Question

A cylindrical pipe has inner diameter of $7cm$ and water flows through it at $192.5$ litres per minute. Find the rate of flow in kilometers per hour.

Answer 1

We have

Volume of water that flows per hour $=(192.50\times 60)litres=(192.50\times 60\times 1000){cm}^3.....\left(i\right)$

Inner diameter of the pipe $=7cm$

Inner radius of the pipe $=\frac{7}{2}cm=3.5cm$

Let $h$ cm be the length of the column of water that flows in one hour
Clearly, water column forms a cylinder of radius $3.5cm$ and length $h$ cm
Volume of water that flows in one hour = volume of the cylinder of radius $3.5cm$ and length $h$ cm

$=(\frac{22}{7}\times {\left(3.5\right)}^2\times h){cm}^3$.....$(volumeofcylinder=\pi r^{2}h)$

From (i) and (ii) we have

$\frac{22}{7}\times {\left(3.5\right)}^2\times h=192.50\times 60\times 1000$

$\Rightarrow h=\frac{192.50\times 60\times 1000\times 7}{22\times 3.5\times 3.5}cm=3km/hr$