Question

Water is flowing through two horizontal pipes of different diameter which are connected together. The diameter of the two pipes are $3cm$ and $6cm$ respectively. If the speed of water in the narrower tube is $4m/s$. Then, the speed of water in the wider tube is :

• A. $16m/s$
• B. $1m/s$
• C. $4m/s$
• D. $2m/s$

Answer 1

The correct option is B $1m/s$

Radius of tube $1=\left[\frac{Diameteroftube1}{2}\right]=\left[\frac{3}{2}\right]cm$

Radius of tube $2=\left[\frac{Diameteroftube2}{2}\right]=\left[\frac{6}{2}\right]cm=8cm$

According to the equation of continuity :-

$A_1{V}_1=A_2{V}_2$

or $R_1^2{V}_1=R_2^2{V}_2$

Where

$R_1=$ Radius of tube 1

$R_2=$ Radius of tube 2

$V_1=$ Speed of water in narrow tube

$V_2=$ Speed of water in in wider tube

$\Rightarrow (\frac{3}{2}{)}_2\times 4=(3{)}_2\times V_2$

$\Rightarrow \frac{9}{4}\times 4=9\times V_2$

$\Rightarrow V_2=1m/s$