why is pressure a scalar quantity ?

Question

it is the normal force applied per unit area.
so, if i push on a table,with some force,then surely my pressure has got a definite direction?
it does not follow the laws of vector addition?
plz explain .

hey plz can u compare both force n pressure in this regard so that i may be more clear ?

Answer 1

You are right that you're hand is exerting a force on the table in a specific direction. Are you exerting a pressure in a given direction? Yes, in all directions equally, as a matter of fact. Pressure on the table downward, pressure on your hand to the sides and upward. Easier to see if you put an air balloon between your hand and the table, as the balloon reveals the effect of pressure to the sides quite clearly. Your hand should easily notice a pressure against it (upward). So an equal pressure on all surfaces reveals that pressure cannot be directed solely in a vectorial manner, but vectorial forces do result when objects react/respond differently to changes in pressure.

As an experiment, though, try to create pressure which acts only in one direction. Most people might think to create pressure gradients (differences), but these only illustrate that forces arise at normal angles to tangential areas of resistance to equilibrium. Put a steel ball bearing in a balloon, fill it with pressured air, and try to use the equilibrium pressure to act on the bearing in any given direction. This may be frustrating until it is accepted that the normal area vector to pressure gradient interfaces is required to produce a vectorial force.

Answer 2

Scalar nature of pressure
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In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large 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. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

A closely related quantity is the stress tensor σ which relates the vector force F to the vector area A via

\mathbf{F}=\mathbf{\sigma A}

This tensor may be divided up into a scalar part (pressure) and a traceless tensor part shear. The shear tensor gives the force in directions parallel to the surface, usually due to viscous or frictional forces. The stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.

Answer 3

Definition of Pressure

There are two ways to look at pressure: (1) the small scale action of individual air molecules or (2) the large scale action of a large number of molecules. The small scale action is described by the kinetic theory of gases and we have no evidence that the Wright brothers were familiar with this theory when they designed the aircraft and engine. So we will not discuss the details of this theory at this web site; if you wish to explore the kinetic theory of gases you should visit: http://www.grc.nasa.gov/WWW/K-12/airplane/kinth.html.
The most important result from the small scale view of pressure is that the pressure in a gas is related to the momentum of the individual moving gas molecules. Momentum is mass times velocity. So the higher the velocity of the molecules of a gas, the greater the pressure. The temperature of a gas depends on the average kinetic energy (mass times velocity squared) of the molecules of the gas, so the temperature and pressure of a gas are related to each other through an equation of state. Considering the large scale, pressure P is defined to be the force F acting on an area A divided by the area that it acts on.

P = F / A


Scalar Quantity

Let us look at a gas that does not appear to move or flow. Actually, while the gas 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 large number of molecules (nearly infinite) 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 will detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per area (the pressure) will be the same. (If the gas as a whole were moving, the measured pressure would be different in the direction of the motion, as described by Bernoulli's equation .) We could shrink the size of our "container" down to an infinitely small point, and the pressure would have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity, like velocity that has a specified direction associated with it. Pressure has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

Magnitude of Pressure Force

The magnitude of the pressure force is equal to the pressure (force/area) times the surface area, and the direction is perpendicular to the surface. In the figure, we have a gas (in red) that is confined in a box. A force is applied to the top of the box. The pressure force within the box opposes the applied force. And the pressure equals the external force divided by the area of the top of the box. Inside the gas, the pressure acts in all directions. So the pressure would also push on the bottom of the box and on the sides. This is different from simple solid mechanics. If the red gas were a solid, there would be no forces applied to the sides of the box; the applied force would be simply transmitted to the bottom. But in a gas, because the molecules are free to move about and collide with one another, a force applied in the vertical direction causes forces in the horizontal direction.

reff:http://wright.nasa.gov/airplane/pressure.html

Answer 4

Force applied on a surface is definitely a vector because it has direction and magnitude both. But when the force is transmitted into the body gas or liquid or solid, the force per unit area would have different directions as the whole of the surface when divided into tiny areas or grains (in case of solid), the individual tiny unit surfaces or the grains may have varied orientations, as in the case of spherically inflated balloon, the entire surface of the sphere has different orientations and hence the force, although is a vector, manifests itself in terms of reactive forces per unit area which would have many directions and hence no particular direction or sense. So pressure is believed to be scalar in that sense. But to talk about pressure, pressure gradient is certainly questionable as to be scalar or vector? Similar questions arise for temperature gradient. Because pressure or temperature gradients (del T or del P) generate driving force and force is a vector quantity, so they(del T or del P) are also supposed to be vector quantities in the scalar field? Please respond to this point.

Answer 5

Pressure is a concept applied to fluids. It is force per cross sectional area. Since fluids can move the pressure is in all directions not just the direction of the force, therefore pressure has no defined direction and is a scalar. Force per area on a solid is technically not pressure though many people use that word when they should refer to that as stress.

Answer 6

If you push on a table you are applying a force not pressure. Pressure like you said is an applied force per unit area. THere is no vector associated with pressure.

Answer 7

If the area is a vector the the pressure has direction.
Foprexample the pressure of gravity is a unit of area.That area has a direction on the sphere.The area is usually measured in steradians. You are basically measuring the force resuting on that area. Hence force is directional and so is the pressure.So to describe pressure you have to indicate where the force exists,so location can be expressed as a vector or tensor..

Answer 8

It should be noted that pressure is force per unit area acting perpendicularly to the surface. This means that what we divide by area is not just the force but the dot product of the force and the unit vector perpendicular to the surface. This dot product is a scalar and hence pressure is actually a scalar. (a scalar divided by another scalar is a scalar. )

Answer 9

Pressure is a force that acts in all directions at once. A regular force, like your hand pushing something, acts in only one direction at a time. So the only thing about pressure is how much. But for the hand force you need to know both how much AND what direction.

Answer 10

if i push on a table,with some force,then surely my pressure has got a definite direction

No force has direction, pressure has no direction. This is because:

Pressurex Area=Force
So to force to b a vector, area to be a vector(perp to its plane) pressure has to be scalar.

Also theoratically also, it should be a scalar you know(think tyres filled with air)