Which formula correctly expresses the relationship between wire-to-water efficiency and its components?

Which formula correctly expresses the relationship between wire-to-water efficiency and its components?

• A. Power factor divided by pump efficiency
• B. Power factor plus pump efficiency
• C. Power factor x pump efficiency
• D. Pump efficiency divided by power factor

Answer: (C)

Wire-to-water efficiency is the fraction of electrical power that ends up as hydraulic energy. This comes from two stages: the motor converting electrical power to shaft power (motor efficiency, often represented by the electrical effectiveness with power factor) and the pump converting shaft power to hydraulic power (pump efficiency). Since both stages must work together for the final output, you multiply the two efficiencies to get the overall result. In this context, using power factor as the electrical-side factor and multiplying it by the pump efficiency gives the correct wire-to-water efficiency. For example, if the motor-side factor is 0.9 and the pump efficiency is 0.85, the wire-to-water efficiency is 0.9 × 0.85 = 0.765. Adding them, or dividing one by the other, would not reflect the sequential transfer of energy from electrical input to hydraulic output.

Wire-to-water efficiency is the fraction of electrical power that ends up as hydraulic energy. This comes from two stages: the motor converting electrical power to shaft power (motor efficiency, often represented by the electrical effectiveness with power factor) and the pump converting shaft power to hydraulic power (pump efficiency). Since both stages must work together for the final output, you multiply the two efficiencies to get the overall result. In this context, using power factor as the electrical-side factor and multiplying it by the pump efficiency gives the correct wire-to-water efficiency.

For example, if the motor-side factor is 0.9 and the pump efficiency is 0.85, the wire-to-water efficiency is 0.9 × 0.85 = 0.765. Adding them, or dividing one by the other, would not reflect the sequential transfer of energy from electrical input to hydraulic output.