The efficiency ηof a pump is defined as the (dimensionless)...

The efficiency $\eta$ of a pump is defined as the (dimensionless) ratio of the power developed by the flow to the power required to drive the pump: $$\eta=\frac{Q \Delta p}{\text { input power }}$$ where $Q$ is the volume rate of flow and $\Delta p$ is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure rise of 35 lbf/in $^{2}$ when its flow rate is $40 \mathrm{L} / \mathrm{s} .$ If the input power is $16 \mathrm{hp},$ what is the efficiency?

Key Concepts

Input Power

Input power is the rate at which energy is supplied to operate the pump. It must be expressed in compatible units with the output power (derived from flow rate and pressure work) so that a meaningful efficiency ratio can be calculated.

Unit Conversion

Unit conversion is essential in pump calculations because different quantities like pressure, volume flow rate, and power are often given in different units. Converting them to a consistent set of units ensures that the efficiency calculation is both accurate and dimensionally consistent.

Flow Rate

The flow rate in pump problems represents the volume of fluid moved per unit time. When combined with the pressure increase, it helps quantify the energy transferred to the fluid in a given time period.

Pressure Work

Pressure work refers to the energy delivered to a fluid by the pump. It is calculated as the product of the fluid's volume flow rate and the pressure increase across the pump. This work represents the useful energy that results in the fluid's movement against pressure forces.

Pump Efficiency

Pump efficiency is a dimensionless measure of how effectively a pump converts input power into useful mechanical work on a fluid. It is defined as the ratio of the power imparted to the flow (given by the product of flow rate and the pressure rise) to the input power required to drive the pump.

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