Chapter 10, Problem 39P

To determine

To Calculate: The time taken to fill the pool to a depth of $1.2\mathrm{m}$ , if water is issues from the hose.

Explanation of Solution

Given information:

Diameter, $=\frac{5}{8}\mathrm{inch}$

Swimming pool diameter, $=6.1\mathrm{m}$

Depth of pool, = 1.2 m

Water’s speed = $=0.40m/s$

Formula used:

The flow rate of volume of water from the hose, when multiplied with the time of filling, must be equal to the volume of the pool.

  ${\left(Av\right)}_{house}=\frac{V_{pool}}{t}$

Solution:

  $\begin{array}{l}{\left(Av\right)}_{house}=\frac{V_{pool}}{t}\\ \Rightarrow t=\frac{V_{pool}}{A_{house}{v}_{house}}=\frac{\pi r^{2}h}{A_{house}{v}_{house}}\\ =\frac{3.14\times {\left(3.05\right)}^2\times \left(1.2\mathrm{m}\right)}{\pi {\left[\frac{1}{2}{\left(\frac{5}{8}\right)}^{\text{'}\text{'}}\left(\frac{1m}{{39.37}^{\text{'}\text{'}}}\right)\right]}^{1/2}\left(0.40\text{m/s}\right)}=4.43\times {10}^5\mathrm{s}\end{array}$

Also,

The time taken in days:

  $4.43\times {10}^5\mathrm{s}\left(\frac{1\text{day}}{60\times 60\times 24\mathrm{s}}\right)=5.1\text{days}$

Conclusion:

The time taken to fill the pool to a depth of $1.2\mathrm{m}$ , if water is issues from the hose, is $5.1\text{days}$ .