Help for Calculating the Impeller Tip Speed to Avoid Excessive Erosion Due to Suspended Particles

7/28/2019 Help for Calculating the Impeller Tip Speed to Avoid Excessive Erosion Due to Suspended Particles

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Help for calculating the impeller tip speed to avoidexcessive erosion due to suspended particles

Applets are programs based on the java language that are designed to run on your computer using theJava Run Time environment.

The maximum impeller tip speed is based on tests that were done by the Hydraulic Institute www.pumps.org. You can find more information in The Hydraulic Institute's Centrifugal Pumps for Designand Application ANSI/HI 1.3 standard.

This applet is designed to help you calculate the tip velocity of an impeller vane with the simple v = wrformula.

The recommendations on the maximum tip speed are as follows:

- dirty water - 130 ft/s

- medium slurries up to 25% solids and 200 micron solids - 115 ft/s

- higher slurry concentrations and larger solids - 100 ft/s

- pumps with elastomer impeller - 85 ft/s

Tip speeds that are higher than recommended are likely to cause excessive erosion. Elastomerimpellers are often used in the mining industry for the transfer of tailings which is a highly abrasiveslurry.

The equation used for calculating tip speed is:
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where

v: velocity

D: impeller diameter

RPM: revolutions per minute

Help for calculating the pressure anywhere in a pumpsystem


It is possible to calculate the pressure head, which is the specific energy of pressure, anywherewithin a system and with the pressure head, the pressure can be calculated. If you know theconditions at the outlet of a system then you can calculate the pressure anywhere upstream of thatpoint all the way to the pump. The same is true if you know the conditions at the inlet of the system,then you can calculate the pressure anywhere downstream of that point all the way up to the pump.This is what this applet does for you.

The outlet of the system is defined as the point where the fluid meets a fixed pressure environmentsuch as the fluid surface of the discharge tank where it meets atmospheric pressure for an open tank.Or if the tank is pressurized, at the point where the fluid surface meets the pressurized environmentwithin the tank. The same reasoning is applied to locate the inlet point of the system in the suctiontank.

Determine the pressure anywhere on the discharge side of the pump (see Figure 1 below)

The conditions that must be known at the outlet are:


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z2: the elevation of the outlet point of the system with respect to an arbitrary datum plane, if thepipe is open to atmosphere then z2 is the elevation of the pipe end with respect to the datum plane. Ifthe outlet is the surface of the liquid in the discharge tank then z2 is the elevation of fluid particleson the surface with respect to the datum plane. It does not matter where the datum plane is locatedas long as you use the same one for zx. The pump suction centerline is often used as the level for the

datum plane;

zx: the elevation of point X with respect to the datum plane where the pressure is required;

v2: velocity of the fluid at the outlet, if the outlet is the surface of a discharge tank then thisvelocity is small and close to zero, if the pipe is open to atmosphere than the velocity is the velocity atthe pipe end;

H2: the pressure head at the outlet of the system, if the tank is pressurized then H2 is the pressurehead corresponding to the pressure in the tank. As an example, say the tank is pressurized at 10 psithen H2 = 2.31 x 5 / SG (SG: specific gravity of the fluid), if the fluid is water then SG = 1 and H2=11.5 ft.

SG: the specific gravity of the fluid (non-dimensional), water has an SG value of 1.0.

The pipe friction is Hf or HFX-2 in the equation 1.1 below, between the point where the pressure isrequired, point X, and the outlet must be calculated separtely (this is not done by the applet). You willhave to calculate this using the Darcy and Colebrook equations or tables that are available in theCameron Hydraulic data book, or tables in the Standards book from the Hydraulic Institute.

Lastly, you need to know the equipment friction loss HEQ or HEQX-2 in the equation 1.1 below, for allthe equipment between the point where the pressure is required, point X, and the outlet. Equipmentare items such as a control valve, a heat exchanger, a filter, etc. It is likely that you will have toconsult the manufacturer equipment literature to obtain this information.


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Figure 1

The equation to calculate HX is:

eq. 1.1

You may find that the calculated pressure is negative, it is negative with respect to the outletpressure. This can occur if the position of the point where you require the pressure is higher than theoutlet and the friction between these two points is minimal.

The formula for converting pressure head to pressure is:

eq. 1.2

Determine the pressure anywhere on the suction side of the pump (see Figure 2 below)

Everything that was said above for calculating the pressure anywhere on the discharge side of thepump is true for calculating the pressure on the suction side of the pump. In this case, the conditionsat the inlet of the system must be known and this is generally the conditions at the liquid surface ofthe suction tank.


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z1: the elevation of the inlet point of the system with respect to the datum plane;

zx: the elevation of point X with respect to the datum plane where the pressure is required;

v1: velocity of the fluid at the inlet, the inlet is often the surface of a suction tank, this velocity issmall and close to zero;

H1: the pressure head at the inlet of the system, if the tank is pressurized then H1 is the pressurehead corresponding to the pressure in the tank;

SG: the specific gravity of the fluid (non-dimensional), water has an SG value of 1.0.

The pipe friction Hf or HF1-X in the equation 1.3 below, between the point where the pressure isrequired, point X, and the inlet must also be known. This is the friction loss in the pump suction line.

You will have to calculate this using the Darcy and Colebrook equations or tables that are available inthe Cameron Hydraulic data book, or tables in the Standards book from the Hydraulic Institute.

Lastly, you need to know the equipment friction loss HEQ or HEQ1-X in the equation 1.3 below, for allthe equipment between the point where the pressure is required, point X, and the inlet. Equipment areitems such as a control valve, a heat exchanger, a filter, etc. Equipment is rarely installed in the pumpsuction line so that this term is typically zero. It is likely that you will have to consult themanufacturer equipment literature to obtain this information.


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Figure 2

The equation to calculate HX is:

Eq. 1.3

You may find that the calculated pressure is negative, it is negative with respect to the inlet pressure.This can occur if the position of the point where you require the pressure is higher than the inlet andthe friction between these two points is minimal.

Help for calculating maximum allowable pipingpressure according to the ASME pressure piping

code B31.3


The ASME code recommends an allowable tensile stress level in the pipe material (see the terminologysection at the end of this article). The pressure that can generate this tensile stress level can becalculated taking into account the type of material, temperature and other factors.


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The formula (see B31.3-1999 code, page 20) which gives the relationship between the pressure (p)labeled p (see equation[1]), the outside diameter (D), the allowable tensile stress (S) and the thickness(t) of the pipe is:

[1]

where E: material and pipe construction quality factor as defined in ASME Process Piping code B31.3-1999, Table A-1A

Y: wall thickness coefficient with values listed in ASME Process Piping code B31.3-1999, Table 304.1.1

Formula [1] is re-written in terms of the pressure (p) of the fluid within the pipe:

Calculation example

The pipe is a typical spiral-weld construction assembled according to the specification ASTM A 139-96. The material is carbon steel ASTM A 139. The outside diameter of the pipe is 20.5 inches and thewall thickness is 0.25-inch.

For this material, the ASME code recommends that an allowable stress (S) of 16,000 psi be used for atemperature range of -20F to +100F. The quality factor E for steel A139 is 0.8; the wall thicknesscoefficient Y is 0.4.

Material Minimum tensile strength(psi) ASME code Allowable stress (S)(psi)ASTM A139 48000 16000

The value of the internal fluid pressure that will produce the tensile stress level stipulated by theASME code is 315 psig (see formula [3]).

This pressure should be compared to the normal operating pressure. The pressure in a pump systemcan vary dramatically from place to place. The pressure level vs. location can only be determined on acase by case basis. However, typically the pressure is maximum near the pump discharge anddecreases towards the outlet of the system.


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It is possible that the system could be plugged. When the system plugs, the pump head increases andreaches (at zero flow) the shut-off head in the case of a centrifugal pump. The maximum pressure inthe pump system will then be the pressure corresponding to the shut-off head plus the pressurecorresponding to the pump inlet suction head. Since the system is plugged, this pressure will extend allthe way from the pump discharge to the plug if the plug is at the same elevation as the pump

discharge. The relationship between pressure head and pressure is given in equation [4].

where (H) is the pressure head, (p) the pressure and (SG) the specific gravity of the fluid.

If the shut-off pressure exceeds the allowable operating pressure as calculated by the ASME code,then pressure relief devices may have to be installed. This is not likely to occur in single pumpsystems, but multiple series pump systems may produce excessive shut-off pressures since thepressure at the outlet of the last pump depends on the sum of the shut-off pressures of each pump.

Exceptions are provided for in the code and are relative to the duration of the maximum pressuresevents, if they are of short duration these events may be allowed for short periods.

Rupture disks are often used in these situations. They are accurate, reliable pressure relief devices.However, these devices are not mandatory in many systems and their installation are then a matter ofengineering judgment.

Existing systems

In an existing system, one should not rely on the original thickness of the pipe to do the pressurecalculations. The pipe may suffer from corrosion, erosion or other chemical attacks which may reducethe wall thickness in certain areas. The pipe wall thickness can easily be measured by devices such asthe Doppler ultra sound portable flow meter. The smallest wall thickness should be used as the basisfor the allowable pressure calculations or the damaged areas should be replaced.

New systems

In new systems, consider if a corrosion allowance (depending on the material) should be used. Thecorrosion allowance will reduce the wall thickness that is used in the allowable pressure calculations.

Also the piping code allows pipe manufacturers a fabrication tolerance which can be as high as 12.5%on the wall thickness, this allowance should be considered when determining the design pipe wall

thickness.

Terminology

Figure 1 shows the location of the various stress levels in a typical stress vs. strain graph.

TS: Tensile strength

YP: Yield point


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BS: Breaking strength

The following four figures are excerpts from the ASME Power Piping Code B31.3


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This pdf document provides information on different flange pressure ratings, construction, ANSIclass and materials base on the ASME code B16.5.

This applet will help you calculate the allowable pressure according to the pressure piping code B31.3.You can download an example of this type of calculation as well as the formulas used including anextract of the pressure piping code. The formula for max. pressure is based on the well known hoopstress formula in which two additional factors have been added, Y a factor based on the type of steeland E a factor based on the type and quality of the weld. The pressure piping code is not readilyavailable on the internet. You can probably find it in your local technical university or college librairy.The book "Piping Handbook" by Mohinder L. Nayyar published by McGraw Hill has extracts of thecode. Remember that when you check the maximum allowable piping pressure you must also check the
http://www.pumpfundamentals.com/flange_classes.pdfhttp://www.pumpfundamentals.com/flange_classes.pdfhttp://www.pumpfundamentals.com/max_piping_oper_press.pdfhttp://www.pumpfundamentals.com/max_piping_oper_press.pdfhttp://www.pumpfundamentals.com/max_piping_oper_press.pdfhttp://www.pumpfundamentals.com/flange_classes.pdfhttp://www.pumpfundamentals.com/max_piping_oper_press.pdf


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maximum allowable flange pressure, this depends on the ANSI class of the flange, the material andthe temperature.

CAVITATION PREDICTIONThis document will cover two topics, one a general discussion of this subject and how theequations were developped. The other some specific comments on how the applet functions.

General

There is a multitude of pump designs that are available for any given task. Pump designers haveneeded a way to compare the efficiency of their designs across a large range of pump model andtypes. Pump users also would like to know what efficiency can be expected from a particular pumpdesign. For that purpose pump have been tested and compared using a number or criteria called thespecific speed (NS) which helps to do these comparisons. The efficiency of pumps with the samespecific speed can be compared providing the user or the designer a starting point for comparison oras a benchmark for improving the design and increase the efficiency. The next equation gives thevalue for the pump specific speed, H is the pump total head, N the speed of the impeller and Q theflow rate.

Pumps are traditionally divided into 3 types, radial flow, mixed flow and axial flow. There is a

continuous change from the radial flow impeller, which develops pressure principally from the action ofcentrifugal force, to the axial flow impeller, which develops most of its head by the propelling orlifting action of the vanes on the liquid.
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Specific speed has also been used as a criteria for evaluating the efficiency of standard volute pumps(see next Figure). Notice that larger pumps are inherently more efficient and that efficiency dropsrapidly at specific speeds of 1000 or less.


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SUCTION SPECIFIC SPEED

Suction specific speed is a number that is dimensionally similar to the pump specific speed and is usedas a guide to prevent cavitation.

Instead of using the total head of the pump H, the N.P.S.H.A (Net Positive Suction Head available) isused. Also if the pump is a double suction pump then the flow value to be used is one half the totalpump output.

From the previous article on cavitation, the N.P.S.H.A at the pump suction is :

where HA and Hva are in feet of fluid. The above equation requires that the piping (H F1-S) friction lossand equipment friction loss (H EQ1-S) be calculated. The meaning of some of the variables in the aboveequation is shown in the next Figure.


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We can avoid doing the calculations in the above equation by measuring the N.P.S.H.. The value for theN.P.S.H.A can be deduced by taking a pressure measurement at the pump inlet and using the nextequation

We may be considering an increase in the pumps speed to increase the flow rate. If so, be aware thatan increase in speed will also require an increase in N.P.S.H. required. The suction specific speed valuegive us an indication of what the impeller speed limitation will be for a given N.P.S.H.A . The HydraulicInstitute recommends that the suction specific speed be limited to 8500 to avoid cavitation.

When a pump has a high suction specific speed value, it can mean that the impeller inlet area is largereducing the inlet velocity which is needed to enable a low NPSHR. However, if you continue toincrease the impeller inlet area (to reduce NPSHR), you will reach a point where the inlet area is toolarge resulting in suction recirculation (hydraulically unstable causing vibration, cavitation, erosionetc..). The recommended cap on the S value is to avoid reaching that point. (paragraph contributed byMike Tan of the pump forum group).

Keeping the suction specific speed below 8500 is also a way of determining the maximum speed of apump and avoiding cavitation.

According to the Hydraulic Institute the efficiency of the pump is maximum when the suction specificspeed is between 2000 and 4000. When S lies outside this range the efficiency must be de-ratedaccording to the following figure.

Specific comments

The following graph represents the value of the Thoma cavitation parameter (sigma) vs. the pumpspecific speed and the suction specific speed. This chart can be found in the Pump Handbook publishedby McGraw Hill. It can predict the onset of cavitation and you can use it to help you diagnose if yourpump is cavitating. You will find an article on specific speed and suction specific speed as well as many


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other related articles on the web site of Light my pump at www.pumpfundamentals.com/downloads-free.htm


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The applet allows you to navigate this graph and displays the values of the Thoma sigma number, the

specific speed and the suction specific speed right above the image. This way you don't have to strain your eyes. You can compare the values that you obtain from this graph with the values that you haveentered on the right which are pertinent to your system. Before you use the Calculate button youmust enter the flow rate, the head, the rpm and the N.P.S.H.A. of your pump. I have put in sometypical values as a start. If you change these values, and you press the Calculate button, you will obtainnew values for the specific speed and the suction specific speed.

As you can see there is a safe region in the upper left corner of the graph. If your calculations forthe specific speed and the suction specific speed indicate that you are in that region then everything

should be fine. The lower right region is unsafe and if you are in that region there is no doubt that thepump will cavitate. In the middle is a gray zone where you may or may not cavitate.

HELP FOR EFFICIENCY PREDICTOR APPLET PROGRAM


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Applets are programs based on the java language that are designed to run on your computer using theJava Run Time environment. You will find an article on this topic as well as many other related articleson the web site of Light my pump at www.pumpfundamentals.com/downloads-free.htm

This program is designed to help you predict efficiency values for centrifugal pumps for the purposeof preliminary power calculations. In the initial phase of a project, the pump's head and flow iscalculated, a request for quotation is issued to pump manufacturers which then provide pricing andinformation on the pump that they recommend for the application. After the pump is selected, theefficiency can be obtained and the power calculated. So what happens if you need the powerrequirement prior to receiving the manufacturer's selection. Well you can do your own selection or youcan use this applet and get preliminary power results quickly.

The efficiency is based on a chart (see the Pump Handbook published by McGraw Hill) that providesefficiency values for typical centrifugal pumps over a wide range of flow capacities. It is based ontests made with real pumps and represents the best average of the industry.

(This chart is reproduced from the Pump Handbook published by McGraw-Hill)
http://www.pumpfundamentals.com/downloads-free.htmhttp://www.pumpfundamentals.com/downloads-free.htm


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First input the values for rpm, flow, head and specific gravity (SG) into the textboxes on the righthand side and then click the calculate button. This will calculate the specific speed of the pump whichis displayed at the upper right. The specific speed is calculated with this formula in North Americanunits.

Then use your mouse to scroll over the graph. You will see changing values for specific speed andefficiency that correspond to the position of your mouse on the graph. When you are satisfied that

you have the right specific speed for your flow rate CLICK on the mouse, this will FREEZE theefficiency display above the graph and the power will be calculated and displayed at the upper right.To THAW the efficiency display, click the image again and the efficiency values will be able to changewith the mouse position. This is confirmed by the ON red caption. You can calculate the power at anytime by clicking the Calculate button. The Calculate button also calculates specific speed. Make sure

you have the correct specific gravity, the default value is 1.0, the same value as water at standardconditions. The power is calculated with this formula:


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ENJOY!

Documents

Help for Calculating the Impeller Tip Speed to Avoid Excessive Erosion Due to Suspended Particles