3. A large dynamometer operates a pump that circulates a viscous fluid through a restrictive fluid circuit. Under steady operating conditions, heat loss from the fluid is measured as 150 kW when the shaft is rotating at 1000 rpm, and 275 kW when the shaft speed increases to 2000 rpm. The pump efficiency varies with speed according to the equation:

n. = 0.85-5x10 where Ω is the shaft speed in ipm and n=P out/ P in.

Find the shaft power (in kW) and torque (in N-m) at both shaft speeds. Hint: Assume the heat loss rate in the fluid is due only to friction created by the pumping power.

the efficiency at both shaft speeds, and then the shaft power. From the shaft power and shaft speed, you can find the shaft torque at both speeds.