Question

A student measures pressure of a gas in a container using a mercury manometer and she also measures atmospheric pressure using a mercury barometer. She gave following representation

If $p_1=$ atmospheric pressure,
and $p_2=$ absolute pressure, then

• A. gauge pressure $=h_1+h_2$
• B. gauge pressure $=h_3-h_1$
• C. gauge pressure $=h_3$
• D. absolute pressure $=h_1$

Answer 1

Answer: (B)

As we know that, if $p_1$ represents the atmospheric pressure, then absolute pressure $p^{\prime }=p_1+\rho gh$ and gauge pressure, $p^{\prime \prime }=p^{\prime }-p_1=\rho gh$
From the given figure, we can write, $p_1=\rho g{h}_1$
$\Rightarrow p^{\prime }=p_2=\rho g{h}_1+\rho g{h}_2=\rho g\left(h_1+h_2\right)=\rho g{h}_3$
Similarly, $p^{\prime \prime }=p_2-p_1=\rho g{h}_3-\rho g{h}_1$
$=\rho g\left(h_3-h_1\right)=\rho g{h}_2$
$\therefore$ In terms of height, we can write,
Absolute pressure $=h_3=h_1+h_2$
Gauge pressure $=h_2=h_3-h_1$