Question

Underground water is to be pumped by a 78% efficient 5-kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Assume no head loss in the pipe.

a. Determine the maximum flow rate of water and the pressure difference between the pump inlet and the outlet.

Answer 1

To determine the maximum flow rate and pressure difference in the system, we can use Bernoulli's equation and fluid mechanics principles.

Step-by-step explanation:

To determine the maximum flow rate of water and the pressure difference between the pump inlet and the outlet, we can use the principles of fluid mechanics.

The maximum flow rate of water can be determined using Bernoulli's equation, which states that the total energy of a fluid flowing in a pipe is conserved. In this case, we can use the equation A_1v_1=A_2v_2, where A_1 and A_2 are the cross-sectional areas of the pipe at the intake and discharge sides, and v_1 and v_2 are the velocities of the water at those respective points.

The pressure difference between the pump inlet and the outlet can be determined using the equation P_2-P_1=(1/2)ρ(v_2^2-v_1^2), where P_1 and P_2 are the pressures at the pump inlet and outlet, ρ is the density of the fluid (water), and v_1 and v_2 are the velocities at the pump inlet and outlet, respectively.

By plugging in the given values, we can calculate the maximum flow rate of water and the pressure difference between the pump inlet and the outlet.