An oil pump delivers oil at a steady rate of 13 lbm/s through a 1-in diameter pi
ID: 2997610 • Letter: A
Question
An oil pump delivers oil at a steady rate of 13 lbm/s through a 1-in diameter pipe. The oil, which can be modeled as an incompressible fluid, has a density of 100 lbm/ft^3. The oil experiences a pressure rise of 40 psi from the pump inlet to the exit. There is no significant elevation difference between the inlet and exit of the pump and the change the kinetic energy of the oil is negligible. The pump can be assumed to be adiabatic and there is no noticeable change in temperature as the oil passes through the pump. If pumps are available in 1/4-hp increments, specify the power rating of the pump required for this application.Explanation / Answer
First if you want to find at the end HP (745.7 W), transform all data to SI:
mass debit (m/t) =13 lbm/s =13.0.4536=5.897 kg/s
density rho =100 lbm/ft^3 = 100*0.4536 kg/(0.305 m)^3 =1598.7 kg/m^3
pressure P =40 PSI =2.758*10^5 N/m^2 (google)
Apply Bernouly law for flow of liquid in the pump with no elevation difference:
P =rho*V^2/2
V =sqrt(2P/rho) =sqrt(2*2.758*10^5/1598.7) =sqrt(345)=18.57 m/s
Next find the Power =energy/time required to pump at this speed:
P =W/t = (m*V^2/2)*(1/t) =5.897*18.57^2/2 =1017.2 W =1017.2/745.7 HP =1.364 HP
The power rating of the pump should be 1.5 HP