Impulse Turbines

Establish a relationship between the speed of the jet and the speed of the wheel of a Pelton turbine considering maximum efficiency.

A Pelton wheel is working under a head of $250 \text{ m}$ developing $1000 \text{ kW}$ at $300 \text{ rpm}$. The overall efficiency of the turbine is $85$ and the coefficient of the nozzle is $0.98$. The velocity ratio is $0.46$; determine the diameter of the wheel and diameter of the jet, and the size of bucket and number of buckets.

State and deduce the Euler's equation of work done for fluid machinery form the RTT's.

Design a Pelton wheel for the following data: Head of water = 150 m, power to be developed = 600 kW and speed of the wheel = 360 rpm. Assume, reasonably, the missing data.

Why is Pelton wheel called an impulse turbine? Derive the equation for the maximum efficiency of a Pelton wheel.

A Kaplan turbine operating under a net head of 20 m developed 36750 kW win an overall efficiency of 86%. The speed ratio is 2 and the flow ratio 0.69. The hub diameter of the wheel is 0.35 times the outside diameter of the wheel. Find the diameter and speed of the turbine.

Derive Euler’s equation of energy transfer in rotodynamic machines.

Design a Pelton wheel for a head of $150\text{ meters}$ at a speed of $360\text{ rpm}$. Power to be developed by the turbine is $600\text{ kW}$. Assume the overall efficiency of the wheel as $85$.

Prove that the hydraulic efficiency of a Pelton wheel turbine is maximum when the jet velocity striking the runner is twice the tangential velocity of the runner.

A Pelton wheel is to be designed for a head of $60\text{ m}$ when running at $200\text{ rpm}$. The Pelton wheel develops $95.647\text{ kW}$ shaft power. The velocity of the buckets is $0.45$ times the velocity of the jet. Overall efficiency is $0.85$ and coefficient of velocity is $0.98$.

Derive the equation of hydraulic efficiency of an impulse turbine and hence prove that for maximum efficiency wheel velocity should be the half of the jet velocity.

A Pelton wheel having semi-circular buckets and working under a head of 140meters, is running at 600 rpm. The discharge through the nozzle is 500 litres/sec and diameter of the wheel is 600 mm. Find
Power available at the nozzle, and
Hydraulic efficiency of the wheel, if coefficient of velocity is 0.98. Assume $k=1$.

What is meant by turbomachinery? Derive Euler turbomachinery equation.

A Pelton wheel is required to generate $4000 \text{ kW}$ under an effective head of $400 \text{ m}$. Determine (i) total flow in $\text{m}^3\text{/s}$ and (ii) size of jet. Assume generator efficiency $95$, overall efficiency $85$ and coefficient of velocity $0.98$ and speed ratio $0.46$.