Explain how an open-ended tube manometer measures pressure.

(N/A) An open-tube manometer is a simple device used to measure the pressure of a gas contained in a closed vessel.
It consists of a $U$-shaped tube containing a suitable liquid (often mercury or water).
One end of the tube is open to the atmosphere,and the other end is connected to the system whose pressure $(P)$ is to be measured.
Consider a point $A$ in the limb connected to the gas container and a point $B$ at the same horizontal level in the open limb.
According to the laws of fluid statics,the pressure at points at the same horizontal level in a continuous static fluid is the same.
Therefore,the pressure at point $A$ is equal to the pressure at point $B$: $P = P_B$.
The pressure at point $B$ is the sum of the atmospheric pressure $(P_a)$ and the pressure due to the liquid column of height $h$: $P_B = P_a + h \rho g$.
Thus,the absolute pressure of the gas is given by: $P = P_a + h \rho g$.
Here,$P_a$ is the atmospheric pressure,$h$ is the height difference of the liquid levels,$\rho$ is the density of the liquid,and $g$ is the acceleration due to gravity.
The term $(P - P_a) = h \rho g$ is known as the gauge pressure,which is directly proportional to the height $h$ of the liquid column.