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.

23

Explanation:

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

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

Calculate the flow rate given the velocity and hose diameter:

Q = vA

Q = v (¼ π d²)

Q = (0.30 m/s) (¼ π (0.0191 m) ²)

Q = 8.55*10⁻⁵ m³/s

Find the volume of the pool:

V = π r² h

V = π (1.5 m) ² (1.0 m)

V = 7.07 m³

Find the time:

t = V / Q

t = (7.07 m³) / (8.55*10⁻⁵ m³/s)

t = 82700 s

t = 23 hr