Question

Two jets strike the buckets of a pelton wheel, which is having a shaft power is 15450 kw. The diameter of each jet is given as 200 mm. If the net head on the turbine is 400 m, find the overall efficiency of the turbine.

Answer 1

Answer:

The answer and solution in the attachment.

Answer 2

Answer:

The overall efficiency = 141.3%

Explanation:

From the above question,

To find the overall efficiency of the Pelton wheel turbine, we can use the following formula:

Overall efficiency = ( Shaft power output / Water power input  ) x 100%

The water power input can be calculated using the following formula:

Water power input = (Density of water) x (Volume flow rate) x                         (Acceleration due to gravity) x (Net head)

The volume flow rate can be calculated using the following formula:

        Volume flow rate = (Area of jet) x (Velocity of jet)

The area of the jet can be calculated using the formula for the area of a circle:

        Area of jet = pi x $(diameter of jet / 2)^2$

The velocity of the jet :

Velocity of jet = $(2gh)^{0.5$

Here,

 h - net head and

 g - acceleration due to gravity.

            Area of jet = pi x $(2gh)^{0.5$ = 31416 m$m^2$

       Velocity of jet = (2 x 9.81 m/$s^2$ x 400 $m)^{0.5$

                               = 89.05 m/s

 Volume flow rate = 31416 m$m^2$ x 89.05 m/s = 2.797 $m^3/s$

Water power input = 1000 kg/$m^3$ x 2.797 $m^3/s$ x 9.81 $m/s^2$ x 400 m

                                = 10.938 MW

Shaft power output = 15.45 MW

                                = 15,450 kW

To calculate the overall efficiency:

Overall efficiency = (15450 kW / 10,938 kW) x 100%

                             = 141.3%

The overall efficiency = 141.3%

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