How is hydraulic power of a pump calculated from system pressure and flow?

• A. P_h = η_pump × ΔP × Q
• B. P_h = ΔP × Q
• C. P_h = P_elec × η_pump
• D. P_h = ΔP / Q

Answer: (B)

Hydraulic power is the rate at which the pump does work on the fluid, so it comes directly from how much pressure energy is added to the fluid and how much fluid is moved each second. The pressure rise or system pressure the pump creates, multiplied by the volumetric flow rate, gives the power delivered to the fluid: P_h = ΔP × Q.

Keep units consistent: if ΔP is in pascals and Q is in cubic meters per second, P_h is in watts. If you use bar and liters per second, you must convert to pascals and cubic meters per second first.

The other expressions mix in efficiency or electrical input. ΔP × Q already represents the hydraulic power, the actual energy transfer to the fluid. Including η_pump would pertain to the electrical power required to achieve that hydraulic power, not the hydraulic power itself. Dividing ΔP by Q or other forms similarly misrepresent the basic relation.