RESULT%
Student number(s):
Surname and initials:
MDUTYULWA V.A
Programme:
B Eng Tech (Mechanical Engineering)
Module name:
HYDRODYNAMIC MACHINES III
M
Module code:
Graduate
Attribute (GA)
assessment:
None
1
H
2
3
Practical/Assignment number:
2
Group number:
2
Due date:
Lecturer:
2
0
2
M
4
3
3
5
6
0
2
7
9
A
8
9
1
10
0
DECLARATION OF OWN WORK:
I, MDUTYULWA VUYO AMBROSE____________________________________, student
number__________________________, hereby declare that the content of this assignment/project is
my own work, as defined and constituted in the Rules and Regulations of the Central University of
Technology, Free State (Please consult the Programme Guide of the Department).
Table of Contents
Aim ................................................................................................................................................................ 4
Summary of theory. ...................................................................................................................................... 4
Apparatus ...................................................................................................................................................... 5
4. Procedure .................................................................................................................................................. 6
5. Experimental data & observations............................................................................................................ 6
5.1. Experimental data........................................................................................................................... 6
5.2. Calculations ..................................................................................................................................... 6
5.3. Summary of experimental and calculated data. ................................................................................ 8
6. graphs........................................................................................................................................................ 8
7. Discussion................................................................................................................................................ 11
8.Conclusion ................................................................................................................................................ 11
9.References ............................................................................................................................................... 12
Aim
The objective of this experiment was to study and investigate how the shaft power, input power, torque,
overall efficiency and the flow rate behaves against the speed of the Pelton wheel and how these
quantities can be utilized in a design process of a Pelton wheel
Summary of theory.
Pelton wheel is classified as a hydraulic reaction turbine whereby a jet of water hits the buckets on the
wheel, this type turbine is used in high head application and it requires less flow rate. When the jet of
water exits the nozzle hits the buckets which causes the wheel to rotates thus producing power.
The operating principle is that water flow the reservoir through the penstock to the inlet of the nozzle,
this process will convert the hydraulic energy to kinetic energy as the water hits the buckets. The
buckets change the direction of the water jet thus result in a moment transfer and all this occurs under
atmospheric pressure. Now the head available is converted into a dynamic head by the nozzle causing
the water jets that strikes the vanes at high force resulting in a rotation of the runner, refer to figure 1.
Pelton wheel
Buckets
Double spherical buckets
Spear valve
Nozzle
Water inlet
Figure 1: water jet striking the buckets.
Courtesy of Engineering tutorials accessed at: https://engineering.myindialist.com/2013/to-studyconstructional-features-of-pelton-turbine-bme-lab-manuals/
The power output of the turbine, is defined as the product of the Pelton wheel’s angular speed and its
torque. Where T is torque in N.m and ω as the angular speed in rad/s.
𝑃𝑜𝑢𝑡 (𝑊) = 𝜔𝑇
𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1.
But in order to find the torque of the wheel, the weight difference between the left and right spring
masses must be determined and be multiplied by brake drum radius r(m).
𝑇(𝑁. 𝑚) = (𝑊1 − 𝑊2 )𝑟
𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2.
To determine the quantity of the input power, equation 3 is utilized, defined as the hydraulic power
which incorporates fluids density 𝜌 (𝑘𝑔/𝑚3 ) , gravitationa; acceleration 𝑔 (𝑚/𝑠 2 ), fluids flow rate
𝑉̇ (𝑚3 /𝑠) and the Head H(m)
𝑃𝑖𝑛 (𝑊) = 𝜌𝑔𝑉̇ 𝐻
𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 3.
The overall efficiency of the turbine measured as the ratio of the power output to power input.
𝜂𝑜 =
𝑃𝑜𝑢𝑡
𝑃𝑖𝑛
𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 4.
Apparatus
The apparatus is designed using solidworks software and is not drawn to scale.
10.Load
adjusting device
1.Spring
scales
3. Turbine
2.Pelton wheel
4. pressure gauge
5.On/off switch
6.Bucket
7. Spear valve
8.Flow control valve
9.Electric motor
and a pump
From the solidworks design of the apparatus, there is 1. Spring balances which scale which measure the
weight applied on the wheel, 4. The pressure gauge measure the inlet pressure head, 7. Spear valve is
used to control the flow rate of the of the water at the turbine inlet, 8. Flow control valve control the
volume flow rate in the pump and lastly, 10. Load adjusting devices is used for applying loads on spring
scales.
4. Procedure
4.1 The apparatus was placed top of the channel of the hydraulic bench.
4.2. Ensuring the pipe of the apparatus is properly coupled to hydraulic bench.
4.3. The pony brake was freed from the drum and each spring balance reading was set to zero.
4.4. The pump was switched on and flow control valve on the hydraulic bench was opened slowly.
4.5. The spear control was adjusted until the turbine operated at full speed.
4.6. The tachometer was used to measure wheel’s speed. The inlet pressure head and then flow rate
was determined by measuring how it took for water to make four liters
4.7. the pony brake was adjusted so that the spring-balance read W1 = 1 N and the speed, flow rate, the
inlet pressure head and the readings on the spring W2 balance were measured.
4.7 Repeat the procedure for the values of W1 shown in the table supplied.
5. Experimental data & observations
5.1. Experimental data
The data in below table is obtained at different loadings W1(N).
Table 1: experimental data.
Readings
Rotational speed (RPM)
W1 (N)
W2 (N)
Drum r (m)
Volume(L)
Time (s)
Pressure Head (m)
1
1907
0
0
0.03
4
23,09
15
2
1682
1
0,2
0.03
4
23,65
15,5
3
1321
2
0,5
0.03
4
28,31
15,5
4
1074
3
0,7
0.03
4
28,57
14,5
5
678,8
4
1
0.03
4
27,4
14,5
5.2. Calculations
For demonstration purposes, a set of calculations performed below are based on data reading 1 as
shown in table 1.
5.2.1. converting the rotational speed to angular speed

1907 rev 1 min 2rad


 199.701rad / s
min
60s
1
5.2.2. Calculating torque using equation 2;
T  W1  W2 r
T  0  0.0.03  0 N .m
6
425,5
5
1,4
0.03
4
26,5
15
5.2.3. using values from subsections 5.2.1 and 5.2.2 to determine the power output as defined by
equation 1.
Pout  T  199.701 0  0W
5.2.4. calculating the volume flow rate using the measured time and volume.
.
V
Volume(l )
4

time( s)
23.09
.
V  0.1732 L / s  0.1732  10 3 m 3 / s
Although the summarized calculated may display the flow rate in L/s the calculation in the section
bellows uses the flow rate strictly in cubic meter per second.
5.2.5. the power input using equation 3, flow rate from subsection 5.2.4 and the inlet pressure head.
.
Pin  g V H
Pin  998kg / m 3  9.81m / s 2  0.1732m 3 / s  15m
Pin  25.4406W
5.2.6. Overall efficiency using equation 4;
O 
Pout
0
 100 
 100  0
Pin
25.4406
By the repeating the calculation from subsection 5.2.1. to 5.2.6 a summary of calculated quantities is
represented in table 2 in section 5.3 below, it is imported from the Microsoft excel spreadsheet.
5.3. Summary of experimental and calculated data.
Since the calculations were based the on the data obtained experimentally, the table can be
summarized as follows.
Table 2: summary of calculated and experimental data.
Reading
R.p.m
w (rad/s)
W1(N)
W2(N)
W1-W2(N)
Drum r (𝒎 × 𝟏𝟎−𝟑 )
Torque (N.m)
P out(W)
Volume(L)
time
vol (l/s)
flow rate (m3/s)
Pressure Head (m)
P in(W)
efficiency %
1
1907
199.7007
0
0
0
30
0
0
4
23.09
0.173235
0.000173
15
25.44057
0
2
1682
176.1387
1
0.2
0.8
30
0.024
4.2273
4
23.65
0.169133
0.000169
15.5
25.66611
16.47047
3
1321
138.3349
2
0.5
1.5
30
0.045
6.2251
4
28.31
0.141293
0.000141
15.5
21.44131
29.03306
4
1074
112.4691
3
0.7
2.3
30
0.069
7.7604
4
28.57
0.140007
0.00014
14.5
19.87547
39.04495
5
678.8
71.0838
4
1
3
30
0.09
6.3975
4
27.4
0.145985
0.000146
14.5
20.72416
30.86997
6
425.5
44.5583
5
1.4
3.6
30
0.108
4.8123
4
26.5
0.150943
0.000151
15
22.1669
21.70937
6. graphs
The graphs below were plotted using the data from table 2.
6.1. Graph of the shaft power (power output) versus bucket speed of the wheel (angular speed).
Shaft power VS angular speed
9
Shaft power P out(W)
8
7
6
5
4
3
2
1
0
0
50
100
150
angular speed (rad/s)
200
250
Graph 1: Power output versus wheel speed.
6.2. graph of the power input versus the wheel speed.
Input power VS angular speed
30
Input power(W)
25
20
15
10
5
0
0
50
100
150
200
250
Angula speed(rad/s)
Graph 2: Power input versus wheel speed.
6.3. Graph of torque versus the wheel speed.
Torque VS angular speed
0,12
Torque(N.m)
0,1
0,08
0,06
0,04
0,02
0
0
50
100
150
Angular speed (rad/s)
Graph 3: Torque versus wheel speed.
6.4.the graph of the overall efficiency versus wheel speed.
200
250
Overall efficiency VS angular speed
0,45
0,4
0,35
Efficiency
0,3
0,25
0,2
0,15
0,1
0,05
0
0
50
100
150
200
250
Angular Speed(rad/s)
Graph 4: Overall efficiency versus wheel speed.
6.5. the graph of the flow rate versus wheel speed.
Flow rate VS angular speed
0,2
Volume floe rate(L/s)
0,18
0,16
0,14
0,12
0,1
0,08
0,06
0,04
0,02
0
0
50
100
150
200
Angular speed(rad/s)
graph 5: volume flow rate versus wheel speed.
250
7. Discussion
From the curves plotted in section 6, there are curves that are similar in shape, the curve of output
power versus speed is similar to that one of overall efficiency versus angular speed, this similarity
solidifies the existing relationship between overall efficiency and the output that is they are
proportional, these quantities reach their peaks at the approximately same angular speed, and they
have zero values when the angular speed is running that maximum.
Similar to graph 5 and graph 2, They produce similar curve. This is simply because the power input is also
defined as the hydraulic power which is the power produced by the water as such, the input power is
dependent on the volume flow rate of the water, an increase in the volume flow rate will definitely
increase the input power due to the intensity of the force.
And lastly for graph 3, it can be observed that torque in inversely proportional to the wheel’s angular
speed, this is concluded due to the fact the when torque is at maximum (the loads applied on the wheel)
the wheel’s angular speed is at the minimum and the wheel will continue running at maximum speed
when there’s no load applied on the it.
8.Conclusion
The objective of the experiment was successfully achieved, the shape of the curves plotted in section 6
shows the slight margin error as to how smooth these curves should be however these curves can be
improved my implementing the use of the digital data recording devices in the apparatus so to avoid
having constraint such as human error, overall, I was able to see the principle of how a Pelton wheel
operates and principles should be considered in the process of the designing a hydro plant.
9.References

Hochstein, J.I. and Gerhart, A.L., 2021. Young, Munson and Okiishi's A Brief Introduction to Fluid
Mechanics. John Wiley & Sons.

Kumar, Er.A. (2021) Pelton wheel turbine: Definition, parts, working principle, advantages,
application [Notes & PDF], THEMECHANICALENGINEERING.COM. Available at:
https://themechanicalengineering.com/pelton-wheel-turbine/ (Accessed: 06 September 2023).

Hung, J. and Altuger-Genc, G., 2018. Development of Assessment Plan for Online Thermo-Fluid
Science Courses. Development, 9(3).