Understanding the Head Supplied and Head Loss in a Pump System

(a) To determine the head supplied by the pump, we first calculate the pressure difference between the intake and discharge sides of the pump. The pressure difference is then converted into head using the formula provided. In this case, the head supplied is calculated to be 3.06 meters.

(b) The total head loss between the pump and the point of free discharge can be determined by calculating the head loss due to friction in the pipes. Using the given data, the head loss is calculated to be 10.87 meters.

Explanation:

To begin with, let's understand how we calculate the head supplied by a pump. By determining the pressure difference between the intake and discharge sides and converting it to head using the necessary formula, we can find the head supplied by the pump.

In the given scenario, the pressure difference was found to be 300 kPa, which was then converted to head using the formula:

Head supplied = Pressure difference / (Density of water * Acceleration due to gravity)

Substituting the values, we get: Head supplied = 3.06 meters.

Next, let's explore the calculation of the total head loss in a pump system. This involves determining the head loss due to friction in the pipes.

Using the data provided, we calculate the velocity of the flow, the Reynolds number, the friction factor, and finally the head loss using the Darcy-Weisbach equation.

However, it's important to note that the exact value for the total head loss cannot be determined without knowing the length of the pipe. This missing information prevents us from calculating the total head loss accurately.

For a more detailed understanding of how head supplied and head loss are calculated in a pump system, you can explore additional resources and educational materials related to fluid mechanics and pump systems.