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Water flows into a tank 200m × 150 m through a rectangular pipe 1.5m × 1.25 m at the rate of 20 kmph. In what time (in minutes) will the water rise by 2 meters?

User Pauljeba
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Final answer:

To find the time it takes for the water to rise by 2 meters in a tank, we calculate the flow rate of water into the tank and then determine the volume increase. Converting the water flow to a compatible unit with the tank dimensions, we find it would take approximately 96.62 minutes.

Step-by-step explanation:

The problem is related to fluid dynamics in Mathematics. Given a rectangular tank and pipe, we need to calculate how long it will take for the water to rise a certain height. First, we will convert the velocity of the water from kmph to m/s. Then, find the volume of water needed to raise the tank's water level by 2 meters and finally calculate the time required for the water flow to fill that volume.

Convert the rate of 20 kmph to m/s:
20 km/h * (1000 m/km) / (3600 s/h) = 5.56 m/s.

Calculate the volume needed to raise the water level by 2 meters:
200 m * 150 m * 2 m = 60000 m³.

Flow rate of the pipe (volume per second):
1.5 m * 1.25 m * 5.56 m/s = 10.35 m³/s.

Calculate the time required to fill the tank:
60000 m³ / 10.35 m³/s = 5797.10 s.

Convert seconds to minutes:
5797.10 s / 60 s/min ≈ 96.62 minutes.

Thus, it will take approximately 96.62 minutes for the water to rise by 2 meters in the tank.

User Zi
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