>>13148226Stress is a real, symmetric, second-order tensor called S. In brainlet terms, picture a very small cube oriented in some orthogonal 3D coordinate system (cartesian or cylindrical, for example), and at static equilibrium (it isn't moving or spinning or anything like that). This cube may be located in a fluid, within a solid material, or a chunk of gas, but whatever it is, it must be homogeneous. Then there are nine possible forces acting on the cube: The first three forces (per unit area) are on the x-face acting in the direction of x (S_xx), on the y-face acting in the direction of y (S_yy), and on the z " " " " " z. These are called axial stresses and are located on the diagonal of the matrix of S. Axial stresses are sometimes called "tension" if positive or "compression" if negative. Then, on the x-face for example, you could have a force in the y (S_xy) or z direction (S_xz), and on then on the y-face, and so on. These are shear stresses. That's 3*2=6 shear + 3 axial stresses = 9 components total to the S matrix. By mechanical equilibrium, S_ij=S_ji. S is real and symmetric and so the principal directions of stress are orthogonal up to degeneracy, the principal stresses are eigenvalues of S, the trace of S is invariant to a change in coordinate system and equal to the sum of all principal stresses, blah blah blah.
The punchline is that, because there are no shear stresses in a FLUID at rest (important), we have stress and pressure related by where S is stress, p is pressure, and the delta thingy is something called the Kronecker delta/identity tensor.
>I didn't read all that shitStress is a mechanical quantity and a tensor (meaning: not a single number)
Pressure is a thermodynamic property of a fluid and a scalar (a regular ass number)
Pressure and stress both are described in units of force per area, but they measure fundamentally different things (kinda like energy and torque).
