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Thermodynamis - oil pump efficiency?

 Quote by ..... i left out the oil's density.. dunno if that makes a difference to your query though? word for word the question reads: An oil pump is drawing 35kW of electric power while pumping oil with a density of 860kg/m^3 at a rate of 0.1m^3/s. The inlet and outlet diameters of the pipe are 8cm and 12cm, respectively. If the pressure rise of the oil in the pump is 400 kPa and the motor efficiency is 90%, determine the mechanical efficiency of the pump.
The density of the oil does matter. Let me try to be the teacher that I am and, rather than giving you the answer, ask you some questions that might get you on the right path. First, I will say that figuring out the mechanical input power is correct as one of the first steps. Now for some questions:

1) What do you know about mass flow rate? (Are you familiar with the mass flow rate equation?) If so you can solve for an another important input state variable.
2) You are also given the total pressure increase from the input to the output. Do you think the level-flow form of the Bernoulli's equation might help you get from input to output once you know the input state variable from (1)?
3) Wouldn't the output power = output force * output velocity?

I hope I haven't made it TOO easy!

Rainman