gauge pressure

[logistic_guy]

What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of \(\displaystyle 15 \ \text{m}\)?

 

[khansaheb]

What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of \(\displaystyle 15 \ \text{m}\)?

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[logistic_guy]

What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of \(\displaystyle 15 \ \text{m}\)?

This problem can be solved by Bernoulli's equation:

\(\displaystyle P_1 + \frac{1}{2}\rho v^2_1 + \rho g y_1 = P_2 + \frac{1}{2}\rho v^2_2 + \rho g y_2\)

Since the problem did not restrict us, we are free to choose any set up of where are the initial and final points.

Choosing \(\displaystyle v_1 = v_2 = y_1 = 0\), reduces the solution greatly.

\(\displaystyle P_1 = P_2 + \rho g y_2\)

\(\displaystyle P_{\text{gauge}} = P_1 - P_2 = \rho g y_2 = 1000(9.8)(15) = \textcolor{blue}{147000 \ \text{N/}\text{m}^2}\)