A Pelton wheel works under a water power of 1.3MW. The hydraulic efficiency of turbine is 95%. Find runner power developed. If mechanical efficiency of turbine is 90%. Find overall efficiency and shaft power of turbine.

To solve the problem regarding the Pelton wheel, we need to break it down into a few steps. We have the hydraulic power, the hydraulic efficiency, and the mechanical efficiency. Let’s tackle each part systematically to find the runner power developed, overall efficiency, and shaft power of the turbine.

Step 1: Calculate Runner Power Developed

The runner power developed by the turbine can be calculated using the hydraulic power and the hydraulic efficiency. The formula for runner power (P_r) is:

P_r = Hydraulic Power × Hydraulic Efficiency

Given:

• Hydraulic Power = 1.3 MW = 1300 kW
• Hydraulic Efficiency = 95% = 0.95

Now, substituting the values into the formula:

P_r = 1300 kW × 0.95 = 1235 kW

This means the runner power developed by the Pelton wheel is 1235 kW.

Step 2: Determine Shaft Power of the Turbine

Next, we need to find the shaft power, which takes into account the mechanical efficiency of the turbine. The formula for shaft power (P_s) is:

P_s = Runner Power × Mechanical Efficiency

Given:

• Mechanical Efficiency = 90% = 0.90

Now, substituting the values:

P_s = 1235 kW × 0.90 = 1111.5 kW

Thus, the shaft power of the turbine is approximately 1111.5 kW.

Step 3: Calculate Overall Efficiency

The overall efficiency of the turbine can be calculated by multiplying the hydraulic efficiency by the mechanical efficiency. The formula for overall efficiency (η_o) is:

η_o = Hydraulic Efficiency × Mechanical Efficiency

Substituting the values:

η_o = 0.95 × 0.90 = 0.855

This means the overall efficiency of the turbine is 85.5%.

Summary of Results

To summarize our findings:

• Runner Power Developed: 1235 kW
• Shaft Power of Turbine: 1111.5 kW
• Overall Efficiency: 85.5%

These calculations illustrate how efficiently the Pelton wheel converts hydraulic energy into mechanical energy, and they highlight the importance of both hydraulic and mechanical efficiencies in turbine performance.