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At the end of the summer, a swimming pool is being drained through a very long, small-diameter hose. The hose is smooth, of inner diameter D = 6.0 cm, and of length L = 65 m. The initial height difference from the pool surface to the outlet of the hose is H = 2.20 m. Calculate the volume flow rate in litres per minute (LPM) at the start of draining.?
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At the end of the summer, a swimming pool is being drained through a v...
Calculation of Volume Flow Rate of Draining Swimming Pool


Given Data


  • Inner diameter of hose, D = 6.0 cm

  • Length of hose, L = 65 m

  • Initial height difference, H = 2.20 m



Formula

Volume flow rate, Q = A × v

Where,

  • Q = volume flow rate (LPM)

  • A = cross-sectional area of the hose (m²)

  • v = velocity of water (m/s)



Cross-sectional area of the hose, A = π × (D/2)²

Velocity of water, v = √(2gh)

Where,

  • g = acceleration due to gravity (9.81 m/s²)

  • h = height difference between the pool surface and the outlet of the hose (m)



Solution

First, let's convert the diameter of the hose from cm to m:

D = 6.0 cm = 0.06 m

Cross-sectional area of the hose, A = π × (0.06/2)² = 0.002827 m²

Velocity of water, v = √(2gh) = √(2 × 9.81 × 2.20) = 6.26 m/s

Volume flow rate, Q = A × v = 0.002827 × 6.26 = 0.0177 m³/s

Now, let's convert the volume flow rate from m³/s to LPM:

1 m³/s = 60000 LPM

Therefore, Q = 0.0177 × 60000 = 1062 LPM

Conclusion

The volume flow rate at the start of draining the swimming pool is 1062 LPM.
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At the end of the summer, a swimming pool is being drained through a very long, small-diameter hose. The hose is smooth, of inner diameter D = 6.0 cm, and of length L = 65 m. The initial height difference from the pool surface to the outlet of the hose is H = 2.20 m. Calculate the volume flow rate in litres per minute (LPM) at the start of draining.?
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At the end of the summer, a swimming pool is being drained through a very long, small-diameter hose. The hose is smooth, of inner diameter D = 6.0 cm, and of length L = 65 m. The initial height difference from the pool surface to the outlet of the hose is H = 2.20 m. Calculate the volume flow rate in litres per minute (LPM) at the start of draining.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about At the end of the summer, a swimming pool is being drained through a very long, small-diameter hose. The hose is smooth, of inner diameter D = 6.0 cm, and of length L = 65 m. The initial height difference from the pool surface to the outlet of the hose is H = 2.20 m. Calculate the volume flow rate in litres per minute (LPM) at the start of draining.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At the end of the summer, a swimming pool is being drained through a very long, small-diameter hose. The hose is smooth, of inner diameter D = 6.0 cm, and of length L = 65 m. The initial height difference from the pool surface to the outlet of the hose is H = 2.20 m. Calculate the volume flow rate in litres per minute (LPM) at the start of draining.?.
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