Updated 02/09/09

Pumps in Series and Parallel

Introduction

Pumps are used in a huge variety of applications, ranging from wild-land fire fighting to soft-drink manufacturing to the supply of liquid oxygen on the Space Shuttle. Pumps are used singly and in both parallel and series configurations depending on the flow and pressure required.

Objective

The objective of this laboratory experiment is to measure and compare the performance of a single centrifugal pump to that of two pumps in parallel and series configurations.

Theory

Figure 1. Water enters at the center of the impeller and is accelerated radially in a centrifugal pump.

In a centrifugal pump, the pressure of the water is increased through the conversion of kinematic energy (velocity) to potential energy (pressure). The water enters at the axis of the impeller and then is accelerated radially by the rotation of the impeller, Figure 1. This kinetic energy is then converted to static pressure as it exits the impeller housing into the piping.

Assuming steady, uniform, incompressible flow between the inlet and outlet sections of a piping system containing a pump, the energy conservation equation can be used to illustrate the relationship between kinetic and potential energy of the fluid:

(1)

where the subscripts 1 and 2 refer to inlet and exit sections, respectively [1]. Hp is the 'head' produced by a pump (in meters); Hl_T represents energy losses (in meters) from friction, turbulence, fittings, etc.; p is the static pressure (in Pa); r is the fluid density (in kg/m3); g is the gravitational constant (in meters/sec2); V is the fluid velocity (in meters/sec); and z is the elevation of the measurement point (in meters). For this laboratory, the minor head losses, Hl_T, may be neglected.

One important aspect of pump performance is the pressure, or head, that the pump can produce as a function of flow rate. Generally, the higher the flow rate, the lower the head that the pump can contribute. A parabola is often used to fit this performance data:

(2)

where Q is the volumetric flow rate, A is a constant determined empirically from the data, and H0 is the head delivered at zero flow rate.

For the two pumps in series, the flow Q through the first pump must equal the flow through the next, but each pump adds pressure head. For nominally identical pumps the total head added is

. (3)

For identical pumps in parallel, the pressures at the two inlets and outlets are identical and the maximum head the two pumps can deliver is no greater than that of one pump. The flow rate, however, is doubled for two identical pumps in parallel:

(4)

In practice, these performance curves will not be met because of losses in piping systems and non-identical pumps.

An important objective when selecting a pump for an engineering system is maximizing the efficiency for the desired flow conditions. For a pump, the efficiency is defined as

h = Po/Pi (5)

where Po is the power output from the pump (in Watts), and Pi is the power imparted to the fluid from the pump (in Watts). Output power is determined experimentally with the following equation

Po= ρg*Q*Hp. (6)

The input power to the pump is the output power from the motor. For the pumps used in this lab, Pi can be measured with a wattmeter directly. Pi varies as a function of flowrate.

Equipment

·  Armfield Hydraulics Bench (preferably one with internal pressure gauge)

·  External Pump Accessories

·  Stop Watch

·  Wattmeter

One external pump, one discharge manifold, and one set of hoses are required for this experiment. The components of the hydraulic bench are depicted in the figure below.

Figure 2. The hydraulic benches are located in the basement of the ITLL near the printers.

Procedure

IMPORTANT: BE SURE TO FOLLOW ALL IN DIRECTIONS IN THE ORDER LISTED. NOT DOING SO MAY RESULT IN PUMPS MALFUNCTIONING, OVERHEATING, AND FAILING.

Note: For all pump configurations measure the power consumption using a wattmeter.

Hydraulics Bench

1.  Locate the hydraulics benches on the Broida Lab Plaza (2B Level), outside of the manufacturing center doors. Have your TA assist you with getting the pumps out of the module storage bay.

2.  Rest the discharge manifold on the side channels (4) of the bench top channel (13) on the hydraulics bench, as shown in Figure 3. Take note of the units of pressure used by the gage on the discharge manifold.

Figure 3. The discharge manifold should sit at the edge of the channel of the hydraulics bench.

3.  Position Pump 1 on the floor to the left of the hydraulics bench as in Figure 4. Note that the units of this pressure gage will also have to be converted later.

4.  Check that ALL the valves on the hydraulics bench (including the drain valve (3)) are completely OFF (clockwise).

5.  Make sure the motor control switch (6) on the hydraulics bench and the external pump are OFF.

6.  Plug the pump cords into the wall or floor outlet nearest the hydraulics bench (you may need an extension cord from the check-out office).


Exercise 1: Single, External Pump

  1. Connect tubing according Figure 4. Make sure that the quick-disconnect fittings are secure and their ball bearings are not showing.

Figure 4. Only the external pump is used for Exercise 1.

2.  Open the hydraulics bench drain valve (3) ALL THE WAY (ccw).

3.  Close the discharge control valve on the discharge manifold. Important: Only operate pump(s) with discharge control valve fully closed for short periods of time so as to not overheat motor(s) and pump(s).

4.  Switch ON the external pump. Confirm pump operation by ensuring pump and motor are making sound.

5.  Fully open the discharge control valve on the discharge manifold.

6.  You are now ready to take data. You are going to measure the flow rate as a function of the pressure head (the pressure difference between the inlet pressure of the external pump and the pressure at the discharge manifold). Make sure you read all of the following instructions before proceeding.

a.  Turn off the discharge control valve with the pump running. Record all measurements listed in Table 2 of the Raw Data Tables section. The pressure of the system is the maximum pressure the pump is capable of creating under zero flow conditions.

Important: Do not fully close (or almost fully close) the discharge valve for long periods of time or between readings. This will quickly overheat the pump and cause the pump to fail sporadically.

b.  Close the dump valve (9) on the hydraulics bench via the dump valve handle (10). This is necessary for calculating flow rate. Make sure to open the dump valve between flow rate measurements to ensure the unit doesn’t run out of water or overflow.

c.  Open the discharge-manifold valve slightly. You will need to take measurements for at least five different pressures/flow rates, so do not open the valve too much, but do not open it too little either. Use your own judgment.

d.  Record the measurements listed in Table 1.

e.  Record all measurements listed in Table 2 for each pressure-head condition.

i.  Use the sight tube and scale (1) on the hydraulics bench and a stopwatch to measure the volume change as a function of time.

1.  Only use the upper scale on the sight tube to measure in Liters.

2.  Measure how long it takes the volume to increase from 0 L to 10 L on the sight tube.

ii.  Take three sets of readings at each pressure head so you can do uncertainty analysis.

f.  Repeat steps b-d for at least six different discharge-manifold pressures (not including the zero-flow condition) spread over the entire operation range of the system. Vary the discharge-manifold pressure using the discharge-manifold control valve.

  1. Turn the external pump motor OFF at the end of the experiment.
  2. Open the discharge-manifold control valve, if not already open, to drain the water out of the top hose.

9.  If you are not completing the rest of the experiment at this time, Close (clockwise) the hydraulics-bench drain valve (3) before you remove the hoses, or water will drain from the tank onto the floor.

Exercise 2: Pumps in Series

  1. Connect tubing according to Figure 5. Be sure to clean up any water that is spilled as you adjust the tubing.

Figure 5: The pump in series experiment utilizes the internal and external pumps.

  1. Close the flow-control valve on the hydraulics bench.
  2. Close the discharge-control valve on the discharge manifold.
  3. Switch ON the bench pump.
  4. Open the bench flow-control valve all the way.
  5. Switch ON the external pump.
  6. Open the discharge-control valve all the way. [Note: Allow the pumps a few seconds to stabilize.]
  7. You are now ready to take data again. Record the necessary data in Table 3, and be sure to conduct the experiment for at least seven different pressure heads. As before, make sure to take three sets of readings for calculating the flow rate.
  8. After all data is collected, turn both the pumps OFF.
  9. Open the discharge-control valve on the discharge manifold to drain the water out of the top hose before removing.


Exercise 3: Pumps in Parallel

  1. Replace the top hose with the tee connector as shown in Figure 6. Be sure to clean up any water that is spilled as you adjust the tubing.

Figure 6: Pumps in Parallel

2.  Open the hydraulics bench sump drain valve (3) ALL THE WAY (ccw).

  1. Open the bench flow-control valve (7) ALL THE WAY (failure to do so will cause the pump inside the bench to overheat and shut down).
  2. Close the discharge-control valve on the discharge-control manifold.

Important: Do not fully close (or almost fully close) the discharge valve for long periods of time or between readings. This will quickly overheat the pump and cause the pump to fail sporadically.

  1. READ CAREFULLY: Switch ON both pumps at the same time--the bench pump (6) and the external pump.
  2. FULLY open the discharge control valve.
  3. Allow the pumps a few seconds to stabilize. You should notice, qualitatively, that the flow rate has doubled. If it has not, turn off the both pumps, and repeat steps 3-6.
  4. You are now ready to take data again. Record the necessary data in Table 4, and be sure to conduct the experiment for at least five different pressure heads. As before, make sure to take three sets of readings for calculating the flow rate.
  5. Turn the hydraulics bench pump and the external pump OFF at the end of the experiment.
  6. If not already open, open the discharge-control valve on the discharge manifold to drain the water out of the top hose.
  7. Close (clockwise) the drain valve (3) of the hydraulics bench or water will drain from the tank onto the floor when the hoses are removed.

Exercise 4: Single, Internal Pump

  1. Connect the output of the internal pump to the discharge control manifold.
  2. Repeat steps 2-6 of Exercise 1, but utilize the internal pump and record the data in Table 5.

Shut Down

  1. Open discharge control valve and bench control valve all the way to drain tubing.
  2. Disconnect all tubing and clean up any water you may have spilled.
  3. Completely close the bench control valve.

Results and Questions

  1. What is the uncertainty in your measurements of water volume, collection time, and head? Propagate your uncertainty through all your calculations. Also find the 95% Confidence Intervals for your flow rates at each pressure head. How do they compare to the measurement uncertainty?
  2. Plot the performance curves (pump head, Hp, as a function of flow rate, Q) for the single pumps, series pumps, and parallel pumps on the same graph.
  3. Derive the single-pump performance curves. Use linear regression to fit to your data from the single-pump measurements and derive values for A. What is your estimated uncertainty in A?
  4. Compare the performance (Hp vs Q) of the pumps in series to that of the single pumps. Is the head doubled for a given flow rate?
  5. Quantify how well the theory of doubled pressure for pumps in series fits the data. Derive equation (3) for your measurements of the pumps in series and compare to what you would predict based on the single pump operation. Discuss possible reasons for the discrepancy.
  6. Compare the performance (Hp vs Q) of the pumps in parallel to that of the single pumps. Is the flow rate doubled for a given head?
  7. Quantify how well the theory of doubled flow rate fits the data. Derive equation (4) for your measurements of pumps in parallel and compare to what you would predict based on the single pump operation. Discuss possible reasons for the discrepancy.
  8. For both the single internal and external pumps, plot the head, Hp, and efficiency, h, as functions of flow rate, Q, on the same graph. From this graph, estimate the desired operating flow rate for maximum efficiency. How closely related are the two pumps?

References

1. Fox, Robert, and McDonald, Alan. Introduction to Fluid Mechanics, Fifth Edition. Wiley and Sons, 1998.

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Updated 02/09/09

Raw-Data Tables

Table 1. Elevation Differences Between Inlet and Outlet of Pumping System

Elevation difference between outlet of external pump and discharge manifold outlet (m)
Elevation difference between inlet of external pump and outlet of reservoir (m)

Table 2. Raw Data for Single, External Pump

Input Power (Watts) / Manifold Pressure
(psi) / Inlet Pressure
( in Hg ) / Inlet Pressure
( psi ) / Outlet Pressure
(psi) / Trial 1 / Trial 2 / Trial 3
Volume / Time / Volume / Time / Volume / Time
(L ) / (s) / (L ) / (s) / (L ) / (s)
0 / 0 / N/A / N/A / N/A / N/A

Table 3. Raw Data for Pumps in Series

Input Power (Watts) / Manifold
Pressure
(psi) / Internal Pump / External Pump / Trial 1 / Trial 2 / Trial 3
Inlet / Outlet / Inlet / Inlet / Outlet
Pressure / Pressure / Pressure / Pressure / Pressure / Volume / Time / Volume / Time / Volume / Time
( psi ) / (psi) / ( in Hg ) / ( psi ) / (psi) / (L ) / (s) / (L ) / (s) / (L ) / (s)
0
0
0
0
0
0
0

Raw-Data Tables, cont.