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Q9PE

Expert-verifiedFound in: Page 428

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) Estimate the time it would take to fill a private swimming pool with a capacity of 80,000 L using a garden hose delivering 60 L/min. (b) How long would it take to fill if you could divert a moderate size river, flowing at \({\bf{5000}}\;{{\bf{m}}^{\bf{3}}}{\bf{/s}}\) , into it?**

**(a) The time to fill the swimming pool with a garden hose is \({\bf{1333}}{\bf{.33}}\;{\bf{min}}\)**

**(b) The time to fill the swimming pool with a moderate size river is \({\bf{1}}{\bf{.6 \times 1}}{{\bf{0}}^{{\bf{ - 2}}}}\;{\bf{sec}}\)**

**(a)**

**Given Data:**

**The capacity of the swimming pool is \(V = 80000\;{\rm{L}}\)**

**The flow rate of water from garden hose is \(q = 60\;{\rm{L}}/\min \)**

**The flow rate of moderate size river is \(Q = 5000\;{{\rm{m}}^3}/{\rm{s}}\)**

**The flow rate of water is the volume of the water passing through the garden hose in per second.**

**The time to fill the swimming pool by garden hose is given as:**

**\(t = \frac{V}{q}\)**

**Here, \(t\) is the duration to fill swimming pool by garden hose**

**\(\begin{aligned}t &= \frac{{80000\;{\rm{L}}}}{{60\;{\rm{L}}/\min }}\\t &= 1333.33\;\min \end{aligned}\)**

**Therefore, the time to fill the swimming pool by garden hose is \(1333.33\;\min \).**

**(b)**

**The time to fill the swimming pool by moderate size river is given as:**

**\(T = \frac{V}{Q}\)**

**Here, \(t\) is the duration to fill the swimming pool by a garden hose**

**\(\begin{aligned}T &= \frac{{\left( {80000\;{\rm{L}}} \right)\left( {\frac{{1\;{{\rm{m}}^3}}}{{1000\;{\rm{L}}}}} \right)}}{{5000\;{{\rm{m}}^3}/{\rm{s}}}}\\T &= 1.6 \times {10^{ - 2}}\;{\rm{sec}}\end{aligned}\)**

**Therefore, the time to fill the swimming pool by moderate size river is \(1.6 \times {10^{ - 2}}\;{\rm{sec}}\).**

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