Question

A rectangular reservoir is $100m$ long and $50m$ wide. Find the speed of the water flowing into it through a square pipe of side $10cm$ such that the water rises by $1m$ in $10$ hours.

• A. $50km/hr$
• B. $45km/hr$
• C. $30km/hr$
• D. $20km/hr$

Answer 1

The correct option is A

$50km/hr$

Length of the reservoir, $l=100m$

Breadth, $b=50m$

Level of water in the reservoir after $10$ hours $=1m$

$\Rightarrow$ Volume of water flown in the reservoir in $10$ hours $=l\times b\times \text{level of water}$

$=100\times 50\times 1=5000m^3$

$\Rightarrow$ Volume of water flown in the reservoir in $1$ hour $=\frac{5000}{10}=500m^3$

Area of the mouth of the square pipe $=10\times 10=100c{m}^2=0.01m^2$

Speed of water per hour $=\frac{500}{0.01}=50000m/hr$

Hence, speed of the water flowing in the reservoir $=50km/hr$