The water level in a rectangular tank with a base of 40m x 30m is 6.5m high.…
2025
The water level in a rectangular tank with a base of 40m x 30m is 6.5m high. In how much time can the tank be emptied by a pipe having square cross section of side 20cm, if the water runs through the pipe at the rate of 5km per hour?
- A.
36 hours
- B.
45 hours
- C.
40 hours
- D.
39 hours
Attempted by 2 students.
Show answer & explanation
Correct answer: D
When a tank is drained through a pipe, the time needed to empty it follows the identity Time = Volume of tank ÷ Volume flow rate of pipe, where the volume flow rate equals the pipe's cross-sectional area multiplied by the speed at which the water travels, with every quantity expressed in consistent units.
Volume of the tank = length × breadth × height = 40 m × 30 m × 6.5 m = 7800 m³.
Side of the square pipe = 20 cm = 0.20 m, so its cross-sectional area = 0.20 m × 0.20 m = 0.04 m².
Speed of water through the pipe = 5 km/hr = 5000 m/hr.
Volume flow rate of the pipe = area × speed = 0.04 m² × 5000 m/hr = 200 m³ per hour.
Time to empty the tank = Volume ÷ Flow rate = 7800 m³ ÷ 200 m³/hr = 39 hours.
As an independent check, multiplying the flow rate back by this time gives 200 m³/hr × 39 hr = 7800 m³, which equals the tank's volume from step 1, confirming that 39 hours is correct.