Multiple choice

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).

  1. 4.625

  2. 6.125

  3. 5.625

  4. 5.125
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C Correct answer
Explanation

Volume of water = Area * Velocity * Time = 0.5 * 180 * 30 = 2700 m^3. Volume of sump = Length * Breadth * Depth = 24 * 20 * Depth = 480 * Depth. 480 * Depth = 2700, so Depth = 2700 / 480 = 5.625 m.

AI explanation

Using the volume flow continuity method, the volume of water flowing into the tank equals the total volume of the sump. The volume of water supplied by the pipe in half an hour is found by multiplying the cross-sectional area of 0.5 square meters by the flow rate of 180 meters per minute and the time of 30 minutes, yielding 2700 cubic meters. The volume of the rectangular sump is its length multiplied by its breadth multiplied by its depth, so 24 m multiplied by 20 m multiplied by the depth equals 2700 cubic meters. Solving for the depth gives 2700 divided by 480, which equals 5.625 meters.

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