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The Centrifugal Pump, Lab Reports of Fluid Dynamics

Mechanical Engineering Lab report on the centrifugal pump

Typology: Lab Reports

2019/2020

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I

The Centrifugal Pump

Orville Thomas

H

MechEnSci 9 – B59EI

Dr. Tadhg O'Donovan

TABLE OF CONTENTS

  • 1.ABSTRACT
  • 2.INTRODUCTION
    • 2.1 OBJECTIVE
    • 2.2 PUMPS
      1. 3 CENTRIFUGAL PUMPS
        1. 3 .1 Disadvantages
      • 2.3.2 Applications
  • 3 .THEORY
      1. 1 TERMINOLOGIES
    • 3.2 BERNOULLI’S PRINCIPLE
      • 3.2.1 Energy Form
      • 3.2.2 Head Form
    • 3.3 POWER INPUT
      1. 4 POWER OUTPUT
      1. 5 SPECIFIC SPEED OF PUMP
      1. 6 PUMP PERFORMANCE & EFFICIENCY
      1. 7 MOTOR POWER
      1. 8 SAMPLE CALCULATIONS
  • 4.EQUIPMENT
  • 5.PROCEDURE....................................................................................................................................
  • 6.RESULTS & DISCUSSION
    • 6.1 GRAPHS.........................................................................................................................................
    • 6.2 MAXIMUM EFFICIENCY
      1. 3 MINIMUM EFFICIENCY
      1. 4 DISCUSSION
      1. 5 ERRORS
      1. 6 RECOMMENDATION
  • 7.CONCLUSIONS................................................................................................................................
  • 8.REFERENCES AND BIBLIOGRAPHY
  • 9.APPENDIX

2 .INTRODUCTION

2.2.1 The main objective of this experiment pump characteristics showing the relationship

between the pressure rise across the pump and the flow rate through it and the efficiency

of this process. [1]

2 .1 Pump

A pump is a device that expends energy (mechanical

energy from the motor which runs on electrical energy

or a steam turbine to create hydrodynamic energy) in

order to raise, transport, or compress fluids (i.e. liquids

or gases). Pumps are mainly classified as centrifugal

and positive displacement pumps.[2]

2. 2 Centrifugal Pump

Centrifugal Pumps are machines that are used to transport fluids by the

conversion of rotational kinetic energy to the hydrodynamic energy for

fluid flow. They are more widely used than any other kinds of pumps in

various industries. Volute pump is the most common centrifugal pump. Volute is the casing in

the machine that receives the gushing fluid that being pumped by the impeller. The casing

maintains the velocity of the fluid. [3]

2.2.2 One of the major disadvantages is cavitation. In centrifugal pumps, cavitation occurs in

impellers. Cavitation is caused due to a reduction in suction pressure and an increase in

suction temperature or an increase in flow rate above than which a said pump is designed

Figure 1 Pump Description

Figure 2 Cavitation

to handle. Cavitation occurs mainly when the suction and the discharge moment of the

fluid happens.

2.2.3 Some industries such as the Oil and Energy industry pumps crude oil, slurry, mud. Waste

Management industry works to pump drainage, gas processing, irrigation and flood

protection; the fire protection industry uses this pump for heating and ventilation, boiler

feed applications, pressure boosting and fire protection sprinkler systems.

Centrifugal Pumps can be distinguished in terms of design, construction, application

within an industry and on the national or industries standards of regulations such as the

ANSI (American National Standards Institute), API (American Petroleum Institute), ISO

(International Standard for general application), ASME (American Society of Mechanical

Engineers) for nuclear pumps etc.

3.THEORY

In genesis, the theory of centrifugal pumps is an evolution of the first principles of Engineering

Fluid Mechanics applied to a controlled volume. They are: -

Mass (Continuity Equation) – [Energy can neither be created nor be destroyed]

Momentum (Newton’s 2

nd

Law of Momentum) [ p = mv] {kgm/s]

Energy (Bernoulli’s Equation) [

𝑝

1

𝜌

𝑉

1

2

2

1

𝑝

2

𝜌

𝑉

2

2

2

2

  • ɛ]

However, the underlying theory to all this is the Buckingham Pi Theorem.

The theorem states that: “If a dimensional dependent variable depends on n - 1 dimensional

independent variables (i.e. n variables are associated with the problem) and if m

independent dimensions are required to define the n variables, then the n variables can be

combined into (n - m) dimensionless variables.”

The theorem helps in problems where the variables associated are interdependent by

rearranging them in dimensionless groups (Mass, Length, Time).

𝑠𝑦𝑠𝑡𝑒𝑚

2

2

1

1

The two pressures at both ends of the pipe are P 1

and P

The water at P 1

will do positive work

since the force points in the same direction as the motion of the fluid. The water at P 2

will do

negative work since it pushes in the opposite direction as the motion of the fluid.

Work can be found with, W = F*d (where, d is the length of the water

displaced by the pressure).

The force from the pressure, F= P*A ( 4 )

So, from (3) and (4), we can say that;

W=PAd ( 5 )

At the initial phase of the pipe, F 1

=P

1

*A

1

and at the final phase of the pipe, F 2

= - (P

2

*A

2

) as it is

in the opposite direction.

So, the work done at both ends will be W 1

=P

1

*A

1

*d 1

and W 2

= - P

2

*A

2

*d 2

Substituting these equations in (1); we get 𝑃

1

1

1

2

2

2

𝑠𝑦𝑠𝑡𝑒𝑚

Since the volume flow rate (Q) must be maintained for an incompressible fluid, A 1

*d

1

= A

2

*d

2

V. This further simplifies the above equation to

1

2

𝑠𝑦𝑠𝑡𝑒𝑚

Therefore, from equations (6) and (2);

1

2

2

2

1

1

If we substitute in the formulas for kinetic and gravitational potential energy, we get: -

1

2

2

2

2

1

2

1

1

As we rearrange the formula and simplify it further by noting that the density, ρ =

𝑚

𝑣

; we get: -

1

1

2

ρv

1

2

  • ρgh

1

2

1

2

ρv

2

2

  • ρgh

2

3.2.1 Energy Form

When this equation is applied to a fluid contained in a control volume fixed in space,

mechanical work is irreversibly transformed by fluid friction into heat, leading to “losses” (ɛ).

Also, the pump performs work on the fluid which runs on an input power (𝑊

𝐼𝑁

). Both losses

and input power are included in the energy form of the Bernoulli equation. [5] Therefore: -

2

2

2

2

1

1

2

1

− ɛ − 𝑊

𝐼𝑁

3.2.2 Head Form

In terms of hydrodynamics, the Bernoulli equation can be converted to “head” form by dividing

the energy form by the acceleration due to gravity “g”. We can further simplify it by using (γ =

𝜌𝑔).[6] Therefore: -

2

γ

2

2

2

1

γ

1

2

1

ɛ

𝐼𝑁

The head developed by the pump can be ℎ

𝑝

𝑊

𝐼𝑁

𝑔

and the head loss can be termed as

𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛

𝑓

ɛ

𝑔

Hence the head form of the energy equation can be written as[7]: -

2

γ

2

2

2

1

γ

1

2

1

𝑓

𝑝

3.3 Power Input

The pump input power (𝑃

𝐼𝑁

) is the mechanical power taken by the pump shaft. The SI unit of

measurement for power input is watts (W).[8]

𝐼𝑁

𝜌𝑔𝐻𝑄

𝜂

[where 𝜂 is the pump efficiency and H is the Head of the Pump]

3.4 Power Output

The pump output power is the useful work delivered by the pump. It is the desired output of a

pump. It is also known as Hydraulic Power (P h

). [9]

𝑜𝑢𝑡

3.5 Specific Speed of Pump

3.6 Sample Calculations

Table 1 Sample Calulation for a random RPM value

Calculations

−𝟒

3

3

𝐷

5

𝑠

𝐼𝑁

𝐷

𝑠

𝑜𝑢𝑡

𝑜𝑢𝑡

𝐼𝑁

0.92 is the motor efficiency

4. EQUIPMENT

Figure 3 VFD Control

Panel

Figure 4 Voltage

Response Analyzer Figure 5 Rotameter

Figure 6 Wilo Pump

Figure 7 Tachometer

  1. Variable Frequency

Drive control panel

with external control.

It’s a frequency

conversion device to

control any three

phase AC motor

under 1.5KW

  1. Single Phase

Power Analyzer

to measure the

volt and ampere

that is used by

the pump.

  1. 40 GPM pipeline

flowmeter or rotameter

to measure the single-

phase flow of liquid or

gas.

  1. Wilo water

pump with Q max =

14

𝒎

𝟑

= 3. 89

𝒎

𝟑

𝑠

And H max

=47m

  1. Tachometer to measure

the RPM on the impeller

of the pump.

Figure 8 Pressure

Gauge

Figure 9 Suction

Reservoirs

Figure 10 Discharge

Reservoir

Figure 11 Pipelines Figure 12 Centrifugal Pump

Setup

  1. Suction

Pressure gauge

reader

  1. Reservoir

where the

returns

towards after

the initial

discharge

  1. Discharge

reservoir where the

water enters after it

leaves the

flowmeter.

  1. The inlet

and outlet

connections

for water onto

a reservoir

  1. The apparatus

when connected

together as one setup.

6. RESULTS & DISCUSSION

6.1 Graphs

Figure 13 RPM Speed @ 1525 Figure 14 RPM Speed @ 1270

Figure 15 RPM Speed @ 2064 Figure 16 RPM Speed @ 1880

6.2 Maximum Efficiency

Table 2 Values filtered for maximum Efficiency

RPM efficiency Pressure Head Input Power Hydraulic Power

1270 5.28E+01 6.69E+00 1.15E+02 5.58E+

1525 6.22E+01 9.74E+00 1.44E+02 8.13E+

1880 5.74E+01 1.47E+01 2.79E+02 1.47E+

2064 6.13E+01 1.67E+01 3.45E+02 1.95E+

6.3 Minimum Efficiency

Table 3 Values filtered for minimum Efficiency

RPM efficiency Pressure Head Input Power Hydraulic Power

1270 2.64E+01 9.23E+00 9.50E+01 2.31E+

1525 2.90E+01 1.26E+01 1.18E+02 3.15E+

1880 2.50E+01 1.90E+01 2.07E+02 4.76E+

2064 2.67E+01 2.31E+01 2.35E+02 5.78E+

6.4 Discussion

From all the four graphs that are presented above, the results from the lower RPM conditions (1270,1525)

depicts the efficiency curve to slope downwards soon as it reaches flowrates of higher numbers (Q> 5

𝑚

3

𝑠

).

Whereas the higher RPM conditions (1880,2064) depicts the efficiency curve to climb higher and farther

although with a sign of sloping down at a much higher flowrate that streams above 10units rather than 5.

The desired output of any pump operation is to have a high hydraulic power while avoiding a low efficiency

value in terms of losses. From Table 2 , the difference in ratio between hydraulic power and pump efficiency is

least when the RPM is 1525. Similarly, from Table 3 , the difference in ratio between the previously mentioned

hydraulic power and the pump efficiency is the least for the same RPM 1525. This can only explain that the

pump is optimal when the RPM is at 1525. The system loses output power or hydraulic power when it tries to

achieve maximum efficiency. Another parameter that supports the previous statement is the percentile value of

the BEP of the system at the different RPM’S,

Table 4 BEP's of all conditions

RPM’s BEP (%) Flowrate, Q at BEP (LPM)

1270 23.67 60

1525 26 65

1880 19.12 65

2064 19.7 65

[2] Tuthill. "Pump Types." https://www.tuthillpump.com/dam/2525.pdf (accessed 5.12.19.

[3] Thermal_Engineering. "intro to centrifugal pumps." https://www.thermal-

engineering.org/what-is-centrifugal-pump-definition/ (accessed 5.12.19.

[4] Khan_Academy. "Bernoulli's Equation."

https://www.khanacademy.org/science/physics/fluids/fluid-dynamics/a/what-is-bernoullis-

equation (accessed 5.12.19.

[5] Science_Direct. https://www.sciencedirect.com/topics/engineering/bernoulli-equation

(accessed 5.12.19.

[6] Clarkson. "Bernoulli for Hydrodynamics."

https://web2.clarkson.edu/projects/subramanian/ch330/notes/Engineering%20Bernoulli%

0Equation.pdf (accessed 5.12.19.

[7] Energy_Education. "Bernoulli Equation."

https://energyeducation.ca/encyclopedia/Bernoulli%27s_equation (accessed 5.12.19.

[8] ksb. "Power Input Centrifugal Pump." https://www.ksb.com/centrifugal-pump-lexicon/power-

input/191088/ (accessed.

[9] thermexcel. "pumps." https://www.ksb.com/centrifugal-pump-lexicon/power-input/191088/

(accessed 5.12.19.

[10] neutrium. "pump power calculation." https://neutrium.net/equipment/pump-power-

calculation/ (accessed 5.12.19.

9. APPENDIX

9 .1 CALCULATIONS MADE IN MATLAB

%% Exerimental Results and Calculations %%

% General Data Required %

g = 9.81 ; % gravitational acceleration (m/s^2) %

rho = 1000; % Water Density (kg/m^3)%

zd = .57 ; % Outlet above the Datum (m) %

zs = 0 ; % Inlet on the Datum (m) %

Ps = [0,0,0,0,0,0,0]'; % Suction Pressure (Pa) %

Q = [15,20,30,40,50,60,70]'.0.000017; %Flow Rate Values%*

Eff_motor = 0.92; % Motor Efficiency (92%) %

% Results for set conditions%

% At N_1 = 1525 RPM %

Pd_1 = [1.18,1.15,1.13,1.1,0.9,0.75,0.59]'.10e4;*

V_1 = [71.93,72.82,72,71.9,71.8,71.02,71.95]'./sqrt(2);

I_1 = [3.29,3.45,3.602,3.82,4.0, 4.26,4.44]'/sqrt(2);

Head_P_1 = (((Pd_1-Ps))./(rhog))+(zd-zs);*

P_in_1 = V_1.I_1;*

Hyd_P_1 = rho.g.Head_P_1.Q;*

Eff_1 = ((Hyd_P_1)./(P_in_1.0.92))100;**

T1 = table(Q,Ps,Pd_1,V_1,I_1,Head_P_1,P_in_1,Hyd_P_1,Eff_1);

% At N_2 = 1270 RPM %

Pd_2 = [0.85,0.809,0.75,0.7,0.6,0.49,0.3]'.10e4;*

V_2 = [60.1,59.84,59.96,59.95,59.82,59.79,54.8]'./sqrt(2);

I_2 = [3.16,3.31,3.47,3.66,3.84,4.03,4.17]'./sqrt(2);

Head_P_2 = (((Pd_2-Ps))/(rhog))+(zd-zs);*

P_in_2 = V_2.I_2;*

Hyd_P_2 = rho.g.Head_P_2.Q;*

Eff_2 = ((Hyd_P_2)./(P_in_20.92))100;**

T2 = table(Q,Ps,Pd_2,V_2,I_2,Head_P_2,P_in_2,Hyd_P_2,Eff_2);

% At N_3 = 2064 RPM %

Pd_3 = [2.21,2.12,2.08,1.95,1.89,1.75,1.58]'.10e4;*

V_3 = [136.51,136.4,136.38,136.28,136.19,136.1,135.98]'./sqrt(2);

I_3 = [3.45,3.686,3.871,4.128,4.445,4.819,5.076]'./sqrt(2);

Head_P_3 = (((Pd_3-Ps))./(rhog))+(zd-zs);*

P_in_3 = V_3.I_3;*

Hyd_P_3 = rho.g.Head_P_3.Q;*

Eff_3 = ((Hyd_P_3)./(P_in_3.0.92))100;**

T3 = table(Q,Ps,Pd_3,V_3,I_3,Head_P_3,P_in_3,Hyd_P_3,Eff_3);

ylabel('Pump Efficiency[Eeta]','fontsize',12)

legend('Head_P_3','Eff_3','location','northeast','FontSize',12)

legend('boxoff')

grid on

9 .2 TABLES GENERATED USING MATLAB

9 .2.1 SPEED @ 1525 RPM

Q Ps Pd V I P head

P IN

P HYD

Efficiency

2.55E- 04 0.00E+00 1.18E+05 5.09E+01 2.33E+00 1.26E+01 1.18E+02 3.15E+01 2.90E+

3.40E- 04 0.00E+00 1.15E+05 5.15E+01 2.44E+00 1.23E+01 1.26E+02 4.10E+01 3.55E+

5.10E- 04 0.00E+00 1.13E+05 5.09E+01 2.55E+00 1.21E+01 1.30E+02 6.05E+01 5.07E+

6.80E- 04 0.00E+00 1.10E+05 5.08E+01 2.70E+00 1.18E+01 1.37E+02 7.86E+01 6.22E+

8.50E- 04 0.00E+00 9.00E+04 5.08E+01 2.83E+00 9.74E+00 1.44E+02 8.13E+01 6.15E+

1.02E- 03 0.00E+00 7.50E+04 5.02E+01 3.01E+00 8.22E+00 1.51E+ 02 8.22E+01 5.91E+

1.19E- 03 0.00E+00 5.90E+04 5.09E+01 3.14E+00 6.58E+00 1.60E+02 7.69E+01 5.23E+

9 .2. 2 SPEED @ 1 270 RPM

Q Ps Pd V I P head

P IN

P HYD

Efficiency

2.55E- 04 0.00E+00 8.50E+04 4.25E+01 2.23E+00 9.23E+00 9.50E+01 2.31E+01 2.64E+

3.40E- 04 0.00E+00 8.09E+04 4.23E+01 2.34E+00 8.82E+00 9.90E+01 2.94E+01 3.23E+

5.10E- 04 0.00E+00 7.50E+04 4.24E+01 2.45E+00 8.22E+00 1.04E+02 4.11E+01 4.29E+

6.80E- 04 0.00E+00 7.00E+04 4.24E+01 2.59E+00 7.71E+00 1.10E+02 5.14E+01 5.09E+

8.50E- 04 0.00E+ 00 6.00E+04 4.23E+01 2.72E+00 6.69E+00 1.15E+02 5.58E+01 5.28E+

1.02E- 03 0.00E+00 4.90E+04 4.23E+01 2.85E+00 5.56E+00 1.20E+02 5.57E+01 5.02E+

1.19E- 03 0.00E+00 3.00E+04 3.87E+01 2.95E+00 3.63E+00 1.14E+02 4.24E+01 4.03E+

9 .2. 3 SPEED @ 2064 RPM

Q Ps Pd V I P head

P IN

P HYD

Efficiency

2.55E- 04 0.00E+00 2.21E+05 9.65E+01 2.44E+00 2.31E+01 2.35E+02 5.78E+01 2.67E+

3.40E- 04 0.00E+00 2.12E+05 9.64E+01 2.61E+00 2.22E+01 2.51E+02 7.40E+01 3.20E+

5.10E- 04 0.00E+00 2.08E+05 9.64E+01 2.74E+00 2.18E+01 2.64E+02 1.09E+02 4.49E+

6.80E- 04 0.00E+00 1.95E+05 9.64E+01 2.92E+00 2.04E+01 2.81E+02 1.36E+02 5.27E+

8.50E- 04 0.00E+00 1.89E+05 9.63E+01 3.14E+00 1.98E+01 3.03E+02 1.65E+02 5.94E+

1.02E- 03 0.00E+00 1.75E+05 9.62E+01 3.41E+00 1.84E+01 3.28E+02 1.84E+02 6.11E+

1.19E- 03 0.00E+00 1.58E+05 9.62E+01 3.59E+00 1.67E+01 3.45E+02 1.95E+02 6.13E+

9 .2. 4 SPEED @ 1 880 RPM

Q Ps Pd V I P head

P IN

P HYD

Efficiency

2.55E- 04 0.00E+00 1.81E+05 8.49E+01 2.43E+00 1.90E+01 2.07E+02 4.76E+01 2.50E+

3.40E- 04 0.00E+00 1.80E+05 8.48E+01 2.56E+00 1.89E+01 2.17E+02 6.31E+01 3.16E+

5.10E- 04 0.00E+00 1.72E+05 8.47E+01 2.68E+00 1.81E+01 2.27E+02 9.06E+01 4.34E+

6.80E- 04 0.00E+00 1.62E+05 8.46E+01 2.87E+00 1.71E+01 2.42E+02 1.14E+02 5.11E+

8.50E- 04 0.00E+00 1 .51E+05 8.46E+01 3.07E+00 1.60E+01 2.60E+02 1.33E+02 5.57E+

1.02E- 03 0.00E+00 1.39E+05 8.45E+01 3.30E+00 1.47E+01 2.79E+02 1.47E+02 5.74E+

1.19E- 03 0.00E+00 1.20E+05 8.45E+01 3.45E+00 1.28E+01 2.91E+02 1.49E+02 5.57E+