Water in a rectangular reservoir having base $80\ m$ by $60\ m$ is $6.5\ m$ deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side $20\ cm$, if the water runs through the pipe at the rate of $15\ km/hr$.

Given:

Water in a rectangular reservoir having base $80\ m$ by $60\ m$ is $6.5\ m$ deep.

The water runs through the pipe at the rate of $15\ km/hr$.

To do:

We have to find the time in which the water can be emptied by a pipe of which the cross-section is a square of side $20\ cm$.

Solution:

Length of the reservoir $(l) = 80\ m$

Breadth of the reservoir $(b) = 60\ m$

Depth of the reservoir $(h) = 6.5\ m$

Therefore,

Volume of water in the reservoir $= lbh$

$= 80 \times 60 \times 6.5$

$= 31200\ m^3$

Area of cross-section of the mouth of the pipe $= 20 \times 20$

$= 400\ cm^2$

$=\frac{400}{10000}\ m^2$

$=\frac{4}{100} \mathrm{~m}^{2}$

Speed of the water $=15 \mathrm{~km} / \mathrm{h}$

Length of flow of water in the pipe $=\frac{\text { Volume }}{\text { Area of cross - section }}$

$=\frac{31200 \times 100}{4}$

$=780000$

$=780 \mathrm{~m}$

Time taken $=\frac{\text { Length }}{\text { Speed }}$

$=\frac{780}{15}$

$=52$ hours 

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Updated on: 10-Oct-2022

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