It is for Fluid Mechanics Laboratory about Centrifugal Pump please fallow the format

img_0211.jpg

lab_6___centrifugal_pump__1_.docx

example_report.pdf

mod_asme_report_format__5_.docx

Unformatted Attachment Preview

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

…

Purchase answer to see full

attachment