Question

Pressure is vector quantity. State true or false.

Answer 1

Hint: Pressure is defined as the thrust applied per unit area. Mathematically it is defined as the ratio of force perpendicular to a surface and the area of the surface. According to this, we will discuss why the pressure will be a scalar of a vector. We will also discuss how Pascal's law gives the nature of pressure.

Complete answer:
The pressure is defined as the thrust per unit area on a surface. Thrust is the perpendicular force on the surface. So, overall pressure is defined as the amount of perpendicular force per unit area. So according to this there must be some direction associated with the pressure as it is some force acting perpendicular to the unit area. However, that is not the case to define the force acting perpendicular to the surface. We will need to take the scalar product of force and area and then we will divide this whole quantity by the area on which the force is acting. So, mathematically we get
$\dfrac{\overrightarrow{F}.\overrightarrow{A}}{|\overrightarrow{A}|}$as the force perpendicular to the area and the pressure as $\dfrac{\overrightarrow{F}.\overrightarrow{A}}{|\overrightarrow{A}{{|}^{2}}}$. For static fluids, the force is always perpendicular to the area, so the formula is written as $\dfrac{|\overrightarrow{F}|}{|\overrightarrow{A}|}$. Also, according to pascal’s law Pressure exerted anywhere on a confined incompressible liquid is transmitted equally and undiminished throughout the entire liquid. This also tells us that there is no direction to pressure. Hence the pressure will be a scalar quantity. So, the statement given in the question is false.

Note:
The direction of force on the surface can change by changing the orientation of the surface but the amount of pressure will always remain the same and will have no direction. So, pressure must never be considered as a vector quantity.