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.


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.

  • $\begingroup$ 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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