91Ó°ÊÓ

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

Pressure can be mathematically expressed as

$$\begin{gathered} P=\frac{F}{A} \\ =h\mathrm{ÒÏ}g \end{gathered}$$

Here, P is the pressure, Fis the force, Ais the area, his the depth,ÒÏ is the densityand,gis the acceleration due to gravity.

Pressure unit millimetres of mercury, centimetres of water and inches of mercury can be easily converted into newton per meter squared if we know the depth, density and acceleration due to gravity.

Millimetres, centimetres, and inches are the units of depth.

The density of mercury and water and the acceleration due to gravity are also known.

$$\begin{gathered} \mathrm{ÒÏ}ofmercury=13545.848kg/m^3 \\ \mathrm{ÒÏ}ofwater=997.77kg/m^3 \\ g=9.8m/s^2 \\ 1inch=0.0245m \end{gathered}$$

Conversion can be by multiplyingÒÏ,gandh.

$$\begin{gathered} \text{1 mm of Hg}={10}^{-3}m×13545.848 kg/m^3×9.8 m/s^2 \\ =132.75 N/m^2 \\ \text{1 cm of water}={10}^{-2} m×997.77 kg/m^3×9.8 m/s^2 \\ =98.78 N/m^2 \\ \text{1 inch of Hg}=0.0254 m×13545.848 kg/m^3×9.8 m/s^2 \\ =3371.83 N/m^2 \end{gathered}$$

Therefore, the conversion to newtons per meter squared can be done manually by multiplying height, density, and acceleration due to gravity.