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).

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

Tardigrade Admin · Accepted Answer

Let the depth of the sump be h m. Volume of water flowing through the pipe =(180) (0.5) m 3 / minute =90 m 3 / minute. Total volume of water which must flow through to fill the sump =(90)(30)=2700 cm 3. ∴(24)(20)(h)=2700 h=5.625.

Q. 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).

4.625

6.125

5.625

5.125

Let the depth of the sump be $hm$ .
Volume of water flowing through the pipe $= (180)$
$(0.5) m^{3} /$ minute $= 90 m^{3} /$ minute.
Total volume of water which must flow through to fill the sump $= (90) (30) = 2700 c m^{3}$ .
$∴ (24) (20) (h) = 2700$
$h = 5.625$ .

Q. A rectangular sump has an inner length and breadth of 24m and 20m, respectively. Water flows through an inlet pipe at 180m per minute. The cross-sectional area of the pipe is 0.5m2. The tank takes half an hour to get filled. Find the depth of the sump (in m).