why stress & pressure are two different physical quantities though they have same formula force/area?

Answer 1

I liked Dr. R's answer, because it was accurate, succinct and complete. However, to state it somewhat more plainly to the uninitiated, what we commonly call "pressure" would be more accurately termed hydrostatic compression. This is actually just a special case of the more general term "stress."

A state of stress is said to be hydrostatic when the three normal components of its stress tensor (σ_xx, σ_yy and σ_zz) are equal in magnitude and of the same sign. Under this condition, all six of the shear stress components are of zero magnitude. "Pressure", or hydrostatic compression, is when all three are equal and of negative sign (pushing inward). Similarly, "vacuum" (negative pressure), or hydrostatic tension, is when all three are equal and of positive sign (pulling outward).

In summary, "pressure" is not a different physical quantity from "stress", it's merely one particular kind of it. And by convention, we use the term "pressure" almost exclusively in reference to stresses in fluids (liquids and gases), because hydrostatic conditions are always(?) present there.

Answer 2

Stress has units of pressure, and hydrostatic pressure is indeed one form of stress. There is also tensile stress (the force per unit area on a uniaxially stretched or compressed solid) and shear stress (the force per unit area on a shear plane resulting from lateral deformation of a solid). All these effects may be combined into something called a stress tensor (a matrix with 9 elements) that is used in the equation of motion for continuum dynamics.

Answer 3

well, you are asking about the difference between them?

I think Dr.R went so far in his Answer.

coz the asker asks about the main difference between them and Dr.R went into unnecessary details.

any why the answer is :

Yes, both have the same formula but if

Force is applied on a cross-sectional area in SOLIDS then the result will called Stress.

but

If force is applied on a cross-sectional area in liquids then the result will called Pressure.





Good Luck.