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MEHB221 Fluid Mechanics Lab 2012
1
Experiment No. 1
PERFORMANCE OF PELTON WHEEL TURBINE
Objective
To investigate the performance of the Pelton Wheel turbine with different range of flow
rates and rotational speeds.
Summary of theory
Pelton Wheel turbine is an impulse type of hydraulic turbine. The total drop in pressure
of the fluid takes place in stationary nozzles. A proportion of the kinetic energy of a high
velocity jet is converted into mechanical work delivered to the shaft, the remainder being
dissipated by fluid friction and partly retained as kinetic energy of fluid leaving the cups.
The fluid transfers its momentum to buckets mounted on the circumference of a wheel.
Pelton Wheel or impulse type hydraulic turbine is used in hydroelectric scheme when the
head available exceeds about 300m. The turbine is supplied with water under high head
through a long conduit called penstock. The water is then accelerated through a nozzle
and discharge at high-speed free jet at atmospheric pressure, which then impinges the
cascade of impulse buckets.
Control Volume
Consider Pelton Wheel rotating in an anti-clockwise direction (refer to figure 2) with an
angular velocity, ω, due to the combined action of an incident water jet and a clockwise
resisting moment τ. We take a control volume that is moving at a constant velocity with
the bucket on the Pelton Wheel as shown in figure 3.
The velocity of the incident jet relative to the bucket is given by: -
Vr1 = V1 - U
= V1 - ωR
Where R is the mean radius of the wheel.
Since the incident and emergent jets are both exposed to atmospheric pressure, the
magnitude of the emergent jet will be only slightly less than the frictional resistance
which can be allowed for by introducing a frictional resistance coefficient k1 so that: -
Vr2 = K1Vr1
MEHB221 Fluid Mechanics Lab 2012
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The jet will be deflected so that the emergent jet is at an acute angle θ to the incident jet.
The change in the component of relative velocity in the plane of the wheel (i.e. in the line
of the incident jet) will be: -
∆Vr = Vr1 + Vr2 Cos θ
= Vr1 (1 + k1 Cos θ)
= (V1 – U) (1 + k1 Cos θ)
Which can be written as:
∆Vr = (V1 – U) (1 + c)
Flow Discharge
The discharge through the nozzle, Q from an inlet height H at pressure P is given by:
H = P/ρg
Q = AnV1
Where An is the nozzle opening area. But,
Hence,
Where Cv is the nozzle flow coefficient.
Power Output
Using the force-momentum equation, the force, F exerted on the bucket by the water jet
is given by:
F = ρQ∆Vr
The torque acting on the shaft of the Pelton Wheel is then:
τ = FR
= ρQ∆VrR
gH2CV v1 =
gH2CAQ vn=
MEHB221 Fluid Mechanics Lab 2012
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And the power output, Wout is:
Wout = τω
= ρQ∆VrU
Substituting for ∆Vr gives:
Wout = ρUQ (V1 – U) (1 + k1 Cos θ)
Efficiency
The input hydraulic power, Win to the Pelton Wheel is the product of the inlet pressure
and flow rate.
Win = PQ
= ρgHQ
and the efficiency of the Pelton Wheel is
η = Wou t/ Win
= U∆V / gH
Procedures
In this experiment, we will fix the flow rate and gradually varying the brake load from
zero load to a maximum load. The speed is influenced by the coefficient of friction
between the band and the shaft pulley, which is influenced by temperature; therefore, it is
necessary at each condition to wait for the speed to stabilize before taking readings. The
torque produced can be then determined knowing the force applied and the wheel speed.
The experiment will be repeated for 3 different flow rates (3 different pressure values).
1. Zero the tension gauge at no load.
2. Prepare the friction band and weight hanger (weighing 350g) of the friction
dynamometer.
3. Make sure that the suction valve and volumetric measuring valve are open (in line).
4. Fully open the bench flow-regulating valve.
5. Switch on the Hydraulic Bench pump.
6. Slowly increases the pump speed regulator until maximum (the ‘white-line’ pointed
to the downward direction).
7. Adjust the nozzle spear valve until the inlet pressure reads approximately 0.8 bar.
8. Wait until the condition has stabilized.
9. Record the weight (i.e. 350g) and the reading of the tension gauge.
10. Using the non-contact optical tachometer, measure the speed of rotation of the wheel
in rpm. Point the light beam to a position least affected by the water in order to obtain
MEHB221 Fluid Mechanics Lab 2012
4
better accuracy. At low speed, the variation in the reading will be quite significant.
(call the instructor to use the optical tachometer)
11. Add another 100 grams weight and repeat steps 8 to 10.
12. Repeat 11 in the step of 100 grams until the wheel stall (the wheel stop rotating).
13. Remove all the weight from the hanger.
14. Measure the flow rate. To measure the flow rate, close the volumetric measuring
valve and note the time taken for the water to fill a certain volume using the scale
(take 10 liters).
15. Open back the volumetric measuring valve.
16. Adjust the nozzle spear valve until the inlet pressure is approximately 1.0 bar and
repeat steps 8 to 15.
17. Adjust the nozzle spear valve until the inlet pressure is approximately 1.2 bar and
repeat steps 8 to 15.
18. Switch off the hydraulic bench pump.
Data, Observation and Results
• Record the results of the experiment on the results sheet provided.
• Calculate the inlet head (H), the discharge or flow rate (Q) and the power input (Win).
Where ρ = 1000 kg/m3
g = 9.81 m/s2
• Calculate the measured torque (τm), the measured power output (Wout,m) and the
measured efficiency (ηm).
Where W = Applied weight in grams
S = Tension gauge reading in grams
Rd = Radius of dynamometer wheel
= 0.03 meter
60xt
VolQ =
[ ]dm gRx1000
)SW( −=τ
WattQxPx
Win
60
)10)(10( 35 −
=
mg
)10Px(H
5
ρ=
MEHB221 Fluid Mechanics Lab 2012
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ηm = Wout,m / Win
• Calculate the theoretical values of output torque (τth), power output (Wout,th) and
efficiency (ηth).
Where K1 = 0.8
θ = 25o
ηth = Wout,th / Win
• Calculate the velocity ratio U/V1.
Where R = 0.05m
Cv = 0.94
• Plot the graph of measured power against wheel speed for all conditions. (All three
conditions on the same graph – Graph 1)
• Plot the graph of measured efficiency against wheel speed for all conditions. (All
three conditions on the same graph – Graph 2)
Analysis and Discussion
• Explain the working principle of Pelton Wheel Turbine.
• Comment on Graph 1 and Graph 2.
• Discuss the performance of the Pelton Wheel turbine with respect to different range
of flow rates and different range of rotational speeds.
• List the possible sources of errors and safety precaution.
Watt60
2W
mm,out
πωτ=
( )Rcosk160
2R)gH2(C
60
10Qx1v
3
th θ+
πω−
ρ=τ
−
WattWth
thout
60
2,
πωτ=
[ ] Watt60
2x
gH2C
R
V
U
v1
πω=
MEHB221
Figure 1:
Figure 3:
Fluid Mechanics Lab
6
Figure 1: Detail of Pelton Wheel Buckets
Figure 2: Absolute Velocities
Figure 3: Velocities Relative to Bucket
2012
MEHB221
Figure 4: General Arrangement of Cussons Pelton Wheel
Fluid Mechanics Lab
7
General Arrangement of Cussons Pelton Wheel
2012
MEHB221 Fluid Mechanics Lab 2012
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Example of Result Table
Inlet pressure P = ___________bar
Inlet Head H = ___________ m
Volume of water collected Vol = ___________ liter
Time taken t = ___________ s
Discharge Q = ___________ liter/min
Power Input Win = ___________ Watt
Weight
W
(g)
Tension
S
(g)
Speed
ω (rpm)
Measured
Torque
τm (Nm)
Measured
Power Out
Wout,m
(Watt)
Measured
Efficiency
ηm
Theoretical
Torque
τth (Nm)
Theoretical
Power Out
Wout,th
(Watt)
Theoretical
Efficiency
ηth
U/V1
350
450
550
650
750
850
950
1050
1150
1250
1350
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