Question

A rectangular reservoir is 120 m long and 75 m wide. At what speed per hour must water flow into it through a square pipe of 20 cm wide so that the water rises by 2.4 m in 18 hours ?

Answer 1

Volume of water accumulated in the reservoir in 18 hours = $(120\times 75\times 2.4)m^3$ ........(1)

Let the speed of the water be v km/hr.

Water in the pipe forms a cuboid of width $\frac{20}{100}=\frac{1}{5}m,height=\frac{20}{100}=\frac{1}{5}m$

Length of the water cuboid formed in 18 hours = 18 v km = 18000 v metres

Therefore,

Volume of water accumulated in the reservoir in 18 hours

$=18000v\times \frac{1}{5}\times \frac{1}{5}{m}^3=720v{m}^3$ .......(2)

From 1 and 2, we get,

$720v=120\times 75\times 2.4$

$v=30km/hr$

Hence, water must flow at the speed of 30 km/hr into the reservoir.