Question

A non-viscous liquid is flowing through a non-uniform pipe from section $A$ to section $B$ as shown in the following figure. Cross-sectional area of the pipe at $A$ is less than that at $B$. Which of the following statements are correct?

• A. The pressure at $A$ is greater than that at $B$
• B. Velocity at $A$ is greater than that at $B$
• C. Total energy per unit volume of the liquid is greater at $A$ than at $B$
• D. Axis of the pipe cannot be horizontal

Answer 1

Answer: (A), (B), (D)

Axis of the pipe cannot be horizontal

Since liquid is flowing from $A$ to $B$, hence, $P_A>P_B$.
According to equation of continuity
$a_1{v}_1=a_2{v}_2$
As, $a_2>a_1$, hence $v_1>v_2$
As the liquid is non-viscous, there is not loss of energy, i.e., energy per unit volume of the liquid is same at every point.
So, (c) is wrong.
Here, $P_A>P_B$, $v_A>v_B$ and energy/volume of liquid is same at every point. So $(PE{)}_A<(PE{)}_B$.
Hence, section $A$ must be at lower level than section $B$, i.e., pipe cannot be horizontal.