Question

Pelton turbine, with a single jet, is coupled to an alternator with 5 pole pairs and 60 Hz, and is fed through a reservoir whose upper water level is at an elevation of 400 m with reference to the outlet of the turbine. The combined efficiency of the penstock and the injector is 0.9 The characteristic diameter of the turbine is 1.2 m , Kc1 = 0.97 and α1 = 0 The design of the ladles is such that they deflect the jet through an angle of 160° as shown shown in the figure, also due to the friction of these, the relative speed decreases by 15% from the entrance to the exit. The mechanical efficiency is 96% and the velocity of the water at the turbine inlet is 2 m/s.

a) Height of losses due to friction in the impeller

Answer 1

To determine the height of the losses due to friction in the impeller of the Pelton turbine, calculate the total head of the water at the turbine inlet, then substitute the given values into the power output formula and solve for H.

Step-by-step explanation:

In order to determine the height of the losses due to friction in the impeller of the Pelton turbine, we need to consider the energy loss in the system. The efficiency of the penstock and injector is given as 0.9, and the mechanical efficiency is 96%. The velocity of the water at the turbine inlet is 2 m/s.

First, let's calculate the total head of the water at the turbine inlet. The total head (H) is given by:

H = v12 / (2g) + z1

where v1 is the velocity of the water at the turbine inlet, g is the acceleration due to gravity, and z1 is the elevation of the water level at the inlet.

Substituting the given values, we have:

H = (22 / (2 * 9.8) + 400

H = 0.204 m + 400

H ≈ 400.204 m

We can now calculate the power output of the turbine using the formula:

P = ηc * ηm * ρ * Q * g * H

where P is the power output, ηc is the combined efficiency of the penstock and injector, ηm is the mechanical efficiency, ρ is the density of the water, Q is the flow rate, and g is the acceleration due to gravity.

Since we need to find the height of the losses due to friction in the impeller, we can rearrange the formula and solve for H:

H = P / (ηc * ηm * ρ * Q * g)

Substituting the given values, we have:

H = (P / (0.9 * 0.96 * 1000 * Q * 9.8)

H = (P / (0.864 * Q)

Now let's substitute the power output value and solve for H:

H = (________ kW / (0.864 * ________ m3/s)