Question

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is

• A. 4 times that in the other pipe
• B. times that in the other pipe
• C. 2 times that in the other pipe
• D. times that in the other pipe

Answer 1

The correct option is A 4 times that in the other pipe

$d_4=2cmand{d}_B=4cm\therefore r_A=1cmand{r}_B=2cm$
From equation of continuity av = constant
$\therefore \frac{v_A}{v_B}=\frac{a_B}{a_A}=\frac{\pi {\left(r_B\right)}^2}{\pi {\left(r_A\right)}^2}={\left(\frac{2}{1}\right)}^2\Rightarrow v_A=4v_B$