# Calculating Head Supplied by a Pump and Total Head Loss in a System

What is the head supplied by the pump and the total head loss between the pump and the point of free discharge?

## Head Supplied by the Pump

**To calculate the head supplied by the pump, we need to consider the elevation head and the pressure head at the intake side of the pump.**The elevation head is the potential energy difference between the reservoir and the pump. In this case, the elevation head is 20m. The pressure head is the energy associated with the pressure difference at the intake side of the pump. The gage pressure at the intake side is 150 kPa, which can be converted to absolute pressure by adding the atmospheric pressure. Assuming the atmospheric pressure is 101.3 kPa, the absolute pressure at the intake side is 251.3 kPa. The head supplied by the pump is the sum of the elevation head and the pressure head: Head supplied by the pump = Elevation head + Pressure head Head supplied by the pump = 20m + 251.3 kPa

## Total Head Loss

**Now, let's calculate the total head loss between the pump and the point of free discharge.**The total head loss is the sum of the friction head loss and the minor head losses due to fittings and other factors. Since all pipes are commercial steel with a diameter of 15 cm, we can calculate the friction head loss using the Darcy-Weisbach equation: Friction head loss = (f * L * V^2) / (2 * g * D) Where: f is the Darcy friction factor L is the length of the pipe V is the velocity of the water g is the acceleration due to gravity D is the diameter of the pipe Unfortunately, the question does not provide the length of the pipe or the velocity of the water, so we cannot calculate the friction head loss. However, we can still calculate the minor head losses due to fittings and other factors if the question provides the necessary information.