Introduction:
Centrifugal pumps are used extensively in various industries to transport fluids from one location to another. The discharge of a centrifugal pump is an important parameter that determines its performance. In this response, we will discuss the factors that affect the discharge of a centrifugal pump and explain why it is directly proportional to certain variables.

Factors affecting discharge:
The discharge of a centrifugal pump is affected by various factors, including:

1. Pump speed: The speed of the pump impeller determines the rate at which the fluid is moved through the pump. A higher pump speed results in a higher discharge rate.

2. Pump diameter: The diameter of the pump impeller also affects the discharge rate. A larger impeller diameter can move more fluid and result in a higher discharge rate.

3. Fluid viscosity: The viscosity of the fluid being pumped affects the frictional losses in the pump and can reduce the discharge rate. Higher viscosity fluids require more energy to pump and result in a lower discharge rate.

4. Pump efficiency: The efficiency of the pump affects the amount of power required to move the fluid and can affect the discharge rate. A more efficient pump can move more fluid with the same amount of power and result in a higher discharge rate.

Direct proportionality:
The discharge of a centrifugal pump is directly proportional to the pump speed and impeller diameter. This means that if the pump speed or impeller diameter is increased, the discharge rate will also increase. This relationship is known as the pump's capacity curve, and it is a fundamental parameter used to select pumps for various applications.

Conclusion:
The discharge of a centrifugal pump is affected by various factors, including pump speed, impeller diameter, fluid viscosity, and pump efficiency. The pump speed and impeller diameter are directly proportional to the discharge rate, and increasing these variables results in a higher discharge rate. Understanding the factors that affect pump performance is essential for selecting the right pump for a specific application and optimizing its performance.