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Here is a question, I found two methods to solve it, differing in the answers and I'm not sure why a method is incorrect.

Question: A fire hose of cross section area A is required to direct a jet of water to a height h, the minimum power of the pump needed for this hose is?

Method 1: $$ dp = \rho A dxV$$ $$ F = \rho A V^2$$ $$ P = F.V = \rho A V^3$$

Method 2: $$ m = \rho A dx$$ $$ KE = \frac{1}{2}mV^2 = \frac{1}{2}\rho A dx V^2$$ $$ P = \frac{1}{2}\rho A V^3$$

The correct answer stated is the one obtained from method 2. Can anyone explain why the first method is wrong?

Thanks for your time.

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Your first method is wrong, because the velocity is not constant during the whole trajectory. This is what you implicitly assumed in the last step of the first method.

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  • $\begingroup$ Thanks a lot. I got the error. I will mark it as correct once it allows me too. $\endgroup$ – sushant-hiray May 18 '14 at 6:42

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