flowarea can be computed. From the relationship Q = A ¥ V,the discharge Q can be estimated.

In preliminary fieldwork, this simple procedure is use-ful in obtaining a ballpark estimate for the flow rate, butis not suitable for routine measurements.

EXAMPLE 5.16

Problem:

A floating object is placed on the surface of water flowingin a drainage ditch and is observed to travel a distance of20 m downstream in 30 sec. The ditch is 2 m wide andthe average depth of flow is estimated to be 0.5 m. Esti-mate the discharge under these conditions.

Solution:

The flow velocity is computed as distance over time:

The channel area is:

A = 2 m ¥ 0.5 m = 1.0 m2

The discharge is:

Q = A ¥ V = 1.0 m2 ¥ 0.66 m2 = 0.66 m3/sec

5.13.2 BASIS OF TRADITIONAL FLOW MEASUREMENT

Flow measurement can be based on flow rate, or flowamount. Flow rate is measured in gallons per minute,million gallons per day, or cubic feet per second. Waterand wastewater operations need flow rate meters to deter-

mine process variables within the treatment plant, inwastewater collection, and in potable water distribution.Typically, flow rate meters used are differential pressuremeters, magnetic meters, and ultrasonic meters. Flow ratemeters are designed for metering flow in closed pipe oropen-channel flow.

Flow amount is measured in either gallons or in cubicfeet. Typically, a totalizer, which sums up the gallons orcubic feet that pass through the meter, is used. Most ser-vice meters are of this type. They are used in private,commercial, and industrial activities where the totalamount of flow measured is used in determining customerbilling. In wastewater treatment, where sampling opera-tions are important, automatic composite samplingunits — flow proportioned to grab a sample every so manygallons — are used. Totalizer meters can be the velocity(propeller or turbine), positive displacement, or compoundtypes. In addition, weirs and flumes are used extensivelyfor measuring flow in wastewater treatment plants becausethey are not affected (to a degree) by dirty water or floatingsolids.

5.13.3 FLOW MEASURING DEVICES

In recent decades, flow measurement technology hasevolved rapidly from the old fashioned way of measuringflow we discussed in Section 5.13.1, to the use of simplepractical measuring devices, and finally to much moresophisticated devices. Physical phenomena discoveredcenturies ago have been the starting point for many of theviable flowmeter designs used today. Moreover, the recenttechnology explosion has enabled flowmeters to handlemany more applications than could have been imaginedcenturies ago.

Before selecting a particular type of flow measurementdevice, Kawamura22 recommends consideration of severalquestions.

1. Is liquid or gas flow being measured?

2. Is the flow occurring in a pipe or in an openchannel?

3. What is the magnitude of the flow rate?

4. What is the range of flow variation?

5. Is the liquid being measured clean, or does itcontain suspended solids or air bubbles?

6. What is the accuracy requirement?

7. What is the allowable head loss by the flowmeter?

8. Is the flow corrosive?

9. What types of flowmeters are available to theregion?

10. What types of postinstallation service are avail-able to the area?

V

m

m

=

=

=

D

t

s

20

30

0 67. sec


5.13.3.1 Differential Pressure Flowmeters23

For many years differential pressure flowmeters have beenthe most widely applied flow-measuring device for waterflow in pipes that require accurate measurement at reason-able cost. The differential pressure type of flowmeter makesup the largest segment of the total flow measurementdevices currently being used. Differential pressure-produc-ing meters currently on the market are the venturi, Dalltype, Hershel venturi, universal venturi, and venturi inserts.

The differential pressure-producing device has a flowrestriction in the line that causes a differential pressure orhead to be developed between the two measurement loca-tions. Differential pressure flowmeters are also known ashead meters, and, of all the head meters, the orifice flow-meter is the most widely applied device.

The advantages of differential pressure flowmetersinclude:

1. Simple construction2. Relatively inexpensive3. No moving parts4. Transmitting instruments are external5. Low maintenance6. Wide application of flowing fluid that is suitable

for measuring both gas and liquid flow7. Ease of instrument and range selection8. Extensive product experience and performance

database

The disadvantages include:

1. Flow rate is a nonlinear function of the differ-ential pressure.

2. There is a low flow rate range with normalinstrumentation.

5.13.3.1.1 Operating PrincipleDifferential pressure flowmeters operate on the principleof measuring pressure at two points in the flow, whichprovides an indication of the rate of flow that is passingby. The difference in pressures between the two measure-ment locations of the flowmeter is the result of the changein flow velocities. Simply, there is a set relationshipbetween the flow rate and volume, so the meter instrumen-tation automatically translates the differential pressure intoa volume of flow. The volume of flow rate through thecross-sectional area is given by

Q = A ¥ V(average)

whereQ = the volumetric flow rateA = flow in the cross-sectional areaV = the average fluid velocity

5.13.3.1.2 Types of Differential Pressure Flowmeters

Differential pressure flowmeters operate on the principleof developing a differential pressure across a restrictionthat can be related to the fluid flow rate.

Note: Optimum measurement accuracy is maintainedwhen the flowmeter is calibrated, the flowmeteris installed in accordance with standards andcodes of practice, and the transmitting instru-ments are periodically calibrated.

The most commonly used differential pressure flow-meter types used in water and wastewater treatment are:

1. Orifice2. Venturi3. Nozzle4. Pitot-static tube

5.13.3.1.2.1 OrificeThe most commonly applied orifice is a thin, concentric,and flat metal plate with an opening in the plate (seeFigure 5.22) that is installed perpendicular to the flowingstream in a circular conduit or pipe. Typically, a sharp-edged hole is bored in the center of the orifice plate. Asthe flowing water passes through the orifice, the restrictioncauses an increase in velocity. A concurrent decrease inpressure occurs as potential energy (static pressure) isconverted into kinetic energy (velocity). As the waterleaves the orifice, its velocity decreases and its pressureincreases as kinetic energy is converted back into potentialenergy according to the laws of conservation of energy.However, there is always some permanent pressure lossdue to friction, and the loss is a function of the ratio ofthe diameter of the orifice bore (d) to the pipe diameter(D).

For dirty water applications (i.e., wastewater), a con-centric orifice plate will eventually have impaired perfor-mance due to dirt buildup at the plate. Instead, eccentric

FIGURE 5.22 Orifice plate. (From Spellman, F.R. and Dri-nan, J., Water Hydraulics, Technomic Publ., Lancaster, PA,2001.)

Flow

Upstream

Face A

Downstream

Face B

Axial centerlinedD

Downstream edge

Angle of bevel

Upstream edge

Dam height


or segmental orifice plates (see Figure 5.23) are oftenused. Measurements are typically less accurate than thoseobtained from the concentric orifice plate. Eccentric orsegmental orifices are rarely applied in current practice.

The orifice differential pressure flowmeter is the low-est cost differential flowmeter, is easy to install, and hasno moving parts. However, it also has high permanenthead loss (ranging from 40 to 90%) higher pumping costs,an accuracy of ±2% for a flow range of 4:1, and is affectedwith wear or damage.

Note: Orifice meters are not recommended for perma-nent installation to measure wastewater flow;solids in the water easily catch on the orifice,throwing off accuracy. For installation, it is nec-essary to have 10 diameters of straight pipeahead of the orifice meter to create a smoothflow pattern, and 5 diameters of straight pipeon the discharge side.

5.13.3.1.2.2 Venturi

A venturi is a restriction with a relatively long passagewith smooth entry and exit (see Figure 5.24). It has longlife expectancy, simplicity of construction, and relativelyhigh-pressure recovery (i.e., produces less permanentpressure loss than a similar sized orifice). Despite theseadvantages, the venturi is more expensive, is not linearwith flow rate, and is the largest and heaviest differentialpressure flowmeter. It is often used in wastewater flowssince the smooth entry allows foreign material to be sweptthrough instead of building up as it would in front of anorifice. The accuracy of this type flowmeter is ±1% for aflow range of 10:1. The head loss across a venturi flow-meter is relatively small. It ranges from 3 to 10% of thedifferential, depending on the ratio of the throat diameterto the inlet diameter (also known as beta ratio).

5.13.3.1.2.3 Nozzle

Flow nozzles (flow tubes) have a smooth entry and sharpexit (see Figure 5.24). For the same differential pressure,the permanent pressure loss of a nozzle is of the sameorder as that of an orifice, but it can handle wastewater

and abrasive fluids better than an orifice. Note that for thesame line size and flow rate, the differential pressure atthe nozzle is lower (head loss ranges from 10 to 20% ofthe differential) than the differential pressure for an orifice;hence, the total pressure loss is lower than an orifice’s.Nozzles are primarily used in steam service because oftheir rigidity, which makes them dimensionally more sta-ble at high temperatures and velocities than orifices.

Note: A useful characteristic of nozzles it that theyreach a critical flow condition — a point atwhich further reduction in downstream pressuredoes not produce a greater velocity through thenozzle. When operated in this mode, nozzlesare very predictable and repeatable.

5.13.3.1.2.4 Pitot Tube

A Pitot tube is a point velocity-measuring device (seeFigure 5.25). It has an impact port; as fluid hits the port,its velocity is reduced to zero and kinetic energy (velocity)is converted to potential energy (pressure head). The pres-sure at the impact port is the sum of the static pressureand the velocity head. The pressure at the impact port isalso known as stagnation pressure or total pressure. Thepressure difference between the impact pressure and thestatic pressure measured at the same point is the velocityhead. The flow rate is the product of the measured velocityand the cross-sectional area at the point of measurement.Note that the Pitot tube has negligible permanent pressuredrop in the line, but the impact port must be located in

FIGURE 5.23 Types of orifice plates. (From Spellman, F.R.and Drinan, J., Water Hydraulics, Technomic Publ., Lan-caster, PA, 2001.)

Concentric Eccentric SegmentalFIGURE 5.24 Long radius flow nozzle. (From Spellman,F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lan-caster, PA, 2001.)

FIGURE 5.25 Pitot tube. (From Spellman, F.R. and Drinan,J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

dFlow D

Static pressure port

Total pressure tap


the pipe where the measured velocity is equal to the aver-age velocity of the flowing water through the cross section.

5.13.3.2 Magnetic Flowmeters24

Magnetic flowmeters are relatively new to the water andwastewater industry. They are volumetric flow devicesdesigned to measure the flow of electrically conductiveliquids in a closed pipe. They measure the flow rate basedon the voltage created between two electrodes (in accor-dance with Faraday’s law of electromagnetic induction)as the water passes through an electromagnetic field (seeFigure 5.26). Induced voltage is proportional to flow rate.Voltage depends on magnetic field strength (constant),distance between electrodes (constant), and velocity offlowing water (variable).

Properties of the magnetic flowmeter include:

1. Minimal head loss (no obstruction with line sizemeter)

2. No effect on flow profile3. Suitablity for size range between 0.1 in. to 120 in.4. An accuracy rating of from 0.5 to 2% of flow

rate5. Ability to measure forward or reverse flow.

The advantages of magnetic flowmeters include:

1. No obstruction to flow2. Minimal head loss3. Wide range of sizes4. Bidirectional flow measurement5. Variations in density, viscosity, pressure, and

temperature yield negligible effect.6. Wastewater use7. No moving parts


1. Its metered liquid must be conductive (but youwould not use this type meter on clean fluidsanyway).

2. It is bulky, expensive in smaller sizes, and mayrequire periodic calibration to correct driftingof the signal.

The combination of the magnetic flowmeter and thetransmitter is considered as a system. A typical system,schematically illustrated in Figure 5.27, shows a transmittermounted remote from the magnetic flowmeter. Some sys-tems are available with transmitters mounted integral to themagnetic flowmeter. Each device is individually calibratedduring the manufacturing process, and the accuracy state-ment of the magnetic flowmeter includes both pieces ofequipment. One is not sold or used without the other.

It is also interesting to note that since 1983 almostevery manufacturer now offers the microprocessor-basedtransmitter.

Regarding minimum piping straight run requirements,magnetic flowmeters are quite forgiving of piping config-uration. The downstream side of the magnetic flowmeteris much less critical than the upstream side. Essentially,

FIGURE 5.26 Magnetic flowmeter. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

Flow

Voltage

Electromagnet

FIGURE 5.27 Magnetic flowmeter system. (From Spell-man, F.R. and Drinan, J., Water Hydraulics, Technomic Publ.,Lancaster, PA, 2001.)

Meter

SignalConditioner

mA DC

V AC


all that is required of the downstream side is that sufficientbackpressure is provided to keep the magnetic flowmeterfull of liquid during flow measurement. Two diametersdownstream should be acceptable.25

Note: Magnetic flowmeters are designed to measureconductive liquids only. If air or gas is mixed withthe liquid, the output becomes unpredictable.

5.13.3.3 Ultrasonic Flowmeters

Ultrasonic flowmeters use an electronic transducer to senda beam of ultrasonic sound waves through the water toanother transducer on the opposite side of the unit. Thevelocity of the sound beam varies with the liquid flowrate, so the beam can be electronically translated to indi-cate flow volume. The accuracy is ±1% for a flow velocityranging from 1 to 25 ft/s, but the meter reading is greatlyaffected by a change in the fluid composition

Two types of ultrasonic flowmeters are in general usefor closed pipe flow measurements. The first (time of flightor transit time) usually uses pulse transmission and is forclean liquids, while the second (Doppler) usually usescontinuous wave transmission and is for dirty liquids.

5.13.3.3.1 Time of Flight Ultrasonic Flowmeters26

Time-of-flight flowmeters make use of the difference inthe time for a sonic pulse to travel a fixed distance, firstin the direction of flow and then against the flow. This isaccomplished by opposing transceivers positioned ondiagonal path across meter spool as shown in Figure 5.28.Each transmits and receives ultrasonic pulses with flowand against flow. The fluid velocity is directly proportionalto time difference of pulse travel.

The time of flight ultrasonic flowmeter operates withminimal head loss, has an accuracy range of 1 to 2.5% fullscale, and can be mounted as integral spool piece transduc-ers or as externally mountable clamp-ons. They can mea-sure flow accurately when properly installed and applied.

The advantages of time-of-flight ultrasonic flowmetersinclude:

1. No obstruction to flow2. Minimal head loss3. Clamp-ons

a. Can be portableb. No interruption of flow

4. No moving parts5. Linear over wide range6. Wide range of pipe sizes7. Bidirectional flow measurement


1. Sensitivity to solids or bubble contenta. Interference with sound pulses

2. Sensitivity to flow disturbances3. Alignment of transducers is critical4. Clamp-on — pipe walls must freely pass ultra-

sonic pulses

5.13.3.3.2 Doppler Type Ultrasonic Flowmeters

Doppler ultrasonic flowmeters make use of the Dopplerfrequency shift caused by sound scattered or reflectedfrom moving particles in the flow path. Doppler metersare not considered to be as accurate as time of flightflowmeters. However, they are very convenient to use andgenerally more popular and less expensive than time offlight flowmeters.

In operation, a propagated ultrasonic beam is inter-rupted by particles in moving fluid and reflected toward areceiver. The difference of propagated and reflected fre-quencies is directly proportional to fluid flow rate.

Ultrasonic Doppler flowmeters feature minimal headloss with an accuracy of 2% to 5% full scale. They areeither of the integral spool piece transducer type or exter-nally mountable clamp-ons.

The advantages of the Doppler ultrasonic flowmeterincludes:

1. No obstruction to flow2. Minimal head loss3. Clamp-ons

a. Can be portableb. No interruption of flow

4. No moving parts5. Linear over wide range6. Wide range of pipe sizes7. Low installation and operating costs8. Bidirectional flow measurement

FIGURE 5.28 Time-of-flight ultrasonic flowmeter. (FromSpellman, F.R. and Drinan, J., Water Hydraulics, TechnomicPubl., Lancaster, PA, 2001.)

Flow

Transceiver

Transceiver



1. Minimum concentration and size of solids orbubbles for reliable operation required (seeFigure 5.29)

2. Minimum speed to maintain suspensionrequired

3. Clamp-on type limited to sonically conductivepipe

5.13.3.4 Velocity Flowmeters27

Velocity or turbine flowmeters use a propeller or turbineto measure the velocity of the flow passing the device (seeFigure 5.30). The velocity is then translated into a volu-metric amount by the meter register. Sizes exist from avariety of manufacturers to cover the flow range from0.001 gal/min to over 25,000 gal/min for liquid service.End connections are available to meet the various pipingsystems. The flowmeters are typically manufactured ofstainless steel but are also available in a wide variety ofmaterials, including plastic. Velocity meters are applicableto all clean fluids. Velocity meters are particularly wellsuited for measuring intermediate flow rates on cleanwater.

The advantages of the velocity meter include:

1. High accuracy2. Corrosion-resistant materials3. Long-term stability4. Liquid or gas operation5. Wide operating range6. Low pressure drop7. Wide temperature and pressure limits8. High shock capability9. Wide variety of electronics available

As shown in Figure 5.30, a turbine flowmeter consistsof a rotor mounted on a bearing and shaft in a housing.The fluid to be measured is passed through the housing,causing the rotor to spin with a rotational speed propor-tional to the velocity of the flowing fluid within the meter.A device to measure the speed of the rotor is employedto make the actual flow measurement. The sensor can bea mechanically gear-driven shaft to a meter or an elec-tronic sensor that detects the passage of each rotor bladegenerating a pulse. The rotational speed of the sensor shaftand the frequency of the pulse are proportional to thevolumetric flow rate through the meter.

FIGURE 5.29 Particle concentration effect. The more particles there are the more error. (From Spellman, F.R. and Drinan, J.,Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

FIGURE 5.30 (A) Propeller meter; (B) turbine meter. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ.,Lancaster, PA, 2001.)

Full penetration Partial penetration Poor penetration

Transducer Transducer Transducer

Flow

(A)

Register

Flow

Shaft bearing

Bearingsupport arm

Turbine wheel

(B)


5.13.3.5 Positive-Displacement Flowmeters28

Positive-displacement flowmeters are most commonly usedfor customer metering; they have long been used to measureliquid products. These meters are very reliable and accuratefor low flow rates because they measure the exact quantityof water passing through them. Positive-displacement flow-meters are frequently used for measuring small flows in atreatment plant because of their accuracy. Repair or replace-ment is easy since they are so common in the distributionsystem.

In essence, a positive-displacement flowmeter is ahydraulic motor with high volumetric efficiency thatabsorbs a small amount of energy from the flowing stream.This energy is used to overcome internal friction in drivingthe flowmeter and its accessories and is reflected as apressure drop across the flowmeter. Pressure drop isregarded as unavoidable but must be minimized. It is thepressure drop across the internals of a positive displace-ment flowmeter that actually creates a hydraulically unbal-anced rotor, which causes rotation.

A positive-displacement flowmeter continuouslydivides the flowing stream into known volumetric seg-ments, isolates the segments momentarily, and returnsthem to the flowing stream while counting the number ofdisplacements. A positive-displacement flowmeter can bebroken down into three basic components: the externalhousing, the measuring unit, and the counter drive train.

The external housing is the pressure vessel that containsthe product being measured. The measuring unit is a pre-

cision metering element and is made up of the measuringchamber and the displacement mechanism. The most com-mon displacement mechanisms include the oscillating pis-ton, sliding vane, oval gear, tri-rotor, bi-rotor, and nutatingdisc types (see Figure 5.31). The counter drivetrain is usedto transmit the internal motion of the measuring unit intoa usable output signal. Many positive-displacement flow-meters use a mechanical gear train that requires a rotaryshaft seal or packing gland where the shaft penetrates theexternal housing.

The positive-displacement flowmeter can offer excellentaccuracy, repeatability, and reliability in many applications.It has satisfied many needs in the past and should play avital role in serving the future needs as required.

5.13.4 OPEN-CHANNEL FLOW MEASUREMENT29

The majority of industrial liquid flows are carried in closedconduits that flow completely full and under pressure. How-ever, this is not the case for high volume flows of liquids inwaterworks, sanitary, and stormwater systems that are com-monly carried in open channels. Low system heads and highvolumetric flow rates characterize flow in open-channels.

The most commonly used method of measuring therate of flow in open-channel flow configurations is that ofhydraulic structures. In this method, flow in an open chan-nel is measured by inserting a hydraulic structure into thechannel, which changes the level of liquid in or near thestructure. By selecting the shape and dimensions of thehydraulic structure, the rate of flow through or over the

FIGURE 5.31 Six common positive displacement meter principles. (From Spellman, F.R. and Drinan, J., Water Hydraulics,Technomic Publ., Lancaster, PA, 2001.)

Piston

Tri-rotor Bi-rotor Disc

Sliding vane Oval


restriction will be related to the liquid level in a knownmanner. Thus, the flow rate through the open channel canbe derived from a single measurement of the liquid levelin or near the structure.

The hydraulic structures used in measuring flow inopen channels are known as primary measuring devices.They may be divided into two broad categories, weirs andflumes and are covered in the following subsections.

5.13.4.1 Weirs

The weir is a widely used device to measure open-channelflow. As can be seen in Figure 5.32, a weir is simply a

dam or obstruction placed in the channel so that waterbacks up behind it and then flows over it. The sharp crestor edge allows the water to spring clear of the weir plateand to fall freely in the form of a nappe.

As Nathanson30 points out, when the nappe dischargesfreely into the air, there is a hydraulic relationship betweenthe height and depth of water flowing over the weir crestand the flow rate. This height, the vertical distancebetween the crest and the water surface, is called the headon the weir; it can be measured directly with a meter oryardstick or automatically by float-operated recordingdevices. Two common weirs, rectangular and triangular,are shown in Figure 5.33.

FIGURE 5.32 Side view of a weir. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

Weir crest

Head

Draw down

Flow

Flow

Stream or channel bed

AirNappe

FIGURE 5.33 (A) Rectangular weir; (B) triangular V-notch weir. (From Spellman, F.R. and Drinan, J., Water Hydraulics,Technomic Publ., Lancaster, PA, 2001.)

Rectangle weir

Weir crest

Crest length

Triangular weir

V-notch angle

Head

Head

Weir crest

(A)

(B)


Rectangular weirs are commonly used for large flows(see Figure 5.33A). The formula used to make rectangularweir computations is:

Q = 3.33 ¥ L ¥ h1.5 (5.26)

whereQ = flowL = width of weirh = head on weir (measured from edge of weir

in contact with the water, up to the water surface).

EXAMPLE 5.17

Problem:

A 4-ft high weir extends 15 ft across a rectangular channelin which there are 80 ft3/sec flowing. What is the depthjust upstream from the weir?

Solution:

Q = 3.33 ¥ L ¥ h1.5

80 = 3.33 ¥ 15 h1.5

h = 1.4 ft (w/calculator: 1.6 INV yx1.5 = 1.36 or 1.4)4 ft height of weir + 1.4 ft head of water = 5.4 ft depth

Triangular weirs, also called V-notch weirs, can havenotch angles ranging from 22.5∞ to 90∞, but right anglenotches are the most common (see Figure 5.33B).

The formula used to make V-notch (90∞) weir calcu-lations is

Q = 2.5 ¥ h2.5

whereQ = flowh = head on weir (measured from bottom of notch

to water surface)

EXAMPLE 5.18

Problem:

What should be the minimum weir height for measuringa flow of 1200 gal/min with a 90° V-notch weir, if theflow is mow moving at 4 ft/sec in a 2.5 ft wide rectangularchannel?

Solution:

Q = A ¥ V2.67 = 2.5 ¥ d ¥ 4d = 0.27 ft

Q = 2.5 ¥ h2.5

2.67 = 2.5 ¥ h2.5

h = 1.03 (calculator: 1.06 INV yx2.5 = 1.026 or 1.03)0.27 ft (original depth) + 1.03 (head on weir) = 1.3 ft

It is important to point out that weirs, aside from beingoperated within their flow limits, must also be operatedwithin the available system head. In addition, the opera-tion of the weir is sensitive to the approach velocity ofthe water, often necessitating a stilling basin or poundupstream of the weir. Weirs are not suitable for water thatcarries excessive solid materials or silt, which deposit inthe approach channel behind the weir and destroy theconditions required for accurate discharge measurements.

Note: Accurate flow rate measurements with a weircannot be expected unless the proper conditionsand dimensions are maintained.

5.13.4.2 Flumes

A flume is a specially shaped constricted section in anopen channel (similar to the venturi tube in a pressureconduit). The special shape of the flume (see Figure 5.34)restricts the channel area and/or changes the channelslope, resulting in an increased velocity and a change inthe level of the liquid flowing through the flume. The flumerestricts the flow, and then expands it in a definite fashion.The flow rate through the flume may be determined bymeasuring the head on the flume at a single point, usuallyat some distance downstream from the inlet.

Flumes can be categorized as belonging to one of threegeneral families, depending upon the state of flow induced— subcritical, critical, or supercritical. Typically, flumesthat induce a critical or supercritical state of flow are mostcommonly used. This is because when critical or super-critical flow occurs in a channel, one head measurementcan indicate the discharge rate if it is made far enoughupstream so that the flow depth is not affected by thedrawdown of the water surface as it achieves or passesthrough a critical state of flow. For critical or supercriticalstates of flow, a definitive head-discharge relationship canbe established and measured based on a single head read-ing. Thus, most commonly encountered flumes aredesigned to pass the flow from subcritical through criticalor near the point of measurement.

The most common flume used for a permanent waste-water flowmetering installation is called the Parshallflume, shown in Figure 5.34.

Formulas for flow through Parshall flumes differ,dependent on throat width. The formula below can be usedfor widths of 1 to 8 feet, and applies to a medium rangeof flows.

Q = 4 ¥ W ¥ Ha1.52 ¥ W .026 (5.27)

1200 gpm

60 sec min .48 ft

gal ft33

¥=

72 67. sec


where

Q = flow

Ha = depth in stilling well upstream

W = width of throat

Note: Parshall flumes are low maintenance items.

5.14 CHAPTER REVIEW QUESTIONS AND PROBLEMS

5.1. What should be the minimum weir height formeasuring a flow of 900 gal/min with a 90°V-notch weir, if the flow is now moving at3 ft/sec in a 2-ft wide rectangular channel?

5.2. A 90° V-notch weir is to be installed in a30-in. diameter sewer to measure 600gal/min. What head should be expected?

5.3. For dirty water operations, a ___________or _________ orifice plate should be used.

5.4. A _________ has a smooth entry and sharpexit.

5.5. A _____________ sends a beam of ultra-sonic sound waves through the water toanother transducer on the opposite side ofthe unit.

5.6. Find the number of gallons in a storage tankthat has a volume of 660 ft.3

5.7. Suppose a rock weighs 160 lb in air and 125 lbunderwater. What is the specific gravity?

5.8. A 110-ft diameter cylindrical tank contains1.6 MG H2O. What is the water depth?

5.9. The pressure in a pipeline is 6400 psf. Whatis the head on the pipe?

5.10. The pressure on a surface is 35 psi gauge. Ifthe surface area is 1.6 ft2, what is the force(lb) exerted on the surface?

5.11. Bernoulli’s principle states that the totalenergy of a hydraulic fluid is ___________________.

5.12. What is pressure head?

5.13. What is a hydraulic grade line?

5.14. A flow of 1500 gal/min takes place in a 12-in.pipe. Calculate the velocity head.

5.15. Water flows at 5.00 mL/sec in a 4-in. lineunder a pressure of 110 psi. What is thepressure head (ft H2O)?

5.16. In Question 5.15, what is the velocity headin the line?

5.17. What is velocity head in a 6-in. pipe con-nected to a 1-ft pipe, if the flow in the largerpipe is 1.46 ft3/sec?

5.18. What is velocity head?

5.19. What is suction lift?

5.20. Explain energy grade line.

REFERENCES

1. Spellman, F.R. and Drinan, J., Water Hydraulics, CRCPress, Boca Raton, FL (originally published by Tech-nomic Publishing, Lancaster, PA). 2001, p. 5.

2. Magnusson, R.J., Water Technology in the Middle Ages,The John Hopkins University Press, Baltimore, MD,2001, p. xi.

3. Magnusson, R.J., Water Technology in the Middle Ages,The John Hopkins University Press, Baltimore, MD,2001, p. 36.

FIGURE 5.34 Parshall flume. (From Spellman, F.R. and Drinan, J., Water Hydraulics, Technomic Publ., Lancaster, PA, 2001.)

Throat

Top view

Flow

Converginginlet Diverging

outlet

Stilling well formeasuring hear


4. Nathanson, J.A., Basic Environmental Technology:Water Supply, Waste Management, and Pollution Con-trol, 2nd ed., Prentice Hall, Upper Saddle River, NJ,1997, pp. 21–22.

5. This section adapted from information contained inHauser, B.A., Hydraulics for Operators, Lewis Publish-ers, Boca Raton, FL, 1993, pp. 16–18; Basic ScienceConcepts and Applications: Principles and practices ofWater Supply Operations, 2nd ed., American WaterWorks Association, Denver, 1995, pp. 351–353.

6. Holman, S., A Stolen Tongue, Anchor Press, Doubleday,New York, 1998, p. 245.

7. Spellman, F.R., The Science of Water: Concepts &Applications, Technomic Publ., Lancaster, PA, 1998, pp.92–93.

8. Adapted from Nathanson, J.A., Basic EnvironmentalTechnology: Water Supply, Waste Management, and Pol-lution Control, 2nd ed., Prentice Hall, Upper SaddleRiver, NJ, 1997, pp. 29–30.

9. Krutzsch, W.C., Introduction and classification ofpumps, in Pump Handbook, Karassik, I.J. et al.,McGraw-Hill, Inc., New York, 1976, p. 1-1.

10. Adapted from Cheremisinoff, N.P. and Cheremisinoff,P.N., Pumps/Compressors/Fans: Pocket Handbook,Technomic Publ., Lancaster, PA, 1989, p. 3.

11. Adapted from Water Transmission and Distribution, 2nded., American Water Works Association, Denver, 1996,p. 358.

12. Adapted from Arasmith, S., Introduction to Small WaterSystems, ACR Publications, Inc., Albany, OR, 1993, pp.59–61.

13. A more complete listing of hydraulic terms may befound in Lindeburg, M.R., Civil Engineering ReferenceManual, 4th ed., Professional Publications, Inc., SanCarlos, CA, 1986, pp. 5-2–5-3.

14. Metcalf & Eddy, Wastewater Engineering: Collectionand Pumping of Wastewater, McGraw-Hill, New York,1981, p. 11.

15. Adapted from Lindeburg, M.R., Civil Engineering Ref-erence Manual, 4th ed., Professional Publications, Inc.,San Carlos, CA, 1986, p. 3-20.

16. Lindeburg, M.R., Civil Engineering Reference Manual,4th ed., Professional Publications, Inc., San Carlos, CA,1986, p. 3-26.

17. Viessman, W., Jr., and Hammer, M.J., Water Supply andPollution Control, 6th ed., Addison-Wesley, Menlo Park,CA, 1998, p. 119.

18. Adapted from McGhee, T.J., Water Supply and Sewer-age, 2nd ed., McGraw-Hill, New York, 1991, p. 45.

19. Nathanson, J.A., Basic Environmental Technology:Water Supply, Waste Management, and Pollution Con-trol, 2nd ed., Prentice Hall, Upper Saddle River, NJ,1997, p.34.

20. Adapted from Hauser, B.A., Practical Hydraulics Hand-book, 2nd ed., Lewis Publishers, Boca Raton, FL, 1996,p. 91.

21. From Water Treatment: Principles and Practices ofWater Supply Operations, 2nd ed., American WaterWorks Association, Denver, 1995, pp. 449–450.

22. Kawamura, S., Integrated Design and Operation ofWater Treatment Facilities, 2nd ed., John Wiley & Sons,New York, 2000.

23. Adapted from Husain, Z.D. and Sergesketter, M.J., Dif-ferential pressure flow meters, in Flow Measurement,Spitzer, D.W., Ed., Instrument Society of America,Research Triangle Park, NC, 1991, pp. 119–160.

24. Adapted from Flow Instrumentation: A Practical Work-shop on Making Them Work, The Water & WastewaterInstrumentation Testing Association and United StatesEnvironmental Protection Agency, Section A, Sacra-mento, CA, May 16–17, 1991.

25. Mills, R.C., Magnetic flow meters, in Flow Measurement,Spitzer, D.W., Ed., Instrument Society of America,Research Triangle Park, NC, 1991, pp. 175–219.

26. Adapted from Brown, A.E., Ultrasonic flow meters, inFlow Measurement, Spitzer, D.W., Ed., Instrument Soci-ety of America, Research Triangle Park, NC, 1991, pp.415–432.

27. Adapted from Oliver, P.D., Turbine flow meters, in FlowMeasurement, Spitzer, D.W., Ed., Instrument Society ofAmerica, Research Triangle Park, NC, 1991, pp.373–414.

28. Barnes, R.G., Positive displacement flow meters for liq-uid measurement, in Flow Measurement, Spitzer, D.W.,Ed., Instrument Society of America, Research TrianglePark, NC, 1991, pp. 315–322.

29. Adapted from Grant, D.M., Open channel flow measure-ment, in Flow Measurement, Spitzer, D.W., Ed., Instru-ment Society of America, Research Triangle Park, NC,1991, pp. 252–290.

30. Nathanson, J.A., Basic Environmental Technology:Water Supply, Waste Management, and Pollution Con-trol, 2nd ed., Prentice Hall, Upper Saddle River, NJ,1997, p. 39.


Documents

The practice and study of water hydraulics / Hidraulicki proracuni