Question

Consider a U-tube, open at left end and closed at right end. If the pressure above the liquid in the right arm is $P$, find the value of $P$.
Given: ${\rho }_2=2\times 13.6{\text{g/cm}}^3,{\rho }_1=13.6{\text{g/cm}}^3$, Atmospheric pressure $P_a=76$ cm of $Hg$.

• A. $P_a$
• B. $2P_a$
• C. $3P_a$
• D. $4P_a$

Answer 1

The correct option is B $2P_a$


The line $AB$ is passing through the same liquid. Now, the pressure in the liquid at the same level is the same, i.e., at $A$ and $B$ the pressure will be equal. The manometric equation is,
$P_a+{\rho }_{2}yg+{\rho }_{1}xg=P$

$P_a+13.6\times {10}^3\times 2\times 0.25\times g+13.6\times {10}^3\times 0.26\times g=P$

$P_a+0.76\times 13.6\times {10}^3\times g=P....\left(i\right)$

Now, $P_a=76\text{cm}$ of mercury

$\therefore P_a=0.76\times 13.6\times {10}^3\times g....\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$, we can write,

$P=2P_a$

Hence, $\left(B\right)$ is the correct answer.

Key concept: In the same liquid, pressure will be same at all points, which are at the same level.