CENTRIFUGAL PUMP
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CENTRIFUGAL PUMP
Objectives
1.
At constant pump speed, determine the characteristic curve (pressure
change vs. flow rate) of a centrifugal pump.
2.
At constant pump speed, determine the efficiency as a function of flow
rate for a centrifugal pump.
3.
At constant speed, determine the efficiency as a function of power output
for an electric motor.
Theory
A pump is a device for supplying energy to a fluid. The effect of supplying
energy can be studied via the mechanical energy equation.
 2
P 
g
∆ E + ∆   +
∆z + ∆ v
gc
ρ 
 2 α gc

 + ∑ F = Qh - W s


This equation neglects all shearing stresses. Note: all nomenclature is defined at the end
of the section.
In general, the power originates from a pressure change (P 2 > P 1), a change in
kinetic energy (v 22 > v 12), a change in level (z 2 > z 1), or as friction ( ΣF ). Since friction
is always present in mechanical devices, the energy supplied goes partly into friction and
the rest to one of the other effects cited.
For the pump used in the present experiment, the following assumptions are
made.
- ∆E = 0
- ∆v 2 = 0
- Qh= 0
- ∆z = 0
no internal energy change
no kinetic energy change
no heat generated or lost
no significant height change
The energy balance simplifies to
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P
Total Head = - W s = ∑ F + ∆ 
ρ



Thus, the actual shaft work done (W s) is the total work (W T ) minus friction losses
W s = WT - ∑ F
Net Positive Suction Head (NPSH)
NPSH = difference between the static head at the suction inlet and the head at the
inlet at the vapor pressure.
2

NPSH =  P 2 + v2
2 α gc
 ρ

 - PvOVER ρ


or

g
NPSH =  P1 + z 1 - ∑ F
gc
 ρ
 Pv
  ρ

or
2

NPSH =  P3 + v3
2 α gc
 ρ
 Pv
  ρ

Cavitation
At very large flow rates, the pressure (P 3) developed at the undersides of the
blades or positions close to the eye of the impeller blades becomes very small.
-3
If P 3 < P vap
⇒
Bubbles form.
The bubbles form at the low pressure areas, move to the high pressure areas (tip of
impeller blades), and collapse. This collapse causes microjets orientated toward the blade
at extremely high pressures (>10,000 atm). This impact (or cavitation phenomena)
causes severe erosion or erosion/corrosion (in a corrosive medium) of the impeller
blades. Noise and vibration are detected in the pump.
Power (in Watts or Hp) =
Energy (J)
Time (s)
Horsepower (Hp)
Fluid Hp (P f): This is the liquid Hp delivered by the pump (also known as the
P f = Q ∆P = Q x TDH x ρ
hydraulic Hp).
Brake Hp (P b): This is the actual Hp delivered to the pump shaft (also called
Pb = 2 π N Ω =
Q x TDH x ρ
η
“pump input”).
Pe = W
Electric Motor Hp (P e): The electrical Hp delivered by the pump.
Note: Hp = 550 ft-lb f /s = 33,000 ft-lb f /min = 745.67 Watts
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Efficiency (η
η)
In general, the efficiency of a pump is defined as:
η=
Output
Work done by the pump
x 100 =
x 100
Input
Electrical energy supplied by the pump
The numerator is the head supplied by the pump.
P
η m = b x 100
Pe
Motor (η
η m):
ηp =
Pf
x 100
Pb
ηo =
Pf
x 100
Pe
Pump (η
η p):
Overall (η
η o):
Affinity Laws
Known characteristics at one impeller diameter or speed extrapolate to some other
D or N.
Q1
N
= 1
Q2
N2
A.



2
B.
H1 =  N1

H2
 N2



3
C.

Pb1
=  N 1
P b2
 N2
Case I: Impeller diameter (D) = constant
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Case II: Pump Speed (N) = constant
A.
Q1
= D1
Q2
D2
2
B.
H 1 =  D1 


H2
 D2 
3
C.


Pb1
=  D1 
Pb2
 D2 
Acceleration and Deceleration
A centrifugal pump is a device which supplies mechanical energy to a fluid by
accelerating it radially outward and also circumferentially. The sudden reduction in
radial velocity as the casing is encountered plus the equally sudden reduction in
circumferential velocity as the fluid enters the discharge line has the net effect of
increasing the pressure. Thus, the equation of energy can be visualized in two steps.
 2
- W s = ∆ v
 2 α gc
P
∆ 
ρ

 + ∑F


 2

 = - ∆ v

 2 α gc

 - ∑F


Acceleration
Deceleration
In a centrifugal pump, the frictional term arises from a combination of factors:
1.
Friction between the impeller and fluid
2.
Friction between the casing and fluid
3.
Shock losses associated with rapid acceleration and deceleration.
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Friction between the impeller and fluid tends to be greatest at low flow rates, while
friction between the casing and fluid tends to be greatest at high flow rates. Shock losses
tend to be very severe at low flow rates and less severe at high flow rates. Depending on
the actual pump design, shock losses will also tend to be a minimum at some intermediate
flow rate, and the total effect of the three losses on the efficiency is to produce an
intermediate flow range of maximum efficiency. In selecting a pump, this flow rate
range should match the intended operating range. In addition to fluid losses, all pumps
show mechanical losses which generally vary with pump speed. Since the shaft work
includes these losses, the efficiency is also affected by these mechanical losses.
Nomenclature
D
E
ΣF
g
gc
H
m
N
NPSH
Ns
P
Pb
Pe
Pf
Power
P vap
Q
Qh
TDH
v
W
Ws
WT
z
α
γ
ρ
Ω
η
ηm
ηo
ηp
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Impeller diameter (ft)
Internal energy (lb f -ft/lb m)
Sum of all frictional forces (lb f -ft/lb m)
Gravitational force constant (32.2 ft/s 2)
Gravitational conversion factor (32.2 lb m-ft/lb f -s 2)
Total head (ft)
Mass flow rate (lb m /s)
Pump speed (rpm)
Net positive suction head (ft)
Specific speed (complex units)
Pressure from DP cell (inches of Hg)
Brake horsepower (Hp)
Electric horsepower (Hp)
Fluid horsepower (Hp)
Power (ft-lb f /s)
Vapor pressure (lb f /in 2)
Volumetric flow rate or capacity (gal/min or gal/s)
Heat generated (lb f -ft/lb m)
Total Dynamic Head (ft)
Fluid velocity (ft/s)
Wattage (Watts)
Shaft work (ft-lb f /lb m)
Total work (ft-lb f /lb m)
Height (ft)
Kinetic energy correction factor
=
Specific gravity
=
Density (lb m /gal)
=
Torque (lb f -ft/rad)
=
Efficiency
=
Motor efficiency
=
Overall efficiency
=
Pump efficiency
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EXPERIMENTAL EQUIPMENT
Caution:
Do not operate the pump dry. Do not operate the pump with valve
V-3 closed.
The main elements of the system are a centrifugal pump, a rotameter to measure
flow, a valve to control flow, a differential pressure (DP) cell to measure pressure, and a
reservoir, as shown in the figure below. The pump is driven by an electric motor, and the
shaft connecting the motor to the pump is provided with a torque indicator. The motor is
provided with a speed controller and tachometer.
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In operating the equipment, it is necessary that the intake from the reservoir should be at
least 6 inches above the intake. The liquid should also be clean and free of sediment. At
start-up and at other times (as indicated by the next paragraph), air may be in the lines.
This will be observed as air bubbles flowing through the rotameter. Do not attempt to
make any measurements as long as air bubbles are observed. If the problem does not
clear up after a few minutes of operation, the system has a leak and is in need of repair.
In normal operation, the speed is to be controlled using the speed controller and
tachometer, flow is to be controlled using valve V-3, pressures are to be determined from
the DP cell readings, torque is to be measured from the torque meter employing a strobe
light, and flow is to be determined from the rotameter reading.
Speed Control
The speed control regulates the motor rpm’s. To start the motor, set the control to
zero, and flip the on-off switch to on. Flip the brake switch to forward, and adjust the
control until the desired speed is indicated on the tachometer readout.
Flow Control
The valve V-3 controls the flow. With the pump in operation, adjust the valve to
produce the flow rate desired, as indicated by the rotameter float.
DP Cell
The DP cell works by detecting a pressure difference between two points before
and after the pump. The reading is in inches of mercury (note: an offset may need to be
subtracted from the measurement). Maximum full scale reading: 30 inches Hg.
Torque Meter
The torque meter is provided with a vernier scale and indicates torque in lbf -in. A
stroboscopic light is necessary for reading the meter and this stroboscope should also be
used to check the indicated motor speed in rpm’s.
Rotameter
The rotameter reads flow rate directly in gallons per minute for a fluid having a
specific gravity of 1.0. If water is used, flow can be read directly from the rotameter.
The rotameter reading is obtained from the position of the widest part of the float.
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Wattmeter
The wattmeter allows measurement of electrical power input to the motor.
Determine the appropriate k factor based on the wiring of the wattmeter. The k factors
can be located in the lid of the wattmeter. Do not make any changes in the existing
connections.
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EXPERIMENTAL PROCEDURE
1.
Check the DP cell, tachometer, and torque meter to see if they are zeroed
properly. If not, correction or service are needed.
2.
Fill the reservoir to at least 6 inches above the intake to the pump.
Submergence of the return line is desirable.
3.
Make sure valve V-3 is slightly open.
4.
Set the speed control to zero.
5.
Flip the speed control on-off switch to on.
6.
Flip the brake switch to forward.
7.
Adjust the speed control to produce the desired pump speed (rpm), as
indicated on the tachometer.
8.
Adjust the valve V-3 to obtain the desired flow rate, as indicated by the
rotameter.
9.
Read the DP cell.
10. Read the torque on the torque meter using the strobe light. Read the
wattmeter. Determine if a correction factor k is needed for wattmeter
conversions.
11. Using the strobe light, read the pump speed as a check on the tachometer.
12. Repeat steps 8-11 so as to obtain at least 10 data points covering the
maximum range attainable.
13. Repeat steps 7-12 so as to obtain at least 5 data sets covering the range 8001800 rpm.
14. Repeat holding valve wide open, and vary RPM to get at least 10 more data
points.
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SAMPLE DATA SHEET
Run
Number
Flow Rate
(gal/min)
DP Cell
Reading
Wattmeter
(Watts)
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Torque
(lb f -in)
Speed
(rpm)
MINIMUM REPORT REQUIREMENTS
1.
For each speed chosen, determine the electric hp, brake hp, fluid hp, motor
efficiency, pump efficiency, overall efficiency, and specific speed at each
flow rate.
2.
For each speed, plot head vs. flow rate (plot all speed plots on one graph).
3.
For each speed, plot pump efficiency vs. flow rate (plot all speed plots on one
graph).
4.
For each speed, plot log pump efficiency vs. log brake hp at one flow rate
(choose one flow rate that is available at all speeds).
5.
From the literature, find out the relationship between head as a function of
speed (rpm) as well as between brake hp and speed. Use linear regression on
log plots for points constructed from all possible combinations (=45 points
from part 14) to compare these relationships with your data. Use 95%
confidence intervals to compare your data to the affinity law coefficients
6.
Discuss briefly the conditions under which any of the above might be used to
establish the optimum performance level.
7.
Discuss whether it is always most advantageous to use the highest rotational
speed for (a) centrifugal pumps in general and (b) the pump you used in the
lab.
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