Started by Chemister , Sep 16 PM. You cannot start a new topic Please log in to reply. Posted 16 September - PM Pressure is a scalar quantity has magnitude but no direction , while Force is a vector has both magnitude and direction. Reply to quoted posts Clear. Sign In Need an account? Register now! However, strictly speaking, pressure is a tensor , but for gasses, it's isotropic, so it acts as a scalar. This is true in elastic solids, where you can transmit sideways forces to the surface, and in viscous flowing liquids, where the viscous force is also just a stress generalized pressure transmitted to the surface.
You'd need to measure all components of force on 3 surfaces placed in different orientations. Only in gasses, you can rely on the force having the same magnitude no matter the orientation.
Now, that looks like a horrendous way to over-complicate a formula that can be written much more succinctly, so: why am I writing it this way? Basically, because the force-pressure-area relationship is only one simple example of the broader class of ways in which force can be transmitted through a bulk medium.
If said bulk medium is isotropic, like a fluid, then the relationship boils down to the pressure, but if your bulk medium is a bit more complicated then you start getting more interesting things, like. For the simple case of a fluid, the shear stresses must vanish, and the isotropy of the fluid demands that all the diagonal elements be equal, which boil down to make the stress tensor a multiple of the identity matrix. However, that simplicity can often blind you to the larger structures at play, and it is only once you find the appropriate generalization that all the mathematical structures fall into place.
Pressure is a scalar because it does not behave as a vector -- specifically, you can't take the "components" of pressure and take their Pythagorean sum to obtain its magnitude. The way to understand pressure is in terms of the stress tensor, and pressure is equal to the trace of the stress tensor. Once you understand this, the question becomes equivalent to questions like "why is the dot product a scalar?
There is no physical significance to taking the diagonal components of a tensor and putting them in a vector -- there is a physical significance to adding them up, and the invariance properties of the result tells you that it is a scalar.
See also: Why do we need both dot product and cross product? Sign up to join this community. The best answers are voted up and rise to the top.
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Skip to main content. Search SpringerLink Search. Abstract The gradual emergence of a science of hydrostatics during the course of the seventeenth century is testament to the fact that a technical concept of pressure that was up to the task was far from obvious.
Notes 1. Additional information Alan Chalmers is an Honorary Senior Research Fellow in the School of History and Philosophy of Science at the University of Sydney, having joined that institution in with a PhD from the University of London on the introduction of the displacement current into electromagnetism.
Rights and permissions Reprints and Permissions. From the kinetic theory of gases, a gas is composed of a large number of molecules that are very small relative to the distance between molecules. The molecules of a gas are in constant, random motion and frequently collide with each other and with the walls of any container. The molecules possess the physical properties of mass, momentum, and energy. The momentum of a single molecule is the product of its mass and velocity, while the kinetic energy is one half the mass times the square of the velocity.
As the gas molecules collide with the walls of a container, as shown on the left of the figure, the molecules impart momentum to the walls, producing a force perpendicular to the wall.
The sum of the forces of all the molecules striking the wall divided by the area of the wall is defined to be the pressure. The pressure of a gas is then a measure of the average linear momentum of the moving molecules of a gas. The pressure acts perpendicular normal to the wall; the tangential shear component of the force is related to the viscosity of the gas. Let us look at a static gas; one that does not appear to move or flow.
While the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion. Because we are dealing with a nearly infinite number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container.
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