A rectangular water reservoir is 7.2 m by 2.5 m at the base . Water flows into it through a pipe whose cross section is 5cm × 9cm at the rate of 20 m per second . Find the height to which the water will rise in the reservoir in 40 minutes ?
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The first step to the question is to find the volume of water that flows through the pipe within 1 second:
The cross sectional area of the pipe is 5cm by 9cm( This must dimensions of a rectangular pipe):
Volume is cross sectional area × height
Therefore volume per second is:
0.09 m × 0.05 m x 20 m = 0.09m²
0.09m² is the volume of water that enters through the pipe in 1 second.
Find volume that enters through the pipe in 40 minutes(2400 seconds)
that is, 0.09m² / s × 2400s = 216m³
216m³ is the volume of water that entered the tank after the ² 40 minutes.
Find the height of the tank that water of volume 216m² will reach.
volume = base x length x height
216 m³ = 7.2 m × 2.5 m × h
216 m³ = 18m² × h
therefore h = 216m³/18m²
h = 12 m
Therefore the water will reach a height of 12 meters.
The cross sectional area of the pipe is 5cm by 9cm( This must dimensions of a rectangular pipe):
Volume is cross sectional area × height
Therefore volume per second is:
0.09 m × 0.05 m x 20 m = 0.09m²
0.09m² is the volume of water that enters through the pipe in 1 second.
Find volume that enters through the pipe in 40 minutes(2400 seconds)
that is, 0.09m² / s × 2400s = 216m³
216m³ is the volume of water that entered the tank after the ² 40 minutes.
Find the height of the tank that water of volume 216m² will reach.
volume = base x length x height
216 m³ = 7.2 m × 2.5 m × h
216 m³ = 18m² × h
therefore h = 216m³/18m²
h = 12 m
Therefore the water will reach a height of 12 meters.
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