5. proportionality. This is evident from the equation given

5. Discussion of Results

Analysing the charts produced as
a result of the experiments conducted for the two turbines (Francis and Pelton
turbines), it can be seen that the first part of the line is missing because the measured data
were not obtained in the required volume This is
explained by the fact that the experiments have been affected by some of the errors
that occurred during the experiment. This affected the data recorded for these
experiments. 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 only
a small load on the spring and increase this load in small increments.

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5.1. Francis turbine

1)The
maximum torque is obtained at the minimum rotor speed. It was observed from the
results of the laboratory work that when the rotor speed increases then torque will
be reduced, as shown in figure 3. At a guide vane setting of 20, the highest
torque is 0.219 Nm while the rotor speed is 65.8 Hz, which is the lowest. This reduction
in torque is due to the fact that the relationship between these two parameters
is one of inverse proportionality. This is evident from the equation given
below (1).

Pb=2?Tn;
T=Pb/(2?n) (1).

2) It can be seen
from figure 4 that the maximum power output is increased with a rising rotor
speed. This continues until the power output reaches its maximum. Any further
rise in rotor speed does not contribute to an increase in the power output. The
maximum power output is 90.54 W at 65.8 Hz rotor speed. It is the lowest rotor
speed at a guide vane setting of 20. However, the power output trend is decreased.

3) The maximum
efficiency (58.1%) is obtained at a 200 guide vane angle with the
same speed (65.8 Hz) at which power output is the greatest. It is evident from
formula (1) that the efficiency of the turbine and the power output have a
proportional relationship. This means that if the power output of the turbine
is increased then the efficiency of the turbine increases accordingly. In addition, from
figure 5 it can be seen that the turbine efficiency is equal to zero when the
rotor speed is at a maximum. This is due to the fact that at the maximum rotor
speed the turbine works in idle, therefore there is no power output from the
turbine. There is a flow of water, however, and the turbine rotor will still
spin. Electricity is not produced because of the absence of torque or the load
of the turbines.

4) When the flow
rate is reduced, the power output and the maximum efficiency are increased,
then both decrease. The maximum efficiency and power output of the turbine are
not directly dependent on the water flow.

5) Analysing the
results obtained from the experiment using the Francis turbine, it can be seen
that the optimum conditions are a rotor speed of 65.8 Hz, a flow rate of 0.014
m3/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 is
obtained at the minimum rotor speed. The highest torque is equal to 0.30 Nm at a
rotor speed of 17.83 Hz for the lowest inlet head, which is 10 mH20. There
are two reasons that could explain the relationship between torque and rotor
speed. Firstly, it could be due to the fact that the
relation between these two parameters is one of inverse proportionality. This
is 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 the
rotor speed is not involved. As can be seen from the formula, the torque
depends on the speed of the flow. Therefore, their independence from each other
is clear.

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

The maximum power
output 34.29 W, which is obtained from the turbine at a 26 Hz rotor speed while
the inlet head is 15 mH20 (this is taken from the results table
because it is not available from the graph).

3) The maximum
efficiency is not obtained at the same rotor speed at which maximum power
output is obtained. The maximum turbine efficiency (61.65%) is obtained at a rotor
speed of 17.83 Hz at the maximum flow rate (0.000556 m3/sec) while
the inlet head is 15 mH20. “Since the input hydraulic power depends
only on the head and the nozzle area and is independent of the Pelton Wheel
speed then the efficiency is directly proportional to the power output and thus
maximum power and maximum efficiency occur at the same conditions” (PeopleRitEdu,
n.d.).

4) When the flow
is reduced, the maximum efficiency and the maximum power output rise at a 10 mH20
inlet head. “Pelton turbines/wheels are suitable for power extraction when the
water energy is available at high head and low flow rate” (Learning
Engineering, n.d.).

5) Analysing the
results obtained from the experiment with the Pelton turbine, it can be seen
that the optimum conditions for the Pelton turbine are a rotor speed of 17.83
Hz, a flow rate of 0.00056 m3/sec, a torque of 0.3 Nm and 10 mH20
inlet head, which is the maximum for obtaining the maximum turbine efficiency
(61.65%).

6. Conclusion

Two experiments were
conducted using the Francis and Pelton turbines. The purpose for conducting
these two experiments was to examine the operation of the Francis and Pelton
turbines and determine their operating characteristics.

In order to reduce
the rotor speed turbine from its maximum speed to its minimum, a Prony brake
dynamometer was used for both turbines. The torque was measured by the turbine
rotor in different stages. A spear valve was used to vary the volume flow rate
through Pelton turbine.

The data obtained from
the experiments were used to plot graphs of torque, brake power and overall
efficiency versus rotor speed to demonstrate the operating characteristics of
the Francis and Pelton turbines.

From analysing the
charts 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 perhaps
due to the intervals between the stages of measurement, which were perhaps not
optimal. In turn, this prevented us from conducting the complete analysis of
almost all graphs, which were effectively halves due to the lack of relevant
data.

However, using the
available data obtained as measured and calculated, graphs were constructed for
the two turbines and the optimum conditions for their operation were determined.

The optimum operating
conditions for the Francis turbine are a rotor speed of 65.8 Hz, a flow rate of
0.014 m3/sec, a torque of 0.219 Nm and a 200 guide vane
setting, which is the maximum for obtaining the maximum turbine efficiency
(58.1%) and the maximum power output (90.54 W).

For the Pelton
turbine, optimum conditions are a rotor speed of 17.83 Hz, a flow rate of
0.00056 m3/sec, a torque of 0.3 Nm and a 10 mH20 inlet
head, which is the maximum for obtaining the maximum turbine efficiency
(61.65%).