How to Calculate Oil Pump Velocity?

[Gazza-85]

Homework Statement

This problem is regarding an oil suction pipe, pipe A is the the suction pipe and pipe B is the delivery pipe. There is a pump in between which supplies a head of 11.3m. The pressure in pipe A is atmospheric and the pressure in pipe B is 850kPa. The vertical displacement is 0.8m, total head loss in the system is 0.44m and the density of the oil is 850kg/m³.

If the diameter of pipe A is twice the diameter of pipe B, calculate the velocity in pipe A.

Homework Equations

None given... I have tried using Bernoulli's extended equation

P_in/ρg + v_in²/2g + z_in = P_out/ρg + v_out²/2g + z_out + H_losses - H_pump + H_turbine

The Attempt at a Solution

I initially tried to rearrange the the mass equation by subbing in piD^2 / 4 for area and rearranging to discover the relationship between the velocities in the two pipes with the diameter difference. It seems to be a dead end as my workings suggest the velocity for pipe A is half that of pipe B which doesn't make sense, considering the pressure increase is massive in pipe B. I expected the velocity to be higher in the pipe with lower pressure... Maybe my calculations are incorrect.

Another attempt included entering all of the data into bernoulli's extended equation and rearranging. I could only get as far as 'V_in - V_out = 1.62 (approx)' which is another dead end.

The final attempt consisted of suggesting that P_in/ρg + v_in²/2g + z_in = the sum of heads which, when rearranged, produced a figure of 14.77 m/s for V_in. Extended workings for this solution are written in my report but I am not convinced...

Thanks for reading, this is my first post so please let me know if I can improve anything. I could attach photos or word documents of my calculations if necessary/possible.

I hope someone can give me a push in the right direction, thanks again.

 

[SteamKing]

In your description of your calculations, I don't see any mention of the continuity relationship. Is this what you mean by the 'mass equation'?

A velocity of 14 m/s seems rather high for a liquid piping system.

Perhaps you should post the details of what you consider your 'best' calculation.

 

[Gazza-85]

Hi there, thanks for the prompt reply, attached is where I am so far.

Yep, continuity relationship and I meant quarter not half :/

 

[SteamKing]

You've made a major mistake in your manipulation of the Bernoulli equation:

V_{A}^{2} - V_{B}^{2} = Mess

but

\sqrt{V_{A}^{2} - V_{B}^{2}} ≠ V_{A} - V_{B}