Question

Water flows through a 2.9-cm-diameter hose 3.3 m/s. how long, in minutes, will it take to fill a 600 l child's wading pool?

Answer 1

Approximately 4.58 minutes.

Explanation:

The diameter of hose is in centimeters, that is 2.9 cm.

Velocity is in m/s that can be converted into cm/s.

Let the velocity be 'v'.

v = 3.3 m/s= 330 cm/s

The amount of water following through the cross sectional area of the hose is.

`A = \pi * r^2`

diameter = 2.9 cm

`r = 1.45 cm`

`A =\pi * (1.45)^2`

`A = 3.14 * 2.10`

`A = 6.601 cm^2`

The cross sectional are of the hose is approximately
`6.60 cm^2`. To volume of water that flows through the hose each second, multiply its velocity by the cross sectional area of the hose.

Volume/ second =
`330 * 6.60 =2178.61 cm^3/s`

This is approximately
`2718.61 cm^3/s`. There are
`1000 cm^3` in one liter.

Total volume
`= 600 * 1000 = 600,000 cm^3`

To determine the time in seconds, divide the total volume by the volume per second.

t =
`(600,000)/(2178.61) = 275.40 s`

This is roughly 275 seconds.

We can convert 275 seconds into minutes.

t (mins) =
`{275 \over 60 }=4.58` minutes.

So it will take 4.58 minutes to fill the wading pool.