Let’s go through the following subtopics: (1) Pressure definition (2) formula of pressure and (3) SI unit of pressure
Definition of Pressure
Pressure (P) is defined as the normal force F per unit area A over which the force is applied, or P = F/A …………… (1)
To define the pressure at a specific point, the pressure is defined as the force dF exerted by a fluid over an infinitesimal element of area dA containing the point, i.e., P = dF/dA ………….(2)
Formula of Pressure
P = F/A …………… (1)
P = dF/dA ………….(2)
Importance of surface area to calculate pressure
You must have noticed that a sharp needle is able to poke through the skin when a small force is exerted, but applying the same force with a finger does not puncture the skin. While injecting vaccines this is what we notice always.
A given force can have a significantly different effect, depending on the area over which the force is exerted.
For instance, a force applied to an area of 1 mm^2 has a pressure that is 100 times as great as the same force applied to an area of 1 cm^2.
SI unit of Pressure: Pascal
Note that although the force is a vector, pressure is a scalar. Pressure is a scalar quantity because it is defined to be proportional to the magnitude of the force acting perpendicular to the surface area.
The SI unit for pressure is the pascal (Pa), named after the French mathematician and physicist Blaise Pascal (1623–1662), where
1 Pa = 1 N/m^2.