Calculating Energy Required to Pump Oil in Steel Pipe

[chronicals]

Homework Statement

An oil having a density of 833 kg/m^3 and a viscosity of 3.3*10^-3 Pa.s is pumped from an open tank to a pressurized tank held at 345 kPa gage. The oil is pumped from an inlet at the side of the open tank through a line of commercial steel pipe having an inside diameter of 0.07792m at the rate of 3.494*10^-3 m^3/s. The length of straight pipe is 122 m, and the pipe contains two elbows ( 90°) and a globe valve fully open. The level of the liquid in the open tank is 20 m above the liquid level in the pressurized tank. Calculate the energy supplied by the pump.

standard elbow(90)= Le/D=30
globe valve= Le/D=340

Homework Equations

Bernoulli equation

The Attempt at a Solution

i formulated this:

(P_1/ρ+ 〖V_1〗^2/2+gz_1 )- (P_2/ρ+ 〖V_2〗^2/2+gz_12 ) = hl + hl_m - h_pump

The question asks h_pump =? , is my equation correct?

 

[mark726]

Thank you for your question. Your equation looks correct, but there are a few things to consider in order to accurately calculate the energy supplied by the pump.

Firstly, make sure that all units are consistent. In your equation, you have used units of pressure (Pa) and velocity (m/s), but you also need to take into account the units of length (m) and density (kg/m^3).

Secondly, you may need to take into account any losses due to friction in the pipe. This can be done by adding a term for the head loss (hl_f) in your equation:

(P_1/ρ+ 〖V_1〗^2/2+gz_1 )- (P_2/ρ+ 〖V_2〗^2/2+gz_12 ) = hl + hl_m - h_pump - hl_f

The head loss due to friction can be calculated using the Darcy-Weisbach equation:

hl_f = f*L/D*(〖V_1〗^2/2g)

Where f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, and g is the acceleration due to gravity.

Lastly, make sure to take into account the difference in elevation between the two tanks. This can be done by adding a term for the change in elevation (Δz) in your equation:

(P_1/ρ+ 〖V_1〗^2/2+gz_1 )- (P_2/ρ+ 〖V_2〗^2/2+gz_12 ) = hl + hl_m - h_pump - hl_f + Δz

By incorporating these factors into your equation, you should be able to accurately calculate the energy supplied by the pump. I hope this helps, and let me know if you have any further questions. Good luck with your calculations!