Question

Question #14291

Answer 1

Pressure is a scalar quantity.
Stress is a second-order tensor of type (0,2).

Explanation:

Pressure `p` is defined as force applied perpendicular to the surface of an object per unit area over which the applied force is distributed.
Mathematically:
`p = F /A`

where `F` is the normal force and `A` is the area of the surface in contact.

Pressure is always compressive and outcome of perpendicular force applied on the area. It compresses the surface on which it acts. Pressure is often used with fluids (gases or liquids).

It is a scalar quantity. SI unit of pressure is Pascal (Pa) which is equal to one newton per square metre, `Nm^-2 or kgm^(−1)s^(−2)`

Whenever an external force is applied on any object a restoring force is developed inside to restrict its deformation. This is called Stress. It is a measure of the internal restoring force an object experiences per unit cross sectional area whenever an external force is applied on the object. Hence, the formula for calculating stress `σ` is the same as the formula for calculating pressure. However it is denoted as

`σ = F /A`

where `F` is force, and `A` is area cross section of the sample. Its units are also Newtons per square metre or Pascals.
Stress is more often used with solids.

As shown in the figure above it can be of three types.
(a) compressive stress, (b) tension, due to elongation of sample
(c) shear.
(a) and (b) are normal whereas (c) is tangential stress. Stress is a second-order tensor of type (0,2).