Question

Gear pump displacement = 120 cm\(^3\)/rev, speed = 1500 rpm, pressure = 18 MPa, torque efficiency = 90%. Find actual torque (Nm) (round to 2 decimals).

Hint:

For pumps: Actual torque = theoretical torque ÷ torque efficiency.

Answer 1

Correct Answer: 380

Convert displacement: \[ V_d = 120\ \text{cm}^3 = 120 \times 10^{-6}\ \text{m}^3 \] Theoretical torque: \[ T_{th} = \frac{p \, V_d}{2\pi} \] \[ = \frac{18\times10^6 \times 120\times10^{-6}}{2\pi} \] \[ = \frac{2160}{6.28} = 343.6\ \text{Nm} \] Actual torque: \[ T = \frac{T_{th}}{\eta_t} = \frac{343.6}{0.9} = 382.9\ \text{Nm} \] Rounded: \[ \boxed{382.90} \]