Question

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

• A. $4$ time that in the other pipe
• B. $\frac{1}{4}$ times that in the other pipe
• C. $2$ times that in the other pipe
• D. $\frac{1}{2}$ times that in the other pipe

Answer 1

The correct option is A $4$ time that in the other pipe

Answer is A.
An increase or decrease in flow rate will result in a corresponding increase or decrease in velocity. A smaller pipe causes a greater proportion of the liquid to be in contact with the pipe, which creates friction. Pipe size also affects velocity. Given a constant flow rate, decreasing pipe size increases the velocity, which increases friction. The friction losses are cumulative as the fluid travels through the length of the pipe. The greater the distance, the greater the friction losses will be.

As the average velocity increases, pressure losses increase. Velocity is directly related to the flow rate.

From the equation of continuity, $av=$constant.
We have, $d_p=2cm,d_q=4cm,r_p=1cm,r_q=2cm$.
Therefore, $\frac{V_p}{V_q}=\frac{A_p}{A_q}=\frac{\pi {r_p}^2}{\pi {r_q}^2}={\left(\frac{2}{1}\right)}^2=V_p=4V_q$.

Hence, the velocity of flow of water in the pipe of $2cm$ diameter is $4$ times that in the other pipe.