Question

Water is flowing in streamline motion through a tube with its axis horizontal. Consider two points A and B in the tube at the same horizontal level.

• A. The pressures at A and B are equal for any shape of the tube.
• B. The pressures are never equal.
• C. The pressures are equal if the tube has a uniform cross section.
• D. The pressures may be equal even if the tube has a non-uniform cross section.

Answer 1

Answer: (C), (D)

The correct options are
C

The pressures are equal if the tube has a uniform cross section.

D

The pressures may be equal even if the tube has a non-uniform cross section.

We know $A_1{V}_1=A_2{V}_2$
Now if $A_{=}{A}_2$
$\Rightarrow V_1=V_2$
So for the tube of uniform cross - section $V_1=V_2$
Now even if the cross section is not uniform

Consider a situation as shown above,
Now if $A_1=A_2$
$\Rightarrow V_1=V_2$
So velocities can be equal even if the cross section of the pipe is non-uniform.