- #1

LT72884

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- 49

e = (P/rho) + (Ke/m) + (Pe/m) where P is pressure, Ke and Pe are Kinetic and potential energy divided by mass.

Ok, if we look at P/rho and P is defined as rho(g)(h) then the rho's divide out and we are left with the exact same thing as Pe/m or just gh.

My question. How do i know when to use P/rho or Pe/m in a question? yes, i end up with same answer, but my procedure is incorrect.

Ex

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m3/s, determine mechanical power that is converted to thermal energy during this process due to frictional effects.

My procedure is as follows:

e(mechanical) = P/rho. i chose this because there is no change in velocity or PE. granted there is a height difference but P/rho yields (gravity)(height) which is the same as Pe/m.

i then plug e(mech) into `E = `me which yeilds (0.03m3/sec)(9.81m/s2)(45m) = 13.2 kW after a conversion.

here is my issue. i end up with same answer even though i WAS NOT SUPPOSED TO USE (P/rho) I was SUPPOSED TO USE (Pe/m). Yes, i got lucky but why is my approach wrong? To me, in my mind, i said to myself " P/rho is for fluids and is a flow rate. Water is a fluid and it is flowing at some rate into the turbo, producing some amount of power in kj/kg of water"

Thanks. I am just trying to understand how to decifer the problems correctly