A centrifugal pump-motor combination is used to transport crude oil in a refiner

Question

A centrifugal pump-motor combination is used to transport crude oil in a refinery. The pump motor combination has a motor attached to it drawing 50 kW of electric power. The motor spins at a rate of n = 4000 rpm. The torque applied by the motor is 50 N m. The pump motor combination is used to transport crude oil (Specific Volume=0.001176 m^3/kg) in a refinery. The volumetric flow rate of the crude oil through the pump is 0.1 m^3/s. The fluid leaves the pump at the same velocity it entered the pump (AKE=0) and the changes in height are negligible (APE=0). The change in pressure is 100 kPa or 100,000 N/m^2 for the energy equation. What is the shaft work of the motor? What is the efficiency of the motor? Calculate the total energy (J or kj) per unit mass (kg) of fluid. Calculate the mass flow rate of the fluid Determine the efficiency of the centrifugal pump. Calculate the combination motor pump efficiency.

Explanation / Answer

GIVEN THAT

POWER (P) = 50 KW

SPEED (N) = 4000 RPM

TORQUE (T) = 50 Nm

SPECIFIC VOLUME = 0.001176 m3/ KG

VOLUMETRIC FLOW RATE = 0.1m3/S

dKE = 0

dPE = 0

CHANGE IN PRESSURE = 100 Kpa , 10000 N/M2

A ----- SHAFT WORK ---------- Ws = (2 (3.14) T N )/60

= 20933.3 WATTS

= 20.9333 Kw

B ------ EFFICIENCY ---------- n (ETTA) = BREAK POWER / INDIACTED POWER

= 20.9333/50

= 0.41866

= 41 %

3 ----- total energy per unit mass

4------------ mass flow rate = density * volumetric flow rate = 850 * 0.1 = 85 kg/s

density = 1/ specific volume

= 1/ 0.001176

= 850 kg/m3

5 -------------- efficiency of the centrifugal pump = water power / shaft power = (0.000027H/20.9333)

water power = Q * H /3960

= 0.000027 H

6 --------------- total efficiency = motor efficiency * pump efficiency

= 0.41 * 0.00000129 H

= 0.0000005289H

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