Introduction:
The discharge through a Pelton turbine is influenced by the speed of the turbine. The Pelton turbine is a type of impulse turbine that operates based on the principle of jet impact. It consists of a runner with a series of buckets or cups around its periphery. The water jet from the nozzle strikes the buckets, causing the runner to rotate and convert the kinetic energy of the water into mechanical energy.

Effect of speed on discharge:
The speed of the Pelton turbine refers to the rotational speed of the runner, which is directly proportional to the speed of the water jet striking the buckets. The relationship between the speed of the turbine and the discharge can be understood as follows:

1. Increased speed:
When the speed of the Pelton turbine increases, the discharge through the turbine also increases. This is because the kinetic energy of the water jet striking the buckets is directly proportional to the square of the speed. Therefore, an increase in speed results in a higher kinetic energy, which leads to a greater discharge.

2. Decreased speed:
Conversely, when the speed of the turbine decreases, the discharge also decreases. This is because the kinetic energy of the water jet decreases with a decrease in speed, resulting in a lower discharge.

3. Constant speed:
If the speed of the turbine remains constant, the discharge through the turbine will also remain constant. The kinetic energy of the water jet striking the buckets will remain unchanged, resulting in a consistent discharge.

4. First increase then decrease:
In some cases, there might be an optimal speed at which the discharge through the turbine is maximized. This occurs when the increase in speed initially leads to an increase in discharge, but after reaching a certain point, further increases in speed result in a decrease in discharge. This can happen due to various factors such as the design of the turbine and the characteristics of the water flow.

Conclusion:
In conclusion, the discharge through a Pelton turbine generally increases with an increase in speed and decreases with a decrease in speed. However, there may be cases where an optimal speed exists, resulting in an initial increase followed by a decrease in discharge. It is important to consider the specific design and operating conditions of the turbine to determine the exact relationship between speed and discharge.