Is pressure a scalar or a tensor
If force is a vector then why is pressure a scalar? [Duplicate]
Pressure is a proportionality factor. The area gives you the direction. You need to remember that pressure is defined anywhere in the volume, not just on the surface. A gas volume has a defined pressure everywhere. And the direction of the force is up to you - the way you align your surface that you put into the gas.
It is wrong (although more common) to say "the pressure is going one way or the other". The pressure as a scalar has no direction. The force given by the previous relationship to the crowd has a direction, but the pressure does not. If we change the orientation of the surfel, the direction of the normal force changes accordingly, but the pressure remains the same.
I should make this clear the through the pressure caused force calculated so that given the area vector, you get the force perpendicular to the surface. It is the defining Equation and the only one that records what pressure actually does. So it is always true, but it must be understood as a formula for calculating the force from pressure.
If F.⃗ is only caused by the pressure, it can nothing other than perpendicular to the area, otherwise other forces will be present in the system or the liquid will not be isotropic. Apart from that, assuming the F.⃗ is only caused by the pressure, one could calculate p by absolute values:
Mathematically speaking, you've converted a vector equation into a scalar equation, the parallel vectors presupposes. Now you are not allowed to enter anything, only lengths (or projections - similar argument) of F and A, which were otherwise guaranteed to be parallel. You get nonsense. You also lose the pressure mark (this cannot happen with gases, but with elastic solids or liquids it can "pull" due to intermolecular forces).
Strictly speaking, pressure is a Tensor , but for gases it is isotropic so that it acts as a scalar. Furthermore, imagine, without going into details, what a tensor is pA.⃗, p can also change the direction, not just the size of EIN⃗ so the force does not have to point perpendicularly. This applies to elastic solids where you sideways Can transfer forces to the surface, and for viscous fluids where the viscous force is also just a tension (generalized pressure) transferred to the surface. In this situation, p has 6 independent components, so you they don't can only measure by measuring a force on a single surface. You would have to measure all force components on 3 surfaces that are arranged in different orientations. Only with gases can you be sure that the force will be the same regardless of the orientation.
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