# Step-by-Step Solution: Pump Efficiency ## 1. Understanding Pump Efficiency **Pump efficiency** (\(\eta\)) is the ratio of the hydraulic (output) power delivered by the pump to the electrical (input) power consumed by the pump: \[ \eta = \frac{\text{Hydraulic Power Output}}{\text{Electrical Power Input}} \] ## 2. Given Data - **Electrical Power Input:** \(10\, \text{kW}\) - **Hydraulic Power Output:** \(8\, \text{kW}\) ## 3. Substitute Values \[ \eta = \frac{8\, \text{kW}}{10\, \text{kW}} \] ## 4. Calculate the Efficiency \[ \eta = .8 \] ## 5. Convert to Percentage To express efficiency as a percentage, multiply by 100: \[ \eta_{\text{(\%)}} = .8 \times 100 = 80\% \] --- ## Final Answer **The pump's efficiency is \(80\%\).**