Maximizing Pump Efficiency in Moving Water

What is the maximum flow rate of water that can be achieved by a submerged pump?

a. 7 litres per second

Answer:

The theoretical maximum flow rate of the pump under the given conditions is computed to be approximately 7 litres per second.

Underground water is to be pumped by a 70 percent efficient 3-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.

The solution to this problem involves the computation of key values using the principle of fluid dynamics coupled with the pump's efficiency data. The problem talks about a submerged pump being used to move underground water to a higher level, specifically a pool 30m above the water level.

The general equation to determine pump power in fluid systems is given by P = Qρgh, where Q is the volume flow rate, ρ is the fluid density (1000 kg/m³ for water), g is the acceleration due to gravity (9.8 m/s²) and h is the pump head or height the fluid is pumped (30m in this case). Given an 70 percent efficient 3-kW submerged pump (or 0.7 * 3000 = 2100 W), you can rearrange the equation to find Q = P / (ρgh) = 2100 / ((1000 kg/m³)(9.8 m/s²)(30m)) = 0.007 m³/s or 7 litres per second. That corresponds to the theoretical maximum flow rate of the pump under the given conditions.

However, as the pipe diameter decreases from 7cm (intake side) to 5 cm (discharge side), the flow rate will also be reduced due to increased resistance to flow. Furthermore, real-world factors such as pipe material surface roughness and bends in the pipeline can also affect flow rates.