Question

For the L-shaped vessel shown in the figure, determine the value of acceleration a so that pressure at point A becomes equal to $\frac{p_0}{2}$? ($p_0$ is atmospheric pressure)

• A. $g$
• B. $\frac{g}{2}+\frac{{\rho }^o}{2\rho h}$
• C. $\frac{p_0}{2\rho H}+g$
• D. $\frac{3p_0}{2\rho H}+g$

Answer 1

The correct option is C $\frac{p_0}{2\rho H}+g$

$p_A+\rho aH-\rho gH=p_B$
Here, $p_A=\frac{p_0}{2}$ and $p_B=p_0$
$\therefore -\frac{p_0}{2}=\rho gH-\rho aH$
$\Rightarrow \rho H(a-g)=\frac{p_0}{2}\Rightarrow =\frac{p_0}{2\rho H}+g$