Question

A liquid flowing with speed v through a horizontal pipe of cross sectional area A enters into another pipe of double the area of cross section. Now, the speed of the liquid is :

• A. $v$
• B. $2v$
• C. $v/2$
• D. $v/4$

Answer 1

The correct option is C $v/2$

Answer is C.
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.
In this case, the second pipe is of double the area of cross section.
Hence, if the area of cross section is doubled, the speed of the liquid becomes half. That is, v/2.