Chapter 10, Problem 40P

To determine

To Find: The pressure if a firehouse is to spray water to a height of 15 m.

Answer to Problem 40P

The pressure is $1.5\times {10}^5{\text{N/m}}^{\text{2}}$ .

Explanation of Solution

Given information:

Height, $h=15\mathrm{m}$

Formula used:

According to the Bernoulli’s principle, the sum of pressure energy, potential energy and kinetic energy is constant.

  $P_1+\frac{1}{2}\rho v_1{}^2+\rho g{y}_1=P_2+\frac{1}{2}\rho v_2{}^2+\rho g{y}_2$

Where, $P$ is the pressure.

  $\rho$ is the density.

  $v$ is the flow velocity.

  $y$ is the elevation above reference point.

Calculations:

The simplified the above formula and the resulted formula is used to calculate the gauge pressure such as,

  $\begin{array}{l}{P}_1-P_{atm}=\rho g{y}_2=\left(1.00\times {10}^3\right)\left(9.8\right)\left(15\right)\\ =1.5\times {10}^5{\text{N/m}}^{\text{2}}\end{array}$

Conclusion:

If a firehouse is to spray water to a height of $15\text{m}$ , then the gauge pressure in the water is necessary, this pressure is $1.5\times {10}^5{\text{N/m}}^{\text{2}}$ .