18.8 : Application of the Energy Equation

The application of the energy equation to centrifugal pumps is a fundamental principle in fluid dynamics and engineering. In this scenario, the energy equation is used to calculate the flow rate of a centrifugal pump responsible for transferring water between two reservoirs at different elevations. The pump applies an energy input of 7500 joules per second, and the vertical difference between the lower and upper reservoirs is 10 meters. Additionally, the head loss due to friction and other resistances is 5 meters. These parameters are essential to solving the flow rate using the energy equation.

Because both reservoirs are open to the atmosphere, the pressure at both the inlet and outlet of the pump is equal to atmospheric pressure. This allows the pressure terms in the energy equation to cancel out. Furthermore, since the velocities at the inlet and outlet are negligible, the velocity terms in the equation are also eliminated. The energy equation for this specific case only depends on the gravitational head and the pump head.

The head generated by the pump is determined by dividing the net shaft power input by the product of the flow rate and the specific weight of water. Substituting this head into the energy equation and solving for the flow rate of the pump can be determined.