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

Answer:

Approximately 4.58 minutes.

Step-by-step 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.  

$A = \pi \times r^2$

diameter = 2.9 cm

$r = 1.45 cm$

$A =\pi \times (1.45)^2$

$A = 3.14 \times 2.10$

$A = 6.601 cm^2$

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 = $330 \times 6.60 =2178.61 cm^3/s$

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

Total volume $= 600 \times 1000 = 600,000 cm^3$

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

t = $\frac{600,000}{2178.61} = 275.40 s$

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.