Multiple choice

A rectangular tank is $30\ m$ long $20\ m$ broad. Water is being flown into it through a square pipe of side $5\ cm$. What is the speed of water if the level of water in the tank rises by $1\ m$ in $8$ hours?

  1. $30\ km/h$
  2. $36\ km/h$
  3. $40\ km/h$
  4. $None\ of\ these$
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A Correct answer
Explanation

Volume of water in tank = 30 * 20 * 1 = 600 cubic meters. Time = 8 hours. Flow rate = 600 / 8 = 75 cubic meters/hour. Pipe area = 0.05 * 0.05 = 0.0025 square meters. Speed = Flow rate / Area = 75 / 0.0025 = 30000 meters/hour = 30 km/h.

AI explanation

Using the volume equivalence formula, the volume of the tank base is 3000 cm multiplied by 2000 cm, giving 6000000 square cm for the rising water level of 100 cm. The total required volume is 600000000 cubic cm. The cross-sectional area of the square pipe is 5 cm multiplied by 5 cm, equalling 25 square cm. Dividing the total volume of 600000000 cubic cm by the time of 8 hours gives a required flow of 75000000 cubic cm per hour. Dividing this hourly flow rate by the pipe area of 25 square cm yields the water speed of 3000000 cm per hour, which converts to 30 km per hour.

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