Physics > Fluid Mechanics > 2.0 Fluid pressure
Fluid Mechanics
1.0 Introduction
1.1 Ideal liquid
1.2 Density of a liquid $\left( \rho \right)$
1.3 Relative density of a liquid $(RD)$
1.4 Density of a mixture of two or more liquid
1.5 Density variation with temperature
1.6 Density variation with pressure
2.0 Fluid pressure
2.1 Atmospheric pressure
2.2 Pressure variation with depth
2.3 Measurement of pressure
2.4 Pressure difference in accelerating fluids
3.0 Pascal's law
4.0 Buoyant force
5.0 Flow of fluids
6.0 Viscosity
7.0 Stoke's law
8.0 Intermolecular forces
9.0 Angle of contact
2.3 Measurement of pressure
1.2 Density of a liquid $\left( \rho \right)$
1.3 Relative density of a liquid $(RD)$
1.4 Density of a mixture of two or more liquid
1.5 Density variation with temperature
1.6 Density variation with pressure
2.2 Pressure variation with depth
2.3 Measurement of pressure
2.4 Pressure difference in accelerating fluids
Pressure is measured by the two types of devices.
1. Barometer
2. Manometer
2.2.1 Barometer
Barometer is a device which is used to measure atmospheric pressure.
Mercury $(Hg)$ is filled inside the barometer as shown in the figure
As we know, \[\left. \begin{gathered} {P_1} = {P_2} \hspace{1em} \\ {P_O} = {P_1} \hspace{1em} \\ \end{gathered} \right\}\quad ...(i)\] Also, $$\begin{equation} \begin{aligned} {P_2} = P + \rho gh \\ {P_2} = 0 + \rho gh \\ {P_2} = \rho gh\quad ...(ii) \\\end{aligned} \end{equation} $$
From equation $(i)$ and $(ii)$ we get, $${P_1} = \rho gh\quad or\quad {P_O} = \rho gh$$
So, the atmospheric pressure is directly proportional to the height of the mercury column.
For 1 atm pressure, height of the mercury column is 760 $mm$.
2.3.2 Manometer
A manometer is a device which is used to measure the pressure of a gas inside a container.
The U-shaped tube is filled with $Hg$.
Let the pressure exerted by gas be $P$. So, $$P = {P_1}\quad ...(i)$$
As we know that the pressure at the same level is equal. So, $${P_1} = {P_2}\quad ...(ii)$$
Also, $${P_2} = {P_O} + \rho gh\quad ...(iii)$$
From equation $(i)$, $(ii)$ and $(iii)$ we get, $$\begin{equation} \begin{aligned} P = {P_O} + \rho gh \\ \left( {P - {P_O}} \right) = \rho gh \\\end{aligned} \end{equation} $$
$P$: Absolute pressure
$P_O$: Atmospheric pressure
$\left( {P - {P_O}} \right)$: Gauge pressure
So, $${\text{Gauge pressure}} = \rho gh$$
Therefore, the manometer measures gauge pressure.
