# 5. proportionality. This is evident from the equation given

5.

Discussion of Results  Analysing the charts produced asa result of the experiments conducted for the two turbines (Francis and Peltonturbines), it can be seen that the first part of the line is missing because the measured datawere not obtained in the required volume This isexplained by the fact that the experiments have been affected by some of the errorsthat occurred during the experiment. This affected the data recorded for theseexperiments. In these experiments, the interval data load for both springs was large;in order to get a proper and complete diagram, it is needed to start with onlya small load on the spring and increase this load in small increments. 5.1. Francis turbine 1)Themaximum torque is obtained at the minimum rotor speed. It was observed from theresults of the laboratory work that when the rotor speed increases then torque willbe reduced, as shown in figure 3. At a guide vane setting of 20, the highesttorque is 0.

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219 Nm while the rotor speed is 65.8 Hz, which is the lowest. This reductionin torque is due to the fact that the relationship between these two parametersis one of inverse proportionality. This is evident from the equation givenbelow (1).

Pb=2?Tn;T=Pb/(2?n) (1). 2) It can be seenfrom figure 4 that the maximum power output is increased with a rising rotorspeed. This continues until the power output reaches its maximum. Any furtherrise in rotor speed does not contribute to an increase in the power output. Themaximum power output is 90.

54 W at 65.8 Hz rotor speed. It is the lowest rotorspeed at a guide vane setting of 20.

However, the power output trend is decreased.  3) The maximumefficiency (58.1%) is obtained at a 200 guide vane angle with thesame speed (65.

8 Hz) at which power output is the greatest. It is evident fromformula (1) that the efficiency of the turbine and the power output have aproportional relationship. This means that if the power output of the turbineis increased then the efficiency of the turbine increases accordingly. In addition, fromfigure 5 it can be seen that the turbine efficiency is equal to zero when therotor speed is at a maximum. This is due to the fact that at the maximum rotorspeed the turbine works in idle, therefore there is no power output from theturbine.

There is a flow of water, however, and the turbine rotor will stillspin. Electricity is not produced because of the absence of torque or the loadof the turbines. 4) When the flowrate is reduced, the power output and the maximum efficiency are increased,then both decrease. The maximum efficiency and power output of the turbine arenot directly dependent on the water flow.

5) Analysing theresults obtained from the experiment using the Francis turbine, it can be seenthat the optimum conditions are a rotor speed of 65.8 Hz, a flow rate of 0.014m3/sec, a torque of 0.

219 and a 200 guide vane setting,which allows for maximum turbine efficiency (58.1%) and maximum power output(90.54 W).  5.2. Pelton turbine  1) As shown figure 7, the maximum torque isobtained at the minimum rotor speed.

The highest torque is equal to 0.30 Nm at arotor speed of 17.83 Hz for the lowest inlet head, which is 10 mH20. Thereare two reasons that could explain the relationship between torque and rotorspeed. Firstly, it could be due to the fact that therelation between these two parameters is one of inverse proportionality.

Thisis evident from equation (1). Secondly,according to the equation T = ?Qvr (2) (source data:Pelton), it can be seen that the determination of the torque that therotor speed is not involved. As can be seen from the formula, the torquedepends on the speed of the flow. Therefore, their independence from each otheris clear.

2) From figure 8,it is noticeable that, in general, the maximum power output increases with risingrotor speed. This continues until maximum power output is reached. Any furtherrise in rotor speed does not contribute to an increase in the power output, butrather decreases it.

The maximum poweroutput 34.29 W, which is obtained from the turbine at a 26 Hz rotor speed whilethe inlet head is 15 mH20 (this is taken from the results tablebecause it is not available from the graph). 3) The maximumefficiency is not obtained at the same rotor speed at which maximum poweroutput is obtained. The maximum turbine efficiency (61.65%) is obtained at a rotorspeed of 17.83 Hz at the maximum flow rate (0.000556 m3/sec) whilethe inlet head is 15 mH20.

“Since the input hydraulic power dependsonly on the head and the nozzle area and is independent of the Pelton Wheelspeed then the efficiency is directly proportional to the power output and thusmaximum power and maximum efficiency occur at the same conditions” (PeopleRitEdu,n.d.).  4) When the flowis reduced, the maximum efficiency and the maximum power output rise at a 10 mH20inlet head.

“Pelton turbines/wheels are suitable for power extraction when thewater energy is available at high head and low flow rate” (LearningEngineering, n.d.).  5) Analysing theresults obtained from the experiment with the Pelton turbine, it can be seenthat the optimum conditions for the Pelton turbine are a rotor speed of 17.83Hz, a flow rate of 0.00056 m3/sec, a torque of 0.3 Nm and 10 mH20inlet head, which is the maximum for obtaining the maximum turbine efficiency(61.65%).

6. Conclusion Two experiments wereconducted using the Francis and Pelton turbines. The purpose for conductingthese two experiments was to examine the operation of the Francis and Peltonturbines and determine their operating characteristics.In order to reducethe rotor speed turbine from its maximum speed to its minimum, a Prony brakedynamometer was used for both turbines. The torque was measured by the turbinerotor in different stages. A spear valve was used to vary the volume flow ratethrough Pelton turbine. The data obtained fromthe experiments were used to plot graphs of torque, brake power and overallefficiency versus rotor speed to demonstrate the operating characteristics ofthe Francis and Pelton turbines.From analysing thecharts produced as a result of these experiments, it was noted that during the experiments,the measured data were not obtained in the required volume.

This was perhapsdue to the intervals between the stages of measurement, which were perhaps notoptimal. In turn, this prevented us from conducting the complete analysis ofalmost all graphs, which were effectively halves due to the lack of relevantdata. However, using theavailable data obtained as measured and calculated, graphs were constructed forthe two turbines and the optimum conditions for their operation were determined.The optimum operatingconditions for the Francis turbine are a rotor speed of 65.8 Hz, a flow rate of0.

014 m3/sec, a torque of 0.219 Nm and a 200 guide vanesetting, which is the maximum for obtaining the maximum turbine efficiency(58.1%) and the maximum power output (90.54 W).

For the Peltonturbine, optimum conditions are a rotor speed of 17.83 Hz, a flow rate of0.00056 m3/sec, a torque of 0.3 Nm and a 10 mH20 inlethead, which is the maximum for obtaining the maximum turbine efficiency(61.

65%).