Question

A rectangular sump has an inner length and breadth of 24 m and 20 m respectively. Water flows through an inlet pipe at 180 m per minute. The cross-sectional area of the pipe is 0.5 m${}^2$. The tank takes half an hour to get filled. Find the depth of the sump (in m).

• A. 4.625
  
• B. 6.125
  
• C. 5.625
  
• D. 5.125
  

Answer 1

The correct option is C 5.625

Let the depth of the sump be h m.

Volume of water flowing through the pipe = $\left(180\right)\left(0.5\right)$ $m^3/minute$ = $90$ $m^3/minute$

Total volume of water which must flow through to fill the sump = $\left(90\right)\left(30\right)=2700$ $c{m}^3$

Therefore,

$24\times 20\times h=2700$

$h=5.625$