Question

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

Answer 1

Length of the reservoir = 120 m
Breadth of the reservoir = 75 m
The height of the water level in 18 hours = 2.4 m
Volume of the water collected in the reservoir = 120 × 75 × 2.4
= 21600 m³
Let the speed of the flowing water = x m/hr
the water flowing in the pipe eventually forms a cuboid of width 20 cm or 0.2 m and height of 20 cm or 0.2 m.
The length of the cuboid so formed in the pipe in 18 hours = 18x m
Therefore, the volume of the water flows out of the pipe in 18 hours = 0.2 × 0.2 × 18x
= 0.72x m³
Therefore,Volume of the water collected in the reservoir = volume of the water flows out of the pipe in 18 hours.
21600 = 0.72x
x = 21600/0.72
x = 30000 m/hr
Or, speed of the water = 30 km/hr