Question

Two water pipes P and Q having diameters $2\times {10}^{-2}m$ and $4\times {10}^{-2}m$, respectively, are joined in series with the main supply line of water. The velocity of water flowing in pipe P is:

• A. $4$ times that of Q.
• B. $2$ times that of Q
• C. $\frac{1}{2}$ times that of Q
• D. $\frac{1}{4}$ times that of Q

Answer 1

The correct option is A $4$ times that of Q.

Answer is A.
An increase or decrease in flow rate will result in a corresponding increase or decrease in velocity. 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 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 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, velocity of flow of water in the pipe of 2 cm diameter is 4 times that in the other pipe.