Lesson 8

Objective

In this lesson we will learn:

• 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.

Read the online lecture and any related source material and here.

Lecture

Introduction

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

Cut-off Head: The head at which the energy supplied by a pump and the energy required to move the liquid 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 per minute.

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

As might be expected, the capacity of a centrifugal pump is directly related to the total head of the system.  If the total head on the system is increased, the volume of the discharge will be reduced proportionately.  Figure 3-2 illustrates a typical head-capacity curve for a centrifugal pump.  While this curve may change with respect to total head and pump capacity based upon the size of the pump, pump speed, and impeller size and/or type, the basic form of the curve will remain the same.  As the head of the system increases, the capacity of the pump will decrease proportionately until the discharge stops.  The head 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 the system.  This friction head can be greatly affected by the size and configuration of the piping and the condition of the system's valving.  If the control valves on the system are closed partially, the friction head can increase dramatically.  When this happens, the total head increases and the capacity or volume discharged by the pump decreases.  In many cases, this method is employed to reduce the discharge of a centrifugal.  It should be remembered, though, that this does increase the load on the pump and drive system causing additional energy requirements and additional wear.

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

Friction head, ft is the amount of energy used to overcome resistance to the flow of liquids through the system.  It is affected by the length and diameter of the pipe, the roughness of the pipe, and the velocity head.  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 their equivalent 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 the material 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 3 fps?  The system's valving is equivalent to an additional 75 feet of pipe.  Reference material indicates a roughness factor of 0.025 for this particular pipe and flow rate.

It is also possible to compute friction head by using a table such as that shown in Figure 2-10.  The calculation 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 the pump.  In each case, it is necessary to determine:

1. the length of pipe
2. the diameter of the pipe
3. velocity
4. pipe equivalent of valves, elbows, tees, etc.

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

Example:

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

Example:

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

1. Find total length of pipe

2. Find equivalent length for valves and Ell's

3. Total pipe length

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

Length = 48 ft  +  745 ft

Length = 793 ft

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

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

Total Head, ft = 52.46 ft

V1= Gate Valve (125 ft pipe equivalent)

V2= Check Valve (150 ft pipe equivalent)

V2= 90° Elbow (65 ft pipe equivalent)

f = 0.03

Pipe Diameter = 9 inches

Velocity 3 fps

Velocity Heads are equal, canceling each other.

Part 2:

Objective

In this section we will answer the following questions:

·         How is shutoff head calculated?

·         How is velocity defined?

Read the online lecture as well as here.

Lecture

Estimating the Shutoff Head of a Centrifugal Pump

In the fifteenth century the Swiss scientist Daniel Bernoulli learned that the combination of head and velocity was a constant throughout a piping system.  He then wrote the formula showing the relationship between this liquid velocity, and resultant head.  As many of you know, I often quote this formula in my pump 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 the shutoff head of a 1750 rpm centrifugal pump by squaring the diameter of the impeller.  How did I come to that 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 discuss velocity are feet/second or meters/second.  In the inch system, the velocity of the impeller outside diameter is determined by the following formula:

d = diameter of the impeller

π  = 3.14

rpm = speed of the impeller outside diameter

12 = twelve inches in a foot

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 the shutoff head actually varies from 90% to 110% of the diameter of the impeller squared.  I elected to use 100% because it is a sensible average and in some cases it accounts for the additional velocity added to the 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 the outside diameter of the impeller squared, times four.

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

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

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 convert pressure 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 reads 20 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 pump is 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:

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.

Review

We learned that the relationship of the shut-off head of a centrifugal pump is equal to the diameter of the impeller squared. This concept is easier to understand if we look at the velocity. This is done by multiplying 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 of the impeller squared. A pump's BEP (Best Efficiency Point) is calculated based on the pump discharge pressure 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 water moves through the system.

Assignment

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

1. What is velocity?
2. ______________ varies from 90% to 110% of the diameter of the impeller squared.
3. What is the name for the type of head that is lost by fluid flowing in a stream or conduit due to friction per unit weight of fluid?
4. TDH is the sum of what?
5.  _______________ refers to the losses in pressure caused by gravity and friction as water moves through the system, most often given in feet of water.

Quiz

Answer the questions in Quiz 8 . When you have completed the quiz, print it out and either mail or fax to the instructor. You may also take the quiz online and directly submit it into the database for a grade.