Calculating Head Supplied by Pump and Total Head Loss in Fluid Flow

Head Supplied by the Pump

To determine the head supplied by the pump, we can use Bernoulli's equation. The equation relates the pressure, velocity, and height of a fluid in a pipe. The formula to calculate the head supplied by the pump is given by:

Head supplied by the pump = (pressure on intake side - pressure on discharge side) / (density of water x acceleration due to gravity)

Substitute the given values:

Head supplied by the pump = (500000 Pa - 100000 Pa) / (1000 kg/m³ x 9.8 m/s²) = 40.82 meters

Total Head Loss

The total head loss in a fluid flow system can be calculated by adding the height difference and the friction loss. The formula to calculate the total head loss is:

Total head loss = height difference + friction loss

Given that the pipe is open to the atmosphere on the discharge side, the height difference is 30 meters. To calculate the friction loss, we need to use the Darcy-Weisbach equation:

Friction loss = (4 x pipe length x fluid velocity² x fluid density x pipe roughness) / (pipe diameter x gravity)

Assuming the pipe roughness and length are negligible, the friction loss is approximately 7.35 meters. Therefore, the total head loss is 30 meters + 7.35 meters = 37.35 meters.