Water at 15^∘ C is pumped at a rate of 20 L / s using a 5 kW pump. If the efficiency of the pu

step 1 Hello students, in this problem we have given water at 15 degree centigrade is pumped with a rat

Water at 15^∘ C is pumped at a rate of 20 L / s using a 5...

Water at $15^{\circ} \mathrm{C}$ is pumped at a rate of $20 \mathrm{~L} / \mathrm{s}$ using a $5 \mathrm{~kW}$ pump. If the efficiency of the pump is $80 \%,$ what is the head added to the water as it passes through the pump?

Key Concepts

Pump Efficiency

Pump efficiency is the measure of how effectively a pump converts the input energy (typically electrical or mechanical) into hydraulic energy delivered to the fluid. It represents the ratio between the useful power imparted to the fluid and the electrical or mechanical power consumed. Understanding pump efficiency is critical in calculating the actual energy available for doing work within a system, as some energy is lost through heat, sound, or friction.

Hydraulic Head

Hydraulic head is a specific measure of the energy per unit weight of a fluid, expressed as the height through which the fluid can be raised. It represents the potential energy component of the fluid and is calculated based on the work done to lift the fluid against gravity. This concept is crucial for understanding how energy is converted into potential energy in fluid systems, such as in pumps or fluid transport mechanisms.

Energy Balance in Fluid Systems

The energy balance principle in fluid systems relates the power input to the pump, the efficiency of energy conversion, and the mechanical energy transferred to the fluid. This principle is typically expressed by the equation that links effective hydraulic power (accounting for efficiency) to the product of fluid density, gravitational acceleration, flow rate, and the hydraulic head. It provides a framework for determining the performance of fluid systems where energy is imparted by pumps.

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