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. πππ’π‘ (π) = ππ πππ’ππ‘πππ 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). π(π. π) = (π1 − π2 )π πππ’ππ‘πππ 2. To determine the quantity of the input power, equation 3 is utilized, defined as the hydraulic power which incorporates fluids density π (ππ/π3 ) , gravitationa; acceleration π (π/π 2 ), fluids flow rate πΜ (π3 /π ) and the Head H(m) πππ (π) = πππΜ π» πππ’ππ‘πππ 3. The overall efficiency of the turbine measured as the ratio of the power output to power input. ππ = πππ’π‘ πππ πππ’ππ‘πππ 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 ο·ο½ 1907 rev 1 min 2ο°rad ο΄ ο΄ ο½ 199.701rad / s min 60s 1 5.2.2. Calculating torque using equation 2; T ο½ ο¨W1 ο W2 ο©r T ο½ ο¨0 ο 0.ο©0.03 ο½ 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 ο½ ο·T ο½ 199.701ο΄ 0 ο½ 0W 5.2.4. calculating the volume flow rate using the measured time and volume. . Vο½ Volume(l ) 4 ο½ time( s) 23.09 . V ο½ 0.1732 L / s ο½ 0.1732 ο΄ 10 ο3 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 ο½ ο²g V H Pin ο½ 998kg / m 3 ο΄ 9.81m / s 2 ο΄ 0.1732m 3 / s ο΄ 15m Pin ο½ 25.4406W 5.2.6. Overall efficiency using equation 4; ο¨O ο½ Pout 0 ο΄ 100 ο½ ο΄ 100 ο½ 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 (π × ππ−π ) 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 ο· Hochstein, J.I. and Gerhart, A.L., 2021. Young, Munson and Okiishi's A Brief Introduction to Fluid Mechanics. John Wiley & Sons. ο· 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). ο· Hung, J. and Altuger-Genc, G., 2018. Development of Assessment Plan for Online Thermo-Fluid Science Courses. Development, 9(3).