UNIVERSITY OF TECHNOLOGY, JAMAICA
Department of Mechanical Engineering
Fluid Power Machinery
CENTRIFUGAL PUMPS IN SERIES
Date: April 2023
Sean Harrison
1
Table of Content
Title
Pages
Objective and Background………………………………………………………..............1-2
Apparatus…………………………………………………………………………………..2
Procedure ……………………………………………………………..……………………6
Results…………………………………………………………………………………….7-9
Graph 1: Depicting Manometric Head against Flow rate…………………………………10
Graph 2: Showing Hydraulic Power, Manometric Head and Efficiency
at 60 Rps vs Flow rate…………………………………………………………………….10
Graph 3: Showing Hydraulic Power, Manometric Head and Efficiency
at 70 rps vs Flow Rate……………………………………………………………………..11
Graph 4: Showing Hydraulic Power, Manometric Head and Efficiency
at 80 rps vs Flow Rate……………………………………………………………………..11
Discussion of Result and Conclusion…………………………………………………….12-13
Reference………………………………………………………………………………….14
Sample Calculations………………………………………………………………...……14-15
2
Objective
To determine the characteristics of two identical centrifugal pumps operating at the same speed
and in series, in comparison to a single pump
To investigate the effect of varying pump speed on delivery pressure and discharge.
Background
Centrifugal pumps may be arranged either in series or parallel. Pumps are considered to
be connected in series when centrifugal pumps are arranged along a single line to supply one
another in series increasing the discharge pressure over time. For the series configuration, the
discharge of one pump feeds into the intake of another pump the total head will be the
combination of all the pumps connected. If there is a case where two unidentical pumps the total
head will be a combination of both pumps regardless.
Figure 1: Pumps connected in Series
Efficiency of a machine is how well its input energy is converted in to meaningful output
energy for work. Volumetric, mechanical, hydraulic, and overall efficiency are all efficiencies
related to dynamic machines. A type of dynamic machine is a centrifugal pump. A basic
definition of a dynamic mechanism is one in which is kinetic energy of a flowing liquid or gas is
transformed into the energy rotating a shaft.
1
An application of centrifugal pumps in series would be if you have water at a lower
elevation and wanted to pump water to a higher elevation while maintaining the same pressure
flow.
Apparatus
Cussons Hydraulics Bench P6100
Stopwatch
2
Stilling Basket
Wattmeter
Thermometer
3
NOMENCLATURE
Q: Volumetric flow rate
WSH: Shaft Power/Brake Power
g: Acceleration due to gravity
ρ: Density
ηem: Combined electrical and mechanical efficiencies
ηo: Overall efficiency
ηm: Maximum efficiency
Hm: Manometric Head
Wi: Power Input (Electrical Power)
Wh: Hydraulic Power
P1: Discharge Pressure 1
P2: Discharge Pressure 2
RPS: Revolutions per second
pv: Vapor pressure of the fluid
Vi: Average velocity of the inlet
4
Figure 1: Showing basic schematic diagram of experimental setup
5
Procedure
The wattmeters were connected to the pumps under test and the pump inlet valve fully
opened. the water level in the reservoir tank was checked. The experimental apparatus was
then mounted onto the working surface of the bench. The bench flexible water supply hose
was connected to the apparatus with the bench regulating valve set in a closed position. the
speed control unit was then adjusted to approximately mid-range. The electrical supply was
then connected to the bench and turned on. The pump flow was adjusted using the bench
regulating valve and the Pump Speed Control Units was used to correct any pump speeds,
ensuring that the correct pump was selected on the P6102 Pump Speed Display Unit. The
speeds of the pumps were maintained at the required values.
The test commenced with the regulating value fully closed and with the pump speeds being
60 revolutions per second (rps) for both pumps. The suction and delivery pressures for each
pump was recorded. The regulating valve was gradually opened to fully open, and the
pressures recorded again. The pressure difference was calculated between the Discharge
values and these readings were used to determine the range. The regulating valve was closed,
and all parameter was recorded for power input and pressures. The pump was then re-opened
to allow the produce a discharge flow with pump #2 discharge pressure about 10% of the
pressure difference less than the initial stagnation figure. All parameters were recorded again
including flow rate. The Speed Control Unit(s) was adjusted to maintain the pump speed of
60 rps in all cases. Finally, the test was repeated for pump speed of 70 rps. Data for the pump
operating at 80 rps was also recorded.
6
Pressure (PSI)
Power (W)
Pump #2
Discharge
Pump #1
Pump #2
Discharge
Volume
m3
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
Suction
Pump #1
Time (s)
Time (s)
Suction
Reading 3
Reading 2
Rotameter
(m3/h)
avg time
Volume (l)
6
0.2
0
111
120
5
9.31
9.47
9.39
1.6
7.5
0.25
0
106
115
5
10.5
9.88
10.19
1.35
9
0.39
0
100
113
5
10.88
9.75
10.315
1.02
10.5
0.4
0
90
99
5
14.12
13.27
13.695
1
12
0.43
0
88
96
5
16.45
15.43
15.94
0.85
13.5
0.59
0
77
84
5
22.33
21.77
22.05
0.59
15
0.6
0
61
71
5
42.43
41.25
41.84
0
16.5
0.62
0
47
65
5
60
61.75
60.875
0
Rotameter
(m3/s)
4.444E-04
3.750E-04
2.833E-04
2.778E-04
2.361E-04
1.639E-04
0.000E+00
0.000E+00
Corrected
discharge
Pressure
Corrected
total
Pump 2
suction Pressure Volumetric Flow
manometric
total hydraulic
Total Shaft
(kPa)
Pump 2 (kPa)
Rate, Q
head (m)
power
Power
48.97
8.98
5.325E-04
9.12E+00
47.36856656
196.35000
59.31
9.32
4.907E-04
1.12E+01
5.363E+01
187.85000
69.65
10.29
4.847E-04
1.32E+01
6.254E+01
181.05000
79.99
10.36
3.651E-04
1.53E+01
5.463E+01
160.65000
90.34
10.56
3.137E-04
1.74E+01
5.336E+01
156.40000
100.68
11.67
2.268E-04
1.95E+01
4.301E+01
136.85000
111.02
11.74
1.195E-04
2.16E+01
2.513E+01
112.20000
121.36
11.87
8.214E-05
2.37E+01
1.896E+01
95.20000
η0
2.412E+01
2.855E+01
3.454E+01
3.401E+01
3.412E+01
3.143E+01
2.240E+01
1.992E+01
Tabl
e 1:
Depi
cting
resul
ts
acqui
red for pump operating at 60 rps
7
Pressure (PSI)
Power (W)
Pump #2
Pump #1
Pump #2
Discharge
Volume
m3
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
Discharge
Suction
Pump #1
Time (s)
Time (s)
Suction
Reading 3
Reading 2
Rotameter
(m3/h)
avg time
Volume (l)
7
1.6
0
145
169
5
7.44
6.65
7.045
1.9
9
1.9
0
156
169
5
7.88
7.33
7.605
1.8
11
0.2
0
147
157
5
9.14
8.33
8.735
1.6
13
0.31
0
139
157
5
9.75
9.37
9.56
1.4
15
0.4
0
129
148
5
11.71
11.57
11.64
1.3
17
0.65
0
118
139
5
14.72
14
14.36
1
19
0.78
0
102
120
5
20.69
19.95
20.32
0.55
21
0.8
0
87
106
5
35.08
34.08
34.58
0
Rotameter
(m3/s)
5.278E-04
5.000E-04
4.444E-04
3.889E-04
3.611E-04
2.778E-04
1.528E-04
0.000E+00
Corrected
discharge
Pressure
Corrected
total
Pump 2
suction Pressure Volumetric Flow
manometric
total hydraulic Total Shaft
(kPa)
Pump 2 (kPa)
Rate, Q
head (m)
power
Power
55.86
18.63
7.097E-04
9.55E+00
6.607E+01
196.35000
69.65
20.70
6.575E-04
1.22E+01
7.798E+01
187.85000
83.44
8.98
5.724E-04
1.62E+01
9.039E+01
181.05000
97.23
9.74
5.230E-04
1.89E+01
9.661E+01
160.65000
111.02
10.36
4.296E-04
2.17E+01
9.093E+01
156.40000
124.81
12.08
3.482E-04
2.44E+01
8.271E+01
136.85000
138.60
12.98
2.461E-04
2.71E+01
6.502E+01
112.20000
152.39
13.12
1.446E-04
2.99E+01
4.217E+01
95.20000
η0
2.412E+01
2.855E+01
3.454E+01
3.401E+01
3.412E+01
3.143E+01
2.240E+01
1.992E+01
Table 2: Depicting results acquired for pump operating at 70 rps
8
Pressure (PSI)
Power (W)
Pump #2
Discharge
Pump #1
Time (s)
Pump #2
Discharge Suction
Pump #1
Time (s)
Volume (l)
Suction
Reading 3
avg time
Rotameter (m3/h)
Reading 2
9
11
13
15
17
19
21
0.18
0.4
0.43
0.6
0.6
0.7
0.8
0
0
0
0
0
0
0
215
213
206
204
190
179
160
229
228
220
218
203
193
183
5
5
5
5
5
5
5
6.39
6.62
6.94
7.51
8.69
10.09
12.28
5.71
5.82
6.76
7.14
8.09
10.09
11.72
6.05
6.22
6.85
7.325
8.39
10.09
12
2.34
2.16
1.95
1.8
1.6
1.4
1.25
23
0.8
0
154
166
5
15.77
15.09
15.43
0.9
Volume
Rotameter
m3
(m3/s)
0.005 6.500E-04
0.005 6.000E-04
0.005 5.417E-04
0.005 5.000E-04
0.005 4.444E-04
0.005 3.889E-04
0.005 3.472E-04
0.005 2.500E-04
Corrected
discharge
Pressure
Pump 2
(kPa)
69.65
83.44
97.23
111.02
124.81
138.60
152.39
166.18
Corrected
suction
Pressure Volumetric total
total
Pump 2
Flow Rate, manometric hydraulic
(kPa)
Q
head (m)
power
8.84 8.264E-04
2.08E+02 1.678E+01
10.36 8.039E-04
1.98E+02 2.018E+01
10.56 7.299E-04
1.88E+02 2.400E+01
11.74 6.826E-04
1.71E+02 3.086E+01
11.74 5.959E-04
1.51E+02 3.820E+01
12.43 4.955E-04
1.31E+02 7.451E+01
13.12 4.167E-04
0.00E+00 0.000E+00
13.12 3.240E-04
0.00E+00 0.000E+00
0.005
1.667E-04
179.97
13.39
2.618E-04
0.005
0.000E+00
193.76
14.15
1.342E-04
Total
Shaft
Power
196.35000
187.85000
181.05000
160.65000
156.40000
136.85000
112.20000
95.20000
Total
0.00E+00 0.000E+00
Shaft
Power
0.00E+00 0.000E+00 196.35000
η0
2.412E+01
2.855E+01
3.454E+01
3.401E+01
3.412E+01
3.143E+01
2.240E+01
1.992E+01
η0
2.412E+01
Table 3: Depicting results acquired for pump operating at 80 rps
9
manometric head (m) vs Flow rate, Q
4.50E+01
total mano
manometric head
total mano
total mano
Series8
Series3
Linear (total mano)
Linear (manometric head)
Linear (total mano)
Linear (total mano)
Manometric Head
4.00E+01
3.50E+01
3.00E+01
2.50E+01
2.00E+01
1.50E+01
1.00E+01
5.00E+00
0.00E+00
0.000E+00 2.000E-04 4.000E-04 6.000E-04 8.000E-04 1.000E-03
Flow Rate Q
Graph 1: Depicting Manometric Head against Flow rate
total mano
60 RPS
7.00E+01
total hydro
6.00E+01
efficiency
5.00E+01
4.00E+01
efficiency
3.00E+01
manometri
c head
2.00E+01
1.00E+01
0.00E+00
0.000E+00
-1.00E+01
hydraulic
power
1.000E-04
2.000E-04
3.000E-04
4.000E-04
5.000E-04
6.000E-04
Flow Rate
Graph 2: Showing Hydraulic Power, Manometric Head and Efficiency at 60 Rps vs Flow
rate
10
1.20E+02
70 RPS
total mano
1.00E+02
total hydro
8.00E+01
Total efficiency
6.00E+01
Efficiency
4.00E+01
Single Hm
2.00E+01
Single Hydraulic
0.00E+00
Pwr
0.000E+00
1.000E-04
2.000E-04
3.000E-04
4.000E-04
5.000E-04
6.000E-04
7.000E-04
8.000E-04
-2.00E+01
Flow Rate
Graph 3: Showing Hydraulic Power, Manometric Head and Efficiency at 70 rps vs Flow
Rate
80 RPS
1.60E+02
1.40E+02
Combined
series head
1.20E+02
Combined
Hydraulic Power
1.00E+02
Series efficiency
8.00E+01
6.00E+01
Single Efficiency
4.00E+01
Single
Manometric
0.00E+00
Head
0.000E+001.000E-042.000E-043.000E-044.000E-045.000E-046.000E-047.000E-048.000E-049.000E-04Single Hydraulic
-2.00E+01
Power
Flow Rate
2.00E+01
Graph 4: Showing Hydraulic Power, Manometric Head and Efficiency at 80 rps vs Flow
Rate
11
Discussion
In this lab the two pumps were connected in series and were later compared to the
results of an individual pump to determine the characteristics between the two. The values
different speeds of were all obtained and recorded. Due to a difference in height 7.6kpa was
added to correct the discharge pressure.
Graph 1 shows the manometric head plotted against the volumetric flow rate for
pumps connected in series while also displaying the single pump characteristics at the same
speed. Analysing the pumps, manometric head and volumetric flow rate is inversely
proportional. From the graph we can see that the shut off head for the pumps in series were
significantly higher at corresponding speeds of that of the single pump characteristic curve.
Also, for the pumps connected in series at various speeds of 60, 70 and 80rps graphs
showing the hydraulic power, manometric head, and overall efficiency versus the volumetric
flow rate. Here we can see in all pumps that the efficiency is much higher than a single pump
with the highest single pump efficiency being just below 19% while the series pumps’ lowest
efficiency is around 20% while also discharging more fluid at that speed showing that at any
point the series configuration is more efficient. At 60rps the trend continues, as manometric
head decreased, hydraulic power increased all while the volumetric flow rate increased. while
the efficiency increased gradually alongside the hydraulic power showing signs that the pump
did not reach maximum output. At 70rps efficiency and hydraulic power characteristics hit a
peak and then decrease ultimately resulting in an almost flat horizontal line of best fit as the
volumetric flow rate increased. at 80rps there was also a peak and then a descent but much
more gradually and the pump maintained a smooth increase in hydraulic power and
efficiency while the manometric head decreased more drastically in comparison as the flow
rate increased. indicating that the highest efficiency was found but would be easier to
12
maintain that efficiency and discharge than the 70 rps operation of the pump resulting
Finally,
There were various sources of error which may have affected the accuracy of the
experiment. One such error was that the measurements recorded from the pressure gauge was
not precise and was experiencing fast repeated up and down movement of the indicator
making it hard to have a accurate reading. Another source of error was the reaction time of
the experimenter/s starting and stopping the stopwatch. This was when they were recording
the flow rate of the water. Their reaction time were off so hence affecting the time recorded
and used for the experiment. However, to reduce this error two-time readings were taken and
averaged. Pumps in this configuration are very useful in everyday life due to their high head
they can be used to overcome high static discharge and pump fluid over long lengths of pipe
such as a community water system. They can also be used in industrial plants to pump slurry
as this method uses less energy than one large pump. Other efficiencies related to dynamic
machines include mechanical efficiency which is effectiveness of the system and casing
efficiency.
Conclusion
In conclusion the total head discharge characteristics, of two identical centrifugal pumps
operating at the same speed an in series were determined. And it can be said that two pumps
operating in this manner greatly increases the flow rate while maintaining an acceptable
efficiency range.
13
References
Evans, J. (2017, November 28). Centrifugal Pump Efficiency-What Is Efficiency? Retrieved
from https://www.pumpsandsystems.com/topics/pumps/pumps/centrifugal-pumpefficiency-what-efficiency
Munson, B. (2006). Fundamental of Fluid Mechanics. John Wiley & Sons.
Calculations
1. Sample calculation for Manometric Head:
The water temperature was 26.667
Therefore, calculating the density of water at 28 degrees
Using method of Interpolation:
y2 − y 1
y − y1
=
x2 − x1
x−x1
It was found to be 996.67991
At 60 rps
Hm = (P2-P1)/ ρg
𝑘𝑔
Where ρ 996.67991𝑚3 at 26.667 degrees Celsius
𝑘𝑔
Hm = (48968.56pa - 0)/ 996.67991 𝑚3 ∗ 9.784 N/kg
Hm = 5.021635487m
Hm = (P2-P1)/ ρg
𝑘𝑔
Hm = (48968.56pa – 8978.95)/ 996.67991 𝑚3 ∗ 9.784 N/kg
Hm = 4.100860524m
Therefore, Combined Manometric Head = = 5.021635487m + 4.100860524m
= 9.12m
14
2. Sample calculation for Flow Rate:Q = Volume/ Average time
= 0.005/9.39s
= 5.325E-04 m3/s
3. Sample calculation the Hydraulic Power:
Wh1= Hm1*Q *9.784*996.69771
= 996.69771*9.784*05.325E-04*5.021635487m
= 26.07484558
Wh2 = 996.69771*9.784* 4.100860524m * 5.325E-04
Wh2= 21.293721
Combined Hydraulic Power
Wh = 21.293721 + 26.07484558
= 47.36856656
4. Sample calculation for Shaft Power:
Wsh1 = (0.85*120) = 102 W
Wsh2 = (0.85*111) = 94.35 W
Combined Shaft Power
Wsh = 102+ 94.35
= 196.35
5. Sample Calculation for Calculating Efficiency:
ηo= Wh/ Wsh
ηo= 47.36856656/196.35
15
ηo= 24.12%
Values provided by lecturer
16