Question

Water is discharged from a pipe of cross-sectional area $3.2c{m^2}$ at the speed of $5m/s$. Calculate the volume of water discharged in $c{m^3}$ per sec.

Answer 1

Hint: Generally the pipes are cylindrical in shape.
To find the volume of water in any shape we multiply the area of the base with the height of water in the solid
Volume = Area $ \times $ Height
Here the height of water in the pipe is calculated using the rate of flow of water or the length covered in 1 second time.

Formula used: Volume of water = Area of cross section $ \times $ Rate of speed of water

Complete step by step solution:
Cross section of any solid shape is the surface which is visible from the top. In case of a pipe the cross section is in the shape of a circle whose area can be calculated by the formula $\pi {r^2}$.
But here it is given that,
Area of cross section $ = 3.2c{m^2}$
The rate of speed $ = 5m/\sec $
First we will convert speed in $cm/\sec $
We know that 1 m $ = $ 100 cm
Hence,
$5m/\sec = 500cm/\sec $
From the formula explained above we can find volume of water per second.
The volume of water flowing per sec $ = $ area of cross section $ \times $ length covered in 1 second
$ = 3.2 \times 500$
$ = 1600c{m^3}$

So volume of water discharged per sec $ = 1600c{m^3}$.

Note: To solve any mathematical problem, the units should be the same.
Here the area of the cross section is given in $c{m^2}$ but the rate of flow of water is given in m/s.
So first we need to convert m/s into cm/s by multiplying the value by 100 otherwise the answer will come out to be wrong.