Is pressure a rank 2 tensor?

ovais

Hi,all I am really very serious about what actually is the nature of pressure as a physical quantity.Books says it has no direction i.e. it is scalar some says it is not.but thinking ourselves it seems pressure has direction in the direction of applied force.Now I want to understand the mathematics behind this thing.I was taught on net some where that all physical quantites can be called tensors, now if the quantity has no direction associated with it then its rank is said to be zero and is given special name as scalar and if the quantity has a direction then it is ranked 1 and given the name vector and some quantities like angular momentum have rank 2, similarly we have quantities of rank 2, 3, and 4 also.I want to know the tensor rank of pressure.thanks a ton

Matthollyw00d

I think this would be better suited in the Physics area. But as far as I know Pressure is a scalar, what sort of argument do you have to think it's of rank 2?

cesiumfrog

Isn't it something like the diagonalisable part of the stress 2-tensor for the material/medium?

ovais

first of all thanks for your reply.I orignally posted this my query in physics area sir.But in time i feel a need to discuss this topic here as such there is some mathematics is involved in it.tensors are better studied in terms of matrices.I have studied scalars are tensors of rank zero because they have no asociation with direction.and vectors have a single direction asociated with them so rank of vectors is one.and quantities which envolve two directions in them are said to have rank 2.Is this true?

ovais

so i thought when a force(whic has some direction) acts on a surface then the force per unit surfce(which is defined as pressure) should act in the same direction and thus must have a direction in the direction normal to the surface.and as such when looking at force and area individually the value of force per unit area i.e. pressure.depends on the magnitude and direction of two things- force and area(as direction of area also matters) this makes me feel that tensor rank of pressure might be 2.please enlig

ovais

yes yes you are right! but i want two know how we get the matrix before we diagonalise it?since when i have to begin i have a force with direction and an area in known direction.now i only can make an area vector and thus left with two vectors-force, and area(with direction taken perpendicular to it.now what to do to obtain stress tensor which is a 3x3 matrix.

Matthollyw00d

I think your confusing pressure with stress; they are closely related.
If you're thinking that pressure has 2 directions, then think about a static gas in a container, at any point inside the gas, the pressure is the same for all directions.

ovais

I do agree that in container containing gas the pressure at any point is the same in all directions.But why is there a need to say this if pressure is a scalar quantity?

ovais

have you ever heared anybody saying, this mass or time at a point (which are scalars)has same value in all direction?.

Matthollyw00d

It was to give reasoning for why it was scalar, if you believe it to be scalar then why make this thread?
No, but does that stop it from being true?

ovais

thanks for your continue support.sir you mistook me when i say i agree that at point the pressure of a gas in a container is same in all direction.What i did want to know if pressure has nothing to do with direction then why do one of the pressure law states that at poin in a static fluid pressure is same every where.And i had made this post in this area to know the tensor analysis that say pressure is the diagonalise part of the stress tensor matrix.