The overall efficiency of a pump is calculated by comparing:

Explanation:

Overall Efficiency of a Pump

• The overall efficiency of a pump is a crucial metric in assessing the performance and energy effectiveness of the pumping system. It is calculated by comparing the hydraulic power output to the mechanical power input. This efficiency measure helps in determining how effectively the pump converts the input mechanical energy into useful hydraulic energy.

To understand why this is the correct option, it is essential to break down both components involved:

• Hydraulic Power Output: This is the useful power delivered by the pump to the fluid, calculated as the product of the flow rate and the head. Mathematically, it can be expressed as:
  • Hydraulic Power (P_h) = ρ × g × Q × H
• Where:
  • ρ = Density of the fluid
  • g = Acceleration due to gravity
  • Q = Volumetric flow rate
  • H = Head
• Mechanical Power Input: This is the power supplied to the pump, typically from an electric motor or an engine. It is the product of the torque and rotational speed of the pump shaft. Mathematically, it can be expressed as:
  • Mechanical Power (P_m) = T × ω
• Where:
  • T = Torque
  • ω (omega) = Angular velocity

The overall efficiency (η) of the pump can then be calculated as:

• η = (Hydraulic Power Output) / (Mechanical Power Input)
• Expressed as a percentage, it is:
• η = (P_h / P_m) × 100%

This ratio provides a direct measure of how efficiently the pump is converting the supplied mechanical energy into hydraulic energy, making it the fundamental metric for evaluating pump performance.