Question

In this figure, an ideal liquid flows through the tube having uniform area of cross-section and is held in vertical plane. Find the ratio of speed of liquid at $A$ and $B$ and also find the pressure difference between these points.

• A. 2 lgh
• B. lgh
• C. $\frac{3}{2}$ lgh
• D. zero

Answer 1

Answer: (B)

As area of cross-section is uniform therefore according to equation of continuity speed of liquid is same at all points
i.e., $v_{A}=v_{B}$
But during motion of liquid from $A$ to $B$ the potential energy decreases.
$\therefore $ According to Bernoulli's theorem,
$\frac{1}{2} v^{2}+g h+\frac{p}{\rho}=$ constant
$\Rightarrow g h+\frac{p_{A}}{\rho}=\frac{p_{B}}{\rho} $
$\Rightarrow p_{B}-p_{A}=\rho g h$