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.