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A garden hose with an inside diameter of 0.75 inches is used to fill a round swimming pool 3.0 m in diameter. How many hours will it take to fill the pool to a depth of 1.0 m if water flows from the hose at a speed of 0.30 m/s? Enter your answer without units.

Respuesta :

MathPhys

Answer:

23

Explanation:

First, we need to convert the hose diameter from inches to meters.

0.75 in Ɨ (2.54 cm / in) Ɨ (1 m / 100 cm) = 0.0191 m

Calculate the flow rate given the velocity and hose diameter:

Q = vA

Q = v (Ā¼ Ļ€ dĀ²)

Q = (0.30 m/s) (Ā¼ Ļ€ (0.0191 m)Ā²)

Q = 8.55Ɨ10ā»āµ mĀ³/s

Find the volume of the pool:

V = Ļ€ rĀ² h

V = Ļ€ (1.5 m)Ā² (1.0 m)

V = 7.07 mĀ³

Find the time:

t = V / Q

t = (7.07 mĀ³) / (8.55Ɨ10ā»āµ mĀ³/s)

t = 82700 s

t = 23 hr

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