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Lab 6: Centrifugal Pump
ENGR 3471 – Fluid Mechanics Laboratory
Introduction
Pumps are used to move fluids by using mechanical work to increase the energy of a fluid stream. In Bernoulli’s
Equation, this work input is included as a negative term on the downstream side of the equation. The energy
input of a pump is often specified in terms of the pump “head,” which has units of length. Historically, the use
of “head” to characterize pump performance was related to the height that a pump could raise a column of
water, but this definition has been extended to included losses in fluid systems, e.g., friction “head.”
Objectives
Investigate the characteristics of a centrifugal pump and compare experimental data with manufacturer data.
Experimental Setup
Figure 1: Centrifugal pump
Procedure
Connect the motor plug to the overhead socket to power the pump.
Open the outlet valve of the tank draining into the sump and turn on the pump switch.
Adjust the pump outlet valve so that the pressure gauge has a fixed pressure reading between 5 and 25
psi.
Turn the pump switch off and allow the accumulated water to drain down to ~50 gal before closing the
outlet valve.
Record the initial water level in the sump pit and the initial volume in the in tank.
Turn the pump on and allow water to accumulate in the tank up to a final volume of ~250 gal.
Record the final water volumes in the tank and the elapsed time, as well as the final water level in the
sump pit.
Repeat the measurement by adjusting the pump outlet valve for five different pressure readings.
Calculation
Calculate the following quantities and show a complete sample calculation of one data point:
o Average water flowrate
o
o
o
o
o
Pressure, elevation, velocity, Reynolds number, and friction factor in the suction pipe
Pressure, elevation, velocity, Reynolds number, and friction factor in the discharge pipe
Total friction head, hf, using the Darcy-Weisbach Equation
Pump head, hP, using Bernoulli’s Equation
Pump power and compare to rated power
Discussion
• Construct a plot of flowrate vs. pump head. Can you extrapolate values of pump head for zero flow and
maximum flowrate (Q when hp = 0)?
• Discuss any deviations in calculated pump power compared to rated pump power.
Derivation
Sump Depth:
𝑈𝑙𝑙𝑎𝑔𝑒
𝑇𝑜𝑡𝑎𝑙
ℎ𝑆𝑢𝑚𝑝 = ℎ𝑆𝑢𝑚𝑝
− ℎ𝑆𝑢𝑚𝑝
𝐴𝑣𝑒𝑟𝑎𝑔𝑒
Average Sump Depth: ℎ𝑆𝑢𝑚𝑝
1
𝐼𝑛𝑖𝑡𝑖𝑎𝑙
𝐹𝑖𝑛𝑎𝑙
= 2 (ℎ𝑆𝑢𝑚𝑝
+ ℎ𝑆𝑢𝑚𝑝
)
Water Volume:
𝐹𝑖𝑛𝑎𝑙
𝐼𝑛𝑖𝑡𝑖𝑎𝑙
𝑉𝑊𝑎𝑡𝑒𝑟 = 𝑉𝑇𝑎𝑛𝑘
− 𝑉𝑇𝑎𝑛𝑘
Water Flowrate:
𝑄 = 𝑉𝑊𝑎𝑡𝑒𝑟 ⁄𝑡
Suction Pressure:
𝑃1 = 𝜌𝑔ℎ𝑆𝑢𝑚𝑝
Discharge Pressure:
𝑃2 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐺𝑎𝑔𝑒 𝑅𝑒𝑎𝑑𝑖𝑛𝑔
Suction Elevation:
𝑧1 = 𝑇𝑎𝑟𝑒 𝐸𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 = 0
Discharge Elevation:
𝑇𝑜𝑡𝑎𝑙
𝑧2 = ℎ𝑆𝑢𝑚𝑝
+ ℎ𝐺𝑎𝑔𝑒
Suction Area:
𝐴1 = 4 𝐷12
Discharge Area:
𝐴2 = 4 𝐷22
Suction Velocity:
𝑣1 = 𝑄 ⁄𝐴1
Discharge Velocity:
𝑣2 = 𝑄 ⁄𝐴2
Suction Reynold’s:
𝑅𝑒1 = 𝜌𝑣1 𝐷1 ⁄𝜇
𝐴𝑣𝑒𝑟𝑎𝑔𝑒
𝜋
𝜋
Discharge Reynold’s: 𝑅𝑒2 = 𝜌𝑣2 𝐷2 ⁄𝜇
Suction friction:
Discharge friction:
1
√𝑓1
𝜀1
⁄𝐷
1
3.70
= −2 log10 [
1
√𝑓2
𝑅𝑒1 √𝑓1
𝜀2
⁄𝐷
ℎ𝑓1 =
Discharge friction head:
Pump head:
2.51
= −2 log10 [ 3.702 +
Suction friction head:
Total friction head:
+
𝑣1 2
2𝑔
]
2.51
𝑅𝑒2 √𝑓2
]
𝐿
[𝑓1 𝐷1 + ∑ 𝐾]
1
𝐿 𝑣2
ℎ𝑓2 = 𝑓2 𝐷2
2
2
2𝑔
ℎ𝑓 = ℎ𝑓1 + ℎ𝑓2
𝑃1
+
𝜌𝑔
𝑣1 2
2𝑔
𝑃
+ 𝑧1 = 𝜌𝑔2 +
𝑣2 2
2𝑔
+ 𝑧2 + ℎ𝑓 − ℎ𝑃
Pump Power:
𝑤𝑃 = 𝜌𝑔𝑄ℎ𝑃
Suction-side K-values: KInlet = 1.0, KCheck Valve = 2.1, KTee = 1.1, KJoint = 0.3
Equations do not include unit conversions
Location 1 refers to the start of the PVC suction pipe in the sump
Location 2 refers to the position of the pressure gage, right before the pump outlet valve
Table 1. Flow Rate Data
hSumpInitial
in
Run
hSumpFinal
in
hSumpAverage
in
VTankInitial
gal
VTankFinal
gal
VWater
gal
t
s
Q
gpm
cfs
1
2
3
4
5
Table 2. Pump Head Calculation
P1
psi
P2
psi
z1
ft
z2
ft
v1
ft/s
v2
ft/s
Re1
Re2
f1
f2
hf
ft
hP
ft
wP
HP
1
2
3
4
5
Constants
wPump = 5 HP
hSumpTotal = 44.75”
hGage = 34.50”
D1 = 2.5”
D2 = 2.0”
L1 = 81.5”
L2 = 26.0”
ε1 = 0.00006” (Smooth PVC Suction Pipe)
ε2 = 0.006” (Cast Iron Discharge Pipe)
Sept. 20, 2019
Pressure Measurement with Bourdon Gauge – Example Report
Drew Fleming1
Arkansas State University
1
Mechanical Engineering, rofleming@AState.edu
ABSTRACT
In this experiment, a Bourdon gauge was used to experimentally measure fluid pressure as a
function of applied weight. The results show that the pressure measurements from the gauge
initially differ from the calculated theoretical pressure, with a measured gauge sensitivity that
results in a 4.9% relative error compared to the theoretical conversion factor of 31.14 kPa/kg. By
accounting for a 6 kPa pressure offset in the gauge, the Bourdon gauge sensitivity decreased to
30.94 kPa/kg, which represents a relative error of less than 1% compared to the theorical value.
As a result, the Bourdon gauge was effectively re-calibrated, and can now be used to more
accurately measure pressure.
NOMENCLATURE
P
Pressure (kPa)
W
Weight (N)
A
Piston Area (mm2)
m
Mass (kg)
g
Gravitational Acceleration (9.21 m/s2)
INTRODUCTION
A Bourdon gauge is a mechanical pressure measurement device that directly transfers applied
weight to pressure, in accordance with Pascal’s Law. In this experiment, a Bourdon gauge is
directly connected to a fluid-filled piston-cylinder assembly, and the fluid pressure in the cylinder
is directly proportional to the applied weight divided by the piston area, as shown in Eq. 1:
𝑃=
#
$
=
%&
(1)
$
[Note: this would be a good place to further explain Pascal’s Law, the operation of a Bourdon
gauge, etc. The info provided in this example is the bare minimum for a passing grade, not
necessarily an A.]
EXPERIMENTAL SETUP
This experiment utilized a radial-style Bourdon gauge attached to a fluid-filled piston-cylinder.
To generate hydrostatic fluid pressure, known weights of 0.5 kg – 4 kg are added to the piston; the
piston itself weighs 1 kg. Pressure measurements are read directly from the radial pressure gauge
in response to the weight applied to the piston for both increasing and decreasing weights, for total
weights of 1 kg – 5 kg (including the piston). This procedure was repeated in triplicate in order to
calculate average pressures for each weight, as well as a standard deviation.
During the measurement procedure, after each weight was added or removed, the piston was gently
rotated to reduce any residual friction in the piston-cylinder assembly. In addition, it was noticed
1
that the Bourdon gauge did not read zero pressure when there was zero weight applied. This nonzero “zero-pressure offset” of 6 kPa was noted for further analysis in the experiment.
[This section is a good place to put any images of the experiment set-up.]
DATA AND RESULTS
A plot of the measured pressure values, for both increasing and decreasing weight, is shown in
Fig. 1, along with theoretical calculated pressure values. There is a slight amount of hysteresis
between the increasing and decreasing weight measurements, but they largely agree. However,
the measured pressure is noticeably offset from the theoretical pressure. This data is summarized
in Table 1, which includes calculated theoretical pressure values, as well as average measured
pressure values and standard deviations for both increasing and decreasing weight.
180
Increasing Weight
160
Decreasing Weight
Pressure (kPa)
140
Theoretical Pressure
120
100
80
60
40
20
0
1
2
3
4
5
6
Applied Mass (kg)
Fig. 1: Calculated and measured pressures as a function of applied mass.
Table 1: Summarized Pressure Calculations and Measurements
Total Mass
Calculated
Increasing Weight
Decreasing Weight
(kg)
Pressure (kPa)
Average
St.Dev.
Average
St.Dev.
Pressure (kPa)
Pressure (kPa)
1
31.14
35.67
0.94
37.00
0.00
1.5
46.71
51.33
1.25
52.00
0.82
2
62.29
67.00
1.41
68.33
0.47
3
93.43
101.00
2.16
99.67
0.47
3.5
109.00
113.33
1.25
113.67
0.47
4
124.57
129.33
0.47
131.00
1.63
4.5
155.71
161.33
1.70
161.00
1.41
In Fig. 2, the measured pressure as a function of applied mass is plotted for increasing weight,
along with a least-squares linear regression line. For this plot, the y-intercept of the regression line
was forced to be zero on physical grounds, since there should be zero pressure measured with zero
2
applied weight. As a result, the slope of the regression line is 32.667 kPa/kg, which somewhat
overestimates the predicted pressure compared to the conversion factor of 31.14 kPa/kg provided
by the manufacturer.
180
y = 32.667x
R² = 0.9973
160
Pressure (kPa)
140
120
100
80
60
40
20
0
1
2
3
4
5
6
Applied Mass (kg)
Fig 2: Average measured pressure values vs. applied mass for increasing weight, along with a
least-squares linear regression line. Errors bars indicate 1 standard deviation, based on 3
measurements.
Finally, in Fig. 3, a “corrected” measured pressure is plotted as a function of applied load. These
corrected values were calculated by subtracting the “zero-pressure offset” of 6 kPa from the
average measured pressure for increasing weight shown in Table 1. The resulting linear trend line
has a slope of 30.94 kPa/kg, which is notably reduced from the slope of 32.667 kPa/kg shown in
Fig. 2.
180
160
y = 30.94x
R² = 0.9992
Pressure (kPa)
140
120
100
80
60
40
20
0
1
2
3
4
5
6
Applied Mass (kg)
Fig. 3: “Corrected” pressure vs. applied mass, generated by subtracting the 6 kPa “zero-pressure
offset” from the measured average pressure for increasing weight.
3
DISCUSSION
In general, there is a linear relationship between applied mass and measured pressure from the
Bourdon gauge, which agrees with the form of Eq. 1. As noted from Fig. 1, however, the pressure
values measured from the Bourdon gauge do not agree with the theoretical calculated pressures,
indicating that the Bourdon gauge may be uncalibrated.
The slope of the linear regression line calculated from the increasing-weight pressure
measurements represents a 4.9% error compared to the conversion factor provided by the
manufacturer. In comparison, the slope of the linear trend line calculated from the “corrected”
pressure data differs from the manufacturer conversion factor by -0.6%, which is a much more
reasonable amount. As a result, correcting the measured pressure data using the “zero-pressure
offset” effectively recalibrates the Bourdon gauge so that it can be used to more accurately measure
pressure. The slope of the linear regression line can be thought of as the “sensitivity” of the
Bourdon gauge, which represents how the measured pressure responds to additional added weight.
Calculated theoretical pressures and “corrected” measured pressures for applied masses are
summarized in Table 2, along with calculated relative errors. As can be seen, the magnitude of
the relative error ranges from 4.74% at 1 kg to 0.24% at 5 kg. This suggests that the Bourdon
gauge is more accurate at higher pressure, or at least less sensitive to experimental uncertainties at
higher pressure. Uncertainties in this experiment could potentially arise from friction in the pistoncylinder assembly, which is the reason for the difference between the increasing- and decreasingweight measurements. During the experiment, the piston was gently rotated to reduce, but not
totally eliminate, the effect of friction on the measurements. Additional uncertainties in the value
of the applied weights could also result in measurement errors.
Table 2: Comparison of Theoretical Pressure to Corrected Measured Pressure
Applied
Theoretical
Corrected
Relative
Mass (kg) Pressure (kPa) Pressure (kPa) Error (%)
1
31.14
29.67
-4.74
1.5
46.71
45.33
-2.96
2
62.29
61.00
-2.06
3
93.43
95.00
1.68
3.5
109.00
107.33
-1.53
4
124.57
123.33
-0.99
4
155.71
155.33
-0.24
CONCLUSION
In this experiment, a Bourdon gauge was used to experimentally measure pressure as a function of
applied weight. The results show that the Bourdon gauge initially measured higher pressure
compared to the theoretical calculations using a conversion factor provided by the manufacturer.
It was found that this could be corrected by accounting for a “non-zero pressure offset,” which
substantially improved the agreement between the measurements and the theoretical conversion
factor. Notably, accounting for this pressure offset resulted in a measured Bourdon gauge
sensitivity that differed from the theoretical conversion factor by less than 1%, which effectively
recalibrated the gauge.
4
REFERENCES
[No references/sources were used in this example report, but there typically will be in a real report.]
PARTICIPATION DISCLAIMER
[Attribution of specific tasks to individual group members, with student signatures.]
APPENDICES
Appendix A: Example Calculation
For an applied mass of 3 kg, the theoretical pressure can be calculated from Eq. 1 as:
m
𝑊 𝑚𝑔 (3 kg)(9.81 s 7 ) (1000)7 mm7
𝑃=
=
=
∙
= 93429 Pa = 93.43 kPa
𝐴
𝐴
(315 mm7 )
m7
[Note: Such a simple calculation may not require a full-on example calculation. Other lab
exercises with more in-depth calculations likely will.]
Appendix [B]: Lab Notebooks
[Staple a copy of every group member’s completed lab handout to the back of the report.]
5
(Date)
(Report Title)
(Student1 Name)1, (Student 2 Name)2….
Arkansas State University
1
(Student1 Dept.), (Student1 astate.edu email), 2(Student2 Dept.), (Student2 astate.edu email)…
ABSTRACT
Roughly 100-300 words describing the experiment performed and the main conclusions.
NOMENCLATURE
Definitions and names of all symbols used throughout the report, with consistent units. For
example:
Volumetric Flow Rate (ft3/s)
V
Density (lbm/ft3)
Cp
Specific Heat at Constant Pressure (BTU/lbm·°F)
Etc…
INTRODUCTION
Concisely describes the background, theory, and specific motivation for the experiment. Equations
should be offset and numbered, for example:
(1)
Q = hADT
EXPERIMENTAL SETUP
Description of the entire experimental setup, including specific equipment models, if applicable.
Labeled photographs/diagrams, with captions, should be included in this section. In addition, any
sample fabrication or measurement procedures should be described.
DATA AND RESULTS
The data and numerical results of the experiment should be described here, with fully-labeled and
captioned tables, graphs, plots, etc.
DISCUSSION
In this section, the implications of the processed data/results of the experiments should be
discussed – such as data trends, comparisons with established theory, unexpected deviations from
theory, calculation of material properties from measurements (e.g., calculation of thermal
conductivity from a plot of heat flux vs. temperature), etc. Uncertainty in the measurements should
be addressed.
CONCLUSION
An overview of the experiment and the key results obtained. No new information should be
introduced in this section.
REFERENCES
If necessary, and in any format. Proper attribution of sources is more important than format.
1
PARTICIPATION DISCLAIMER
Outline the contributions of each group member during data collection and preparation of the lab
report, with student signatures indicating that they are in agreement with the credited contributions.
APPENDICES
If a particular experiment requires extensive calculations to arrive at a result, an example
calculation should be provided in an appendix.
If there is a large amount of data, graphs, etc., that contributed to key experimental
result/conclusion, but can’t be included in the main body of the report in a clear and informative
way, they can also be provided in an appendix.
In general, a copy of your lab data sheet should be submitted with your report in an appendix.
2
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