Lesson 7_.pdf

Lesson 6:Head Loss

Objective

In this section we will learn the following:

How to define head or head loss.Why is head loss a concern in water and wastewater?How to perform some calculations to help plan and design for head loss.What is TDH - Total Dynamic Head?How to estimate the shutoff head of a centrifugal pump.The shutoff head is approximately 90% of the diameter of the impeller squared.How to calculate a pump's BEP, or Best Efficiency Point.Compare the relationships with capacity and efficiency of the head.

Reading Assignment

Read the online lesson as well as Chapter 5 in your textbook.

Lecture

Introduction

Head loss (as discussed in Lesson #7) is the measure of the reduction in the total head of the liquid as itmoves through a system. The total head is the sum of the elevation head, velocity head and pressure head.Head loss is unavoidable and is present because of the friction between the fluid and the walls of the pipeand is also present between adjacent fluid particles as they flow along the pipe. Head loss is a measure ofthe reduction in the total head (sum of elevation head, velocity head and pressure head) of the fluid as itmoves through a fluid system. This is unavoidable in real fluids.

The head loss for fluid flow is directly proportional to the length of the pipe, as flow rate increases thepressure will drop. Friction loss = rough pipes, and the degree of roughness is called the C - Factor.

The HEAD is the vertical distance, height or energy of water above a point. A head of water may bemeasured in either height (ft.) or pressure (psi). To calculate Head Loss in feet you should multiply the psi-pounds per square inch X 2.31 ( a set constant) OR the psi is equal to 0.433 X feet of head. Each can beread with a pressure gauge.

Head loss is the combination of different types of losses. 1- Friction Loss, 2 - other minor losses. Frictionfrom the walls of the pipe on the liquid is the head loss , caused by friction.

Head loss is the reduction in the total head of a fluid caused by the friction present in the fluid's motion.NetCrawl Advertisement

Lesson 7: http://water.me.vccs.edu/courses/CIV240/lesson6_print.htm

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1- Friction loss occurs as the fluid flows through the straight pipes. 2- Minor losses are head losses thatoccur due to bends, elbows, joints, valves, and other fittings in the systems. Whenever there is a change inthe direction of flow or a change in the cross-sectional area a head loss will occur.

Friction losses are very dependent upon the viscosity of the liquid and the amount of turbulence in theflow. Head loss due to friction can be calculated by using the Darcy-Weisbach equation. The frictionfactor for the fluid flow can be determined by using a MOODY CHART if the relative roughness of thepipe and the Reynolds Number of the flow can be determined. Darcy's equation can be used to calculatefrictional losses. A special form of this equation can be used to calculate minor losses. Friction loss is thatpart of the total head loss that occurs as the fluid flows through straight pipes. The head loss for fluid flowis directly proportional to the length of pipe, the square of the fluid velocity, and a term for fluid frictioncalled the friction factor . The head loss is inversely proportional to the diameter of the pipe. Friction lossmust be calculated in order to properly size pipe, elbows, valves, and other fitting along the piping system.Total dynamic head (TDH) is very important in calculating the pump sizes. The TDH involves severaldifferent things:

the vertical distance the water is being pumped to the point of use

the operating pressure desired at the point of use (ft. of water)

the friction losses from water moving through the piping system, which is measured as feet of head loss

Head loss is given in equation 2.8.4 as:

Where:

f = friction factorD = diameterL = LengthV = average velocityg = acceleration due to gravity

f is given by equations for Laminar Flow

Where:

p = densityD = diameterv = velocityu = viscosity


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HEAD is the amount of energy possessed by a unit quantity of water expressed in feet. Water may containenergy due to 1- elevation 2- pressure 3- velocity. Thus a 40 ft. tank will have 40 ft. of head. HEAD that isdue to elevation is called STATIC HEAD, this is the actual elevation difference between water surfaces ora water surface and some reference point.

IF the elevation of tank A is 2100 feet and the elevation of tank B is 2300 feet, then the static head is200 feet.

Pressure head is = feet Velocity head is the energy of motion.

1 psi = 2.31 ft. Velocity head = y(squared) divided by 2g

.433 psi = 1 ft. G = 32.2 ft. per second squared

Head loss in feet of pipe (PVC plastic pipe)

For head loss in feet, multiply PSI by 2.31. For instance, for 20 GPM and 1.5" diameter pipe,multiplying 1.34 PSI by 2.31, you will get 3.1 feet. That is, for every 100 feet of 1.5" pipe with 20GPM flowing through it you will lose 3.1 feet of head due to friction.

1.34 x 2.31 = 3.1 ft

Flow GPM pipe diameter (inches)

Water Withdrawal Estimation by Pipe Diameters

Table 2: Water Withdrawal Estimation by PipeDiameters PipeDiameterin inches Gallonsper MinuteDischarged Gallonsaccumulatedafter 1 Hour HoursTo Reach3 MillionGallons Days

PipeDiameterin inches

Gallonsper MinuteDischarged

Gallonsaccumulatedafter 1 Hour

HoursTo

Reach3

MillionGallons

Days


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2 60 3,600 833.3 34.7

3 93 5,580 537.6 22.4

4 188 11,280 266.0 11.1

5 325 19,500 153.8 6.4

6 500 30,000 100.0 4.2

8 750 45,000 67.7 2.8

10 1,200 72,000 42.7 1.7

Introduction

Head: The head or pressure at which the centrifugal pump will stop discharging. It is also the pressuredeveloped by the pump when it is operated against a closed discharged valve. This is also known as a cutoff head.

Cut-off Head: The head at which the energy supplied by a pump and the energy required to move theliquid to a specified point are equal and no discharge at the desired point will occur.

Shut-off Head: The highest point the pump will lift liquid. At this point the pump will pump 0 gallons perminute.

TDH: (Total Dynamic Head) A combination of two components - Static Head and Friction Head - and isexpressed in feet. Static head is the actual vertical distance measured from the minimum water level inthe basin to the highest point in the discharge piping. Friction head is the additional head created in thedischarge system due to resistance to flow within its components.

Head - Capacity

As might be expected, the capacity of a centrifugal pump is directly related to the total head of thesystem. If the total head on the system is increased, the volume of the discharge will be reducedproportionately. Figure 3-2 illustrates a typical head-capacity curve for a centrifugal pump. While thiscurve may change with respect to total head and pump capacity based upon the size of the pump, pumpspeed, and impeller size and/or type, the basic form of the curve will remain the same. As the head of thesystem increases, the capacity of the pump will decrease proportionately until the discharge stops. Thehead at which the discharge no longer occurs is known as the cut-off head.

As discussed earlier, the total head includes a certain amount of energy to overcome the friction of thesystem. This friction head can be greatly affected by the size and configuration of the piping and thecondition of the system's valving. If the control valves on the system are closed partially, the friction head


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can increase dramatically. When this happens, the total head increases and the capacity or volumedischarged by the pump decreases. In many cases, this method is employed to reduce the discharge of acentrifugal. It should be remembered, though, that this does increase the load on the pump and drivesystem causing additional energy requirements and additional wear.

The total closure of the discharge control valve increases the friction head to the point where all theenergy supplied by the pump is consumed in the friction head and is not converted to pressure head. As aresult, the pump exceeds its cut-off head and the pump discharge is reduced to zero. Again, it is importantto note that even though the operation of a centrifugal pump against a closed discharge may not be ashazardous as with other types of pumps, it should be avoided due to the excessive load placed on the driveunit and pump. There have also been documented cases where the pump produced pressures higher thanthe pump discharge piping could withstand. In these cases, the discharge piping was severely damaged bythe operation of the pump against a closed or plugged discharge.

Friction Head

Friction head, ft is the amount of energy used to overcome resistance to the flow of liquids through thesystem. It is affected by the length and diameter of the pipe, the roughness of the pipe, and the velocityhead. It is also affected by the physical construction of the piping system. The number and types of ell's,values, tees, etc., will greatly influence the friction head for the system. These must be converted to theirequivalent length of pipe and included in the calculation.

The roughness factor (f), varies with length and diameter as well as the condition of the pipe and thematerial from which it is constructed, it is normally in the range of .01-.04.

Example:

What is the friction head in a system which uses 150 ft of 6 inch diameter pipe, when the velocity is 3fps? The system's valving is equivalent to an additional 75 feet of pipe. Reference material indicates aroughness factor of 0.025 for this particular pipe and flow rate.


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It is also possible to compute friction head by using a table such as that shown in Figure 2-10. Thecalculation of friction by this method is illustrated in the Figure.

It is also possible to determine friction head on the suction side of the pump and the discharge side of thepump. In each case, it is necessary to determine:

the length of pipe1. the diameter of the pipe2. velocity3. pipe equivalent of valves, elbows, tees, etc.4.

Velocity Head

Velocity head is the amount of head or energy required to maintain a stated velocity in the suction anddischarge lines. The design of most pumps makes the total velocity head for the pumping system zero.

Mathematically the velocity head is:

Example:

What is the velocity head for a system which has a velocity of 4 fps?


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Example:

Determine Total Head using the data given on the diagram in Figure 7-1.

Determine Static Head, ft.1.

Determine Friction Head, ft2.

Find total length of pipea.

Find equivalent length for valves and Ell'sb.

Total pipe lengthc.


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Length = Pipe Length, ft + Equivalent Pipe, ft (L)

Length = 48 ft + 745 ft

Length = 793 ft

d.

Determine Velocity Head, ft

Due to pump charcteristics total velocity head is stated to be zero.

3.

Determine Total Head, ft

Total Head, ft = Static Head, ft + Friction Head, ft + Velocity Head, ft

Total Head, ft = 48 ft + 4.46 ft + 0

Total Head, ft = 52.46 ft

4.

V1= Gate Valve (125 ft pipe equivalent)

V2= Check Valve (150 ft pipe equivalent)


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V2= 90 Elbow (65 ft pipe equivalent)

f = 0.03

Pipe Diameter = 9 inches

Velocity 3 fps

Velocity Heads are equal, canceling each other.

Estimating the Shutoff Head of a Centrifugal Pump

In the fifteenth century the Swiss scientist Daniel Bernoulli learned that the combination of head andvelocity was a constant throughout a piping system. He then wrote the formula showing the relationshipbetween this liquid velocity, and resultant head. As many of you know, I often quote this formula in mypump and seal schools. The formula looks like this:

V = Velocity or speed of the liquid at the impeller outside diameter (ft/sec. or meters/sec.)

g = gravity = 32.2 feet/sec2 or 9.8 meters.sec2

My students have heard me quote this formula as the basis for my statement that you can estimate theshutoff head of a 1750 rpm centrifugal pump by squaring the diameter of the impeller. How did I come tothat conclusion? Let's look at the formula again, and we will start by defining velocity:

Velocity is a measurement of speed using distance and time as the variables. The terms we use to discussvelocity are feet/second or meters/second. In the inch system, the velocity of the impeller outsidediameter is determined by the following formula:

d = diameter of the impeller

= 3.14

rpm = speed of the impeller outside diameter

12 = twelve inches in a foot


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60 = sixty seconds in a minute

Now we will solve the problem. Substituting 1750 for the rpm we would get:

Going back to the original formula we will substitute the new value for "V"

This means that at 1750 rpm the shutoff head is 90% of the diameter of the impeller squared.

If you will check a typical pump curve as supplied by the pump manufacturers, you will learn that theshutoff head actually varies from 90% to 110% of the diameter of the impeller squared. I elected to use100% because it is a sensible average and in some cases it accounts for the additional velocity added tothe fluid as it moves from the impeller eye to the impeller outside diameter.

If we substitute 3500 rpm for the speed, the new numbers would look like this:

Going back to the original formula we will substitute the new value for "V"

We can round out the 3.6 to 4.0 and say that at 3500 rpm the shutoff head equals approximately theoutside diameter of the impeller squared, times four.

It is a little trickier in the metric system. Instead of using millimeters when measuring the impellerdiameter, move over two decimal places and use decimeters instead. It will make the calculations a lotsimpler because you will be using more convenient, larger numbers.

Inserting the numbers into the formula we would get a velocity of:


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Going back to the head formula we would get:

We can round this off to 3d2

If the pump were running at 2900 rpm you would get:

Going back to the head formula we would get:

We can round this off to 12d2

How do we use this information? You can combine this formula with your knowledge of how to convertpressure to head and come up with an estimate to see if an operating pump is operating close to its BEP(best efficiency point). As an example:

In the inch system a pump discharge pressure gage reads 120 psi. The pump suction pressure gage reads20 psi. The pump is pumping the difference between these readings, so the pump is pumping 100 psi.

At its BEP (best efficiency point) the pump should be running between 80% and 85% of its shutoff head. 100 psi is 83% of 120 psi. The pressure to head conversion is:

The pump has an 8.5 inch impeller running at 3500 rpm. The shutoff head would be (8.5 inches)2 4 =288 feet. Pretty close!

In the metric system we can make the calculation for 295 millimeter impeller turning at 2900 rpm.

The pump discharge pressure gage reads 10 bar. The pump suction pressure gage reads 1 bar. The pumpis pumping the difference between these readings so the pump is pumping 9 bar.

At its BEP (best efficiency point) the pump should be running between 80% and 85% of its shutoff head. 9 bar is 83% of 10.8 bar. The pressure to head conversion is:


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The pump has a 295 mm impeller running at 2900 rpm. The shutoff head would be (2.95 decimeter)2 12= 104.4. Pretty close!

These two graphs show the capacity and efficiency of the Head.


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Review

In this lesson we learned about all the types of head losses. Friction loss, and velocity losses as well asminor losses (within the fittings used in the system) are all involved in properly calculating the head losseswithin the entire system. Head loss is defined as the measure of the reduction in the total head of theliquid as it moves through a system. The total head is the sum of the elevation head, velocity head andpressure head. Head loss is unavoidable and is present because of the friction between the fluid and thewalls of the pipe. Head loss is a measure of the reduction in the total head of the fluid as it moves througha pumping system . Head loss is unavoidable . The head loss for fluid flow is directly proportional to thelength of pipe as it flows through a system.

The head is the vertical distance, height or energy of water above a specific point. A head of water may bemeasured in height, ft. or pressure, psi. To calculate head loss in feet you should multiply the psi times2.31 or the psi is equal to 0.433 times the feet of head.

Each of these can be found by reading or using a pressure gauge. Head loss is the combination of thedifferent types of losses, with Friction loss being the main loss. This is caused by water flowing through apipeline, which through years of use, is no longer smooth and now has scale and corrosion on the inside ofthe pipeline, SLOWING the flow. Friction losses are very dependent upon the viscosity of the liquidand the amount of turbulence in the flow. The head loss is inversely proportional to the diameter of thepipe.

The TDH or Total Dynamic Head, 1 - is the vertical distance the water is being pumped to the point ofuse, 2 - The operating pressure desired at the point of use (expressed in ft. of water) or 3 - the frictionlosses from water moving through the piping system (measured as ft. of head loss). This is used whenwater is being pumped from a well (to determine the distance from the water level to the ground surface).The drop in water level while the pump is in operation, called the drawdown of the well. The verticaldistance the water must be elevated is then the sum of the drawdown, the distance from the normal waterelevation to the wellhead, and the rise from the wellhead to the point of distribution in the water system.

The proper sizing of lines and fittings is very critical to utility operations. Pressure, flow, and source waterare all important information when sizing a pump. But fittings such as elbows, terrain, and curves will


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change all the calculations, water lines do NOT go in straight lines, although it would be easier to calculateif they did. Proper sizing of a pump can be complex and simple at the same time. All you need to know isthe required gallons per minute and the total dynamic head, TDH, we wish, but as you learned from thislesson there are a lot of other factor involved with these calculations as well.

We learned that the relationship of the shut-off head of a centrifugal pump is equal to the diameter of theimpeller squared. This concept is easier to understand if we look at the velocity. This is done bymultiplying pi (3.14) d or diameter rpm by 12 (inches/ft) 60 (sec/min). Using 1750 as the rpms,this is then calculated to mean that at 1750 rpm the shutoff head is approximately 90% of the diameter ofthe impeller squared. A pump's BEP (Best Efficiency Point) is calculated based on the pump dischargepressure and suction pressure. Velocity is a measurement of speed using distance and time as the variable.The term head velocity refers to gains or losses in pressure caused by friction or gravity as the watermoves through the system.

Resources

Water Supply & Pollution Control - 4 th Edition

Water Distribution Operator Training Handbook - AWWA

Op Flow Bulletins - July 1998, Sept. 2000

Assignment

Answer the following questions and either email or fax to the instructor.

For water equations, one hp equals 33,000ft-lb/min. IF you divide 33,000 ft-lb/min by 8.34 lb/gal (1 galwater = 8.34 lb) you will get approx. 3960 gal/min/ft. OR

A pump is pumping against a total head of 46.2 feet at a rate of 800 gpm. What is the water hprequired?

1.

A pump running at 5 hp is delivering a flow of 420 gpm. How much head is it pumping against?2. What is the maximum pumping rate (in gpd) of a 15 hp pump, pumping against a head of 65 ft?3. What is velocity?4. ______________ varies from 90% to 110% of the diameter of the impeller squared.5. What is the name for the type of head that is lost by fluid flowing in a stream or conduit due tofriction per unit weight of fluid?

6.

TDH is the sum of what?7. _______________ refers to the losses in pressure caused by gravity and friction as water movesthrough the system, most often given in feet of water.

8.


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Documents

Lesson 7_.pdf