fluid pump report 2013

5/28/2018 Fluid Pump Report 2013

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ABSTRACT

In the experiment of determination of pump performance with three different configuration that

are single pump, pump in series and parallel configuration. We need to design a completemeasurement technique for fluid flow and determine pump performance which can identified by

the pump head, flow rate, power and the efficiency. A few graph is drawn to the performance

curves of different pumps. We have to determine the scope that the configuration is only three

type which is single pump connected, series or parallel. The experiment is conducted at the fluid

lab. We come to a few questions before conducting the experiment which pump perform better?

What are the flow rate, the head, the power consumed and efficiency? And how is the graph?

These will be further resolved the answer in this experiment

In complex systems, pumps can be connected in series or in parallel. In series operation the

heads are added together and in parallel operation, the flow rates of the pumps are added. Theexperimental unit contains two identical centrifugal pumps and an intake tank with overflow.

The overflow ensures a constant suction head in the tank, regardless of the water supply. Ball

valves in the pipes allow easy switching between series and parallel operation. Intake and

delivery pressures of the two pumps and the pressure in the water drain pipe are displayed on

manometers. The experimental unit is positioned easily and securely on the work surface. The

water is supplied and the flow rate measured. Alternatively, the experimental unit can be

operated by the laboratory supply.

In order to increase the efficiency of the pump, single pump can be arranged in series or parallel

way. Theory stated that the series configuration will have the head added at the same flow ratewhile the parallel configuration will lead to the increase of flow rate at the constant head. The

operating point can get from the graph that involved the system curve and experimental curve of

flow rate and heat. Despite the advantage of increasing efficiency, series pump configuration has

the disadvantage of stopping pumping water after a maximum note, while the parallel pump

configuration need to equiped with more valve system.


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BRIEF BACKGROUND

This experiment is to determine the pump performance curve for single, series and parallel pump

configurations. Pumps are used widely in industry to provide cooling and lubrication services, to

transfer fluids for processing, and to provide the motive force in hydraulic systems. In fact, most

manufacturing plants, commercial buildings, and municipalities rely on pumping systems for

their daily operation.

Parallel Pump (flow rate added)

The term parallel pumping simply means those situations in which two or more pumps will

discharge into a common pipe. In most cases, the suction is also from a common source or line,

but this is not a requirement. In a parallel pumping system, the discharge of one pump does not

feed into the suction of the next. In the more common Parallel Operation, banks of pump are

combined in order to handle a high fluctuation of flows in a common system. This arrangement

is widely used in the Water Treatment business, where the potable water being supplied to a sub-

division from the treatment plant, will experience huge fluctuations in demand from one time of

day to another. The use of multiple pumps on the same system allows the pumps to be switched

on and off as required to meet the varying demand. In such arrangements, all the pumps take

their suction from a common source and discharge into a common header. Each pump will

operate at the same head, but share the flow rate with the other pumps. For any given discharge

head, flows for parallel pumps are additive.


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At any given discharge head flow B will equal the sum of the flow from each pump A.

Furthermore, the power draw of each pump will be the power draw at the contributing flow rate

for each pump. It is generally desirable to use just one pump where one pump can do the job.

Multiple small pumps will have a higher capital installation cost and will combine to draw more

energy than a single properly designed larger pump. However, some other factors, such as

limited Net Positive Suction Head Available (NPSHA), may preclude the use of a single pump.

When two or more pumps are arranged in parallel their resultingperformance curve is obtained

by adding their flow rates at the samehead as indicated. Although the flow capability is additive

for parallel pumps at any given discharge head, the actual output of the pumps will be

determined by the intersection of the system-head curve with the parallel performance curve. For

a system where the system curve is dominated by frictional losses, parallel operation will

generally mean a lower flow than twice the single pump flow (Fig 2). When the discharge head

is variable, such as with a control valve, then flow will be controllable when within the range of

the valve.

System curve

Centrifugal pumps in parallel are used to overcome larger volume flows than one pump can

handle alone. For two identical pumps in parallel, and the head is kept constant, the flow rate

doubles as indicated with point2compared to a single pump.

In practice the combined head and volume flow moves along the system curve as indicated from

1 to 3.

I. point3is where the system operates with both pumps running
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II. point1is where the system operates with one pump running

In practice, if one of the pumps in parallel or series stops, the operation point moves along the

system resistance curve from point 3to point 1- the head and flow rate are decreased.

There are several important formula using in this pump configuration experiment

Efficiency, =

Net Head, H=

Water horsepower, PWH= pgQH

Series Pump (head added)

Two similar pumps operate in the same way as a two-stage centrifugal pump. Centrifugal pumps

are connected in series if the flow rate of one pump is connected to the suction side of a second

pump. Pressure head for series pump is doubled but the flow rate remains the same. Each of the

pumps is putting energy into the pumping fluid, so the result of head is the sum of the each heads

between two pumps. Both pumps must have the same width impeller or the difference in

capacities and must run at the same speed.

When two or more pumps are arranged in serial, their resulting pump performance curve is

obtained by adding their heads at same flow rate as indicated in the figure below.

Centrifugal pump in series are used to overcome larger system head loss than one pump can

handle alone. For two identical pumps in series the head will be twice the head of a single pump

at the same flow rate. With constant flow rate the combined head moves from 1 to 2. In practice

the combined head and flow rated moved along the system curve to 3.


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OBJECTIVE

-To design complete measurement technique for fluid flow and determine pump performance

with single pump, series, and parallel pump configurations.

-To investigate the relationship between pressure head, flow rate, power consumed and

efficiency for a pump.

-To compare the performance curves of different pumps.

Experimental Apparatus

The system comprises two identical centrifugal pumps that are connected together via pipes.

Manual valves make it possible to switch quickly between series and parallel operation. Strain

pressure indicates the pressure at all important points in the pipe system. The pump

characteristics can be recorded and read via dasylab. The hydraulic power output of the pumps

can be determined. The water supply and volumetric flow rate measurement are provided by the

apparatus.


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EXPERIMENT PROCEDURE

The experiment is designed to determine the pump performance with single pump, series and

parallel pump configurations. Hence, the experiment is to investigate the relationship betweenpressure head, flow rate, power consumed and efficiency for a pump. There are two pumps

labelled as pump 1(p1) and pump 2(p2) as the figure below.

Single Pump

1. The pump apparatus are checked to make sure all are in well condition and secured

properly to their parts.

2. The strain gauge is fitted to the pump 1(p1) fittings and the other end is fitted to National

Instrument(NI9219)

3. Flow meter is fitted to National Instrument(NI9201).

4. After the Dasylab has been setup, the reservoir tank is filled with water before pump is

ran.

5. The valve for pump 1(V1 and V6) is opened and switched on the other valves for other

pump are closed.

6. Only pump 1 is turned on when the reservoir tank is filled with water.


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7. The voltage generated by flow sensor transmitted to NI and is converted to frequency by

using dasylab. The volume flow rate is then calculated using formula on Dasylab.

8. The pressures of pump and at outlet at single pump are obtained through digital meter of

Dasylab.

9. Pressure head, flow rate, power consumed and efficiency for the pump were obtained by

using module formula interpreter of Dasylab.

10.Step 8 is repeated 4 times to obtain 4 set of data.

Series Pump



2. The strain gauge is fitted to the pump 1(p1) fittings and the other end is fitted to National

Instrument(NI9219)3. Flow meter is fitted to National Instrument(NI9201).


run.

5. The pump valves which are pump 1 and pump 2(all valves except V3) are opened

corresponding with the series pump path and the other is closed.

6. Both pump 1 and pump 2 are turned on when the reservoir tank is filled with water.




Dasylab.9. Pressure head, flow rate, power consumed and efficiency for the pump were obtained by



Parallel Pump



2.

The strain gauge is fitted to the pump 1(p1) fittings and the other end is fitted to National

Instrument(NI9219)

3. Flow meter is fitted to National Instrument(NI9201).


run.

5. The pump valves which are pump 1 and pump 2(all valves)are opened corresponding

with the series pump path and the other is closed.


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6. Both pump 1 and pump 2 are turned on when the reservoir tank is filled with water.




Dasylab.

9.

Pressure head, flow rate, power consumed and efficiency for the pump were obtained by



Procedure of Setup Virtual Instrument Software

First, NI-DAQ system software is opened. Then Data neighbourhood is clicked to create a new

task. we select The acquire signal is selected and the strain bullet is clicked.


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Flow meter is set to a1 of NI 9201 which means, the sensor is connected to it.

Same with Pump 1, it is set to a1 of NI 9219 as it is connected to it.


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The value for gage factor and gage resistance are set to 2.11 and 119.5 respectively, and Quarter

Bridge 1 for Strain Configuration.

Voltage input is added. The result must be run and saved after it showed.


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Dasylab connection design is being built up to detect the signal gained. A series of formula is

inserted using mathematic interpreter. After the connection is set up, measurement at toolbar is

clicked, to synchronise at hardware setup > NI-DAQmx > synchronise with maxi configuration

are chosen. Button Run is pressed and the results are shown. This is how Pressure head, flow

rate, power consumed and efficiency for the pump are determind.

PRECAUTIONS

1. The parallax error should be avoided while taking readings

2. When fluid is flowing, there may be a fluctuation in the reading, note the mean position

carefully.

3. After the experiment is over, do not forget to keep the delivery valve open and switch-

OFF the mains.

4. Do not exceed 1.5 kg/cm2on pressure gauge reading and never fully close the delivery

valve.


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RESULTS AND GRAPHS

- Attach the original data sheet.-

Attach table of calculation (if any).

a) Single Pump

Table 1: The flow rate, delivery pressure, suction pressure, outflow

pressure, net head and water horse power for single pump

Flow Rate,

Q

(m3s

-1)

Delivery

Pressure,

PD(Pa)

Suction

Pressure,

PS(Pa)

Outflow

Pressure,

PO(Pa)

Net

Head, H

(m)

Power,

P (W)

Efficiency,

(%)

0.000493 180630 -35000 90710 22.05 106.26 16.10

0.000463 186850 -35000 93770 22.68 102.79 15.570.000459 190600 -35000 103600 23.07 101.49 15.38

0.000370 225610 -35000 150380 26.65 109.09 16.53

0.000334 275170 -35000 211750 31.71 102.21 15.49

0.000296 294510 -35000 231790 33.69 97.61 14.79

0.000231 414170 -35000 273670 38.08 85.90 13.02

0.000189 449330 -35000 288190 39.78 73.61 11.15

Figure 1.1 Single Pump System Result 1

Figure 1.2 Single Pump System Result 2


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Figure 1.3

Single Pump

System Result 3

Figure 1.4 Single Pum

System Result 4

Figure 1.5 Single Pump

System Result 5


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System Result 6


System Result 7

Figure 1.8 Single Pum

System Result 8


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b) Series Pump

Flow

Rate,Q

(m3s-1)

Delivery

Presure, (Pa)

Suction

Pressure, (Pa)Outflow

Pressure,

PO(Pa)

Net

Head, H

(m)

Power,

P (W)

Efficiency,

(%)PD1 PD2 PS1 PS2

0.000497 169080 199070 -35000 0 96790 36.59 182.14 27.60

0.000457 198470 259010 -35000 0 155230 50.35 229.29 47.17

0.000425 227040 313810 -35000 0 212100 58.8 244.83 37.10

0.000393 258530 400390 -35000 0 292460 70.95 272.58 41.30

0.000359 272100 419100 -35000 0 310370 74.25 260.70 39.50

0.000320 289270 61870 -35000 0 342720 80.38 251.42 38.09

0.000266 325480 542330 -35000 0 399950 92.31 239.90 36.35

0.000190 376090 655190 -35000 0 471050 109.02 202.10 30.62


pressure, net head and water horse power for series pump

Figure 2.1 Series Pump

System Result 1


System Result 2


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System Result 5


System Result 4


System Result 3


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System Result 6

Figure 2.7 Series Pum

System Result 7

Figure 2.8 Series Pum

System Result 8


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c) Parallel Pump

Flow

Rate,Q

(m3s

-1)

Delivery

Presure, (Pa)

Suction

Pressure, (Pa)Outflow

Pressure,

PO(Pa)

Net

Head, H

(m)

Power,

P (W)

Efficiency,

(%)PD1 PD2 PS1 PS2

0.000509 473330 207350 -35000 0 99420 36.59 182.14 27.60

0.000495 484570 212540 -35000 0 106970 37.43 181.22 27.46

0.000486 538100 343330 -35000 0 109750 46.85 222.77 33.75

0.000399 373390 523510 -35000 0 303480 47.64 185.73 28.14

0.000346 386730 533390 -35000 0 313570 48.83 165.42 25.06

0.000277 415370 563910 -35000 0 334760 51.85 140.62 21.31

0.000237 418900 569980 -35000 0 341190 52.34 121.19 18.36

0.000159 443560 593660 -35000 0 359370 54.81 85.48 12.95


pressure, net head and water horse power for parallel pump

Figure 3.1 Parallel Pump

System Result 1

Figure 3.2 Parallel PumpSystem Result 2


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System Result 3


System Result 4


System Result 5


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System Result 6


System Result 7


System Result 8


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Sample Calculations

At room temperature, Troom=25C

Density of water,p= 997 kg/m

3

Gravitational Force, g= 9.81 ms-2

Dynamic Viscosity= 0.891x 10-3

kg/ms

Input power of the pump=660W

Assumptions : -Water is an incompressible flow

- The inlet and outlet diameters are identical-There are no changes in elevation

Single Pump

Net Head, H=gPP SuctionDelive ry

= (180630- (-35000)) / (997x9.81)= 22.05 m ANS.

Water horsepower, PWH=pgQH= (997) (9.81) (0.000493) (22.05)

= 106.26W ANS.

Efficiency, =

ANS.

Series Pump

Net head, H = headpump1+ headpump2

Net Head, H=g

PP SuctionDelive ry

=(169080+35000+199070)/(997x9.81)

= 41.22 ANS.

Water horsepower, PWH=pgQH= (99) (9.81) (0.000497) (41.22)

= 200.50 W ANS.

Efficiency, =

ANS.


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Parallel Pump

Net head, H = (headpump1+ headpump2)/2

Net Head, H=g

PP SuctionDelive ry

2

=(473330+35000+207350)/(997x 9.81)

= 36.59m ANS.

Water horsepower, PWH=pgQH

= (997) (9.81) (0.000509) (36.59)= 182.14W ANS.

Efficiency, =

ANS.


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- Construct a graph of Pump Pressure Head (vertical axis) against Pump Flow Rate(horizontal Axis).

Based on the graph of head versus volume flow rate above, it is clearly shows that pump head is

increasing significantly with the decreasing of volume flow rate among the three different types

of pumps, that are, single pump, series pump, and parallel pump. For those pumps, the volume

flow rate and the pressures rise at the suction, delivery and outflow area are related. Hence, the

differential pressures will result in different pump head and volume flow rate. A system pump

head graph show the head loss of a piping system increases (usually quadratically) with flow

rate. In actual, the net head produced is high when the volume flow rate is low and differential

pressure is high. There an operating point can find at the intersection of the two curves.

When the head or flow rate of a single pump is not sufficient for a application, pumps are

combined in series or in parallel to meet the desired requirements. Pumps are combined in series

to obtain an increase in head or in parallel for an increase in flow rate. Series pump will add the

head as compared to single pump. The theory is proved with the graph show when the head of

the series pump is higher than single pump. For the parallel pump, the volume flow rate will

double compared to a single and series pump configurations if head is kept constant. This also

proved in the graph when we make a constant line of head=40m, we will find out the flow rate

for single pump is around 0.0002m3/s and the flow rate for the parallel pump is about

0.0005m3/s. Yet, there is still error in the experiment due to method conducted and apparatus.

0

20

40

60

80

100

120

0 0.0002 0.0004 0.0006

PumpPressureHead(m)

Pump Flow Rate (m3s-1)

A Graph of Pump Pressure Head (m) AgainstPump Flow Rate (m3s-1)

single

series

Parallel


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- Construct a graph of Efficiency (vertical axis) against Flow Rate (horizontal axis).

From the graph, we know that the series get the higher efficiency compared to the other two.

Theoretically, the efficiency of pump increased with the increase of flow rate and head. This

theory can be proven with the graph above. However the efficiency of a pump is highest at a

certain combination of head and flow rate. Therefore. a pump that can supply the required head

and flow rate is not necessarily a good choice for a piping system unless the efficiency of the

pump at those conditions is sufficiently high.

- Categorize the pumps into (i) high flow/low pressure or (ii) Low flow/high pressuretypes.

Pump1 operates at high pressures and low flow rates while pump 2 is worked at highflow rate and low flow. This is because that pump 1 is stronger than pump 2 as pump 1

produce higher head compare to the pump 2 at both of the series and parallel pump

configuration experiment. Since the pressure is directly proportional to the head wherewe can see from the formula P=gh, the pressure of pump 1 also higher than pump 2. So

we can conclude that Pump 1 operation at low flow with high pressure while Pump 2

goes oppositely.

0

10

20

30

40

50

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

Efficiency(%)

Flow rate (m3s-1)

Graph of Efficiency(%) Against Flow Rate

(m3s-1)

single

parallel

series


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- Plot comparison of performance curves of the pumps with various configurations.

The characteristic of the pump can be viewed through three parts that are the head,

efficiency and power. Theoretically, the power of the pump increase with the flow rate.

But the head also play a role in affecting the power of the pump. The power of affect the

efficiency of the pump. The higher the power, the higher the performance of the pump

due to more efficient work over input. From the graph, we can see the series pump

configuration performs with higher power compared single and parallel pump

configuration. Yet there are still some error in the reading due to some sorts of mis-

conduction method and apparatus defects.

0

50

100

150

200

250

300

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

Power(W)

Flow Rate (m3s-1)

A Graph of Comparison of

Performance Curves of the Pumps

single

series

parallel


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- Draw the graphs of Head Vs Discharge.

The graph showed when the discharged increased, the head of the three systems there are single,

series and parallel configuration of pump decreased. From here, we can verified that the head is

inversely proportion to the discharge.

0

20

40

60

80

100

120

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

Head(m)

Discharge(m3s-1)

A Graph of Head (m) Against

Discharge(m3s-1)

single

series

Parallel


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QUESTIONS/ DISCUSSIONS

1. Explain how the strain gauge senses the pressure.

Strain gauges are sensing devices used in a variety of physical test and measurement

applications. They change resistance at their output terminals when stretched or

compressed. Because of this characteristic, the gauges are typically bonded to the surface

of a solid material and measure its minute dimensional changes when put in compression

or tension. Strain gauges and strain gauge principles are often used in devices for

measuring acceleration, pressure, tension, and force. The strain gauge measures the

pressure relative to atmospheric pressure. A tire pressure gauge is an example of gauge

pressure measurement; when it indicates zero, then the pressure it is measuring is the

same as the ambient pressure.

2. How can you connect the measuring devices to the DAQ?

Data acquisition begins with the physical phenomenon or physical property to be

measured. Examples of this include temperature, light intensity, gas pressure, fluid flow,

and force. Regardless of the type of physical property to be measured, the physical state

that is to be measured must first be transformed into a unified form that can be sampled

by a data acquisition system. The task of performing such transformations falls on

devices called sensors. An acquisition system to measure different properties depends on

the sensors that are suited to detect those properties. Signal conditioning may be

necessary if the signal from the transducer is not suitable for the DAQ hardware being

used. The signal may need to be filtered or amplified in most cases. The DAQ, included

with NI-DAQmx, is a graphical, interactive guide for configuring, testing and acquiring

measurement data. With a single click, you can even generate code based on your

configuration, making it easier and faster to develop complex operation.


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3. State the advantages and disadvantages of parallel and series pump arrangements.

For the series pump, the net head is high and is used to pump fluid from a low level to a

higher level, and the water horsepower obtained is also high. The rate of the volume is

very high. For the disadvantages, only low volume flow rate of fluid can be transferred

which are when the pump reaches the maximum net head, the pump is no longer to pump

the fluid.

For parallel pump, the volume flow rate obtained is relatively high compare to the series

pump. The advantage of parallel pump is that it is suitable to pump high fluid flow at low

level place. We can achieve higher volume flow rate just from combination of cheap

lower power pumps in parallel configuration rather than having one expensive high

power pump to achieve higher volume flow rate. Besides, pumps can still operating when

one of pump is shut off. The disadvantage of parallel pump configuration is when doing

parallel pump system; there is additional valves and piping that series configuration. This

will add additional head losses of the system and impaired the overall performance of the

parallel pump configuration

4. Draw the velocity diagram for radial flow pump.

5. From your data, what will happen to the flow rate and total head when two pumps are

connected in parallel and series? Explain.

Pumps can be arranged in series or parallel to provide an additional head or flow rate

capacity. When two (or more) pumps are arranged in series their resulting pump

performance curves obtained by adding their heads at the same flow rate. Pumps in

series are used to overcome larger system head loss than one pump can handle alone. For


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two identical pumps in series the head will be twice the head of a single pump at the

same flow rate. Besides, when two or more pumps are arranged in parallel their

resulting performance curve is obtained by adding their flow rateat the same head.

Parallel are used to overcome larger volume flows than one pump can handle

alone.For two identical pumps in parallel, and the head is kept constant, the flow rate

doubles compared to a single pump. If one of the pumps in parallel or series stops, the

head and flow rate are decreased.

6. How can you obtain operating flow rate for the pumps when they are connected in

parallel and series? Discuss.

The operating flow rate for the pumps when they are connected in parallel and series can

be obtained by drawing the system curve which come from the theoretical formula of

finding theoretical or ideal head and the experiment curve which is a graph of head

against flow rate. The operating point is lies on the intersection of the two points. With

the interpolation, the intersection point which the horizontal axis indicates the maximum

flow rate (called the free delivery) that the pump can supply. Pumps are connected in

series if the discharge of one pump is connected to the suction side of a second pump.

Two similar pumps, in series, operate in the same manner as a two-stage pump. Both

pumps must run at the same speed. Pumps are operated in parallel when two or more

pumps are connected to a common discharge line, and share the same suction conditions.

Two pumps in parallel will deliver less than twice the flow rate of a single pump in the

system because of the increased friction in the piping.


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7. Compare the experimental performance curve with theoretical curve, and discuss the

difference (if any).

From the experiments, the experiment performance curve that obtained is quite similar to

the theoretical curve that, the volume flow rate is inversely proportional to the net head

which mean the volume flow rate is increasing with the decreasing of pumps head among

the three different types of pumps, that are, single pump, series pump, and parallel pump.

For the series pump curve, the highest head can be obtained, while for the parallel pump,

the highest flow rate can be obtained. Note that, there is a slightly inaccurate data

collection and experiment setup, whereas both pumps do not operate at the same

capacity. During the experiment, due to the error of apparatus, equipment and error

recording the data will result in inaccurate and inconsistent of the results.

8. In the experiment, when you should shut off one of the pumps? Why?

For series pump, for an example, pump 1 is weaker in overall description than pump 2.

So, pump 1 must be turned off when the flow rates of combined both pumps exceed the

free delivery of pump 1. Besides, for parallel pump, pump 1 must be turned off when the

net head of combined both pumps exceed the shut-off head of pump. The primary pump

performance parameter is volume flow rate. Therefore, the pumps which have the parallel

configuration can deliver a large and maximum volume flow rate. As a result, the seriespump should be shut off if larger volume flow rate need to be achieved.


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CONCLUSION

In the end of the experiment, we come to meet the objective and managed to design complete

measurement technique for fluid flow and determine pump performance with single pump,

series, and parallel pump configurations. The data have been collected using the Dasylab andfurther interpret using graph drawn . Ideally the head will increasE with the flow rate. But In

actual, the head goes down with the flow rate. The head and flow rate is directly proportional to

the power consumed and the efficiency for three of the condition. Overall, series pump

configuration performs better compared to the others in term of head, power consumed and the

efficiency. If want to say separately, the series pump help to increase the head which cannot

achieve by the single pump while the parallel pump configuration function to increase the flow

rate compared to single pump. Two pumps in parallel will deliver less the flow rate of a single

pump in the system because of the increased friction in the piping. In short, the single pump, it

will operate at a higher flow rate than if it were working in parallel with the parallel and series

pump, as the flow rate increase, the head is decrease. The pump performance curve for single,

series and parallel configurations was analyzed. The graph verified the theory that we learn in

Fluid Mechanics subject. It is also undeniable that there is a slightly discrepancies in our

experimental curves compare to the theoretical performance curves. This is mainly due to the

human error and also the pump does not operate at the same capacity.

REFERENCES

1. http://www.retscreen.net/fichier.php/908/Chapter%20Pumps%20and%20Pumping%20Sy

stems.pdf

2. Fluid Mechanics, second edition, YunusA.engal and John M. Cimbala, 2010

3. http://www.gunt.de/static/s3555_1.php

4. http://www.engineeringtoolbox.com/pumps-parallel-serial-d_636.html

5. 1. White, F.M., Fluid Mechanics, 2nd Ed., McGraw-Hill Book Co., New York, 1986.
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