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The problem is:

Water is pumped from a lake to a pool through a 0.05 m diameter pipe. System friction losses are h

_{f}= 50V

^{2}/(2g), where V is the average velocity in the pipe. If the power of the pump is 10 kW, what is the mass flow rate pumped?

The diagram given with the problem is attached as well as the two pages of my work. I was fairly certain that I messed up on the first page so I redid it on the second page and hope that it was the correct approach. Thermodynamics & Fluid Mechanics are tough for me because you really have to know exactly how, when, why, and which formulas to use at precisely the correct time. If somebody could just look over my work and let me know if I was on the right track, what my errors were, and/or the correct approach, I'd really appreciate it!

Thanks,

H.