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,
$\frac{1}{2}{v}^2+gh+\frac{p}{\rho }=$ constant
$\Rightarrow gh+\frac{p_A}{\rho }=\frac{p_B}{\rho }$
$\Rightarrow p_B-p_A=\rho gh$