Chapter 10, Problem 18P

To determine

To Find:The minimum gauge pressure needed in the water pipe leading in to a building on the basis of given information.

Answer to Problem 18P

The minimum gauge pressure is $\text{3}.\text{37}\times \text{1}{0}^{\text{5}}\text{N}/{\text{m}}^{\text{2}}$ .

Explanation of Solution

Given:

The height of fluid $h=38\text{m}$ .

Formula used:

The Pressure is the ratio of force per unit area:

Mathematically it can be written the formula of pressure is

  ${\rm P}=F/A$

The pressure at a depth h in a liquid of constant density $\rho$ is given by

  ${\rm P}=\rho gh$

Where $g$ is acceleration due to gravity.

Calculation:

Write the expression for gauge pressure.

  $\begin{array}{c}{\rm P}=\rho gh\\ =\left(\text{1}.00\times \text{1}{0}^{\text{3}}\text{kg}/{\text{m}}^{\text{3}}\right)\times \left(\text{9}.\text{8m}/{\text{s}}^{\text{2}}\right)\times \left(\text{38}\right) \\ =\text{3}.\text{37}\times \text{1}{0}^{\text{5}}\text{N}/{\text{m}}^{\text{2}} \end{array}$

Conclusion:

The minimum gauge pressure would cause the water to come out of the faucet with very little speed. This means there is a need for gauge pressure to hold the water at this elevation point. The minimum gauge pressure required is 3.37×10⁵N/m².