# Why is the dynamic pressure not a vector quantity? [duplicate]

This question already has an answer here:

I understand that static pressure is a scalar quantity as it acts equally in all directions, then by the same reasoning dynamic pressure should be a vector quantity as it only can be measured by opposing the flow.

I understand that the act of opposing the flow will instantly convert dynamic to static but I am asking in theory?

Thanks all the answers ( @Nikos M. ) and assistance , However I am still unclear as to why dynamic pressure (at any instant) is not thought of to be a force acting in a specific direction (perhaps vector is not the right term ?)

## marked as duplicate by Kyle Kanos, Brandon Enright, ACuriousMind♦, Prahar, JamalSNov 9 '14 at 20:18

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• Do you know why kinetic energy is a scalar, and not a vector? – Bernhard Nov 9 '14 at 10:02
• It is so by its definition. There is a vector quantity, the momentum flux or so, but it is of different dimension - it is not an energy density. – Vladimir Kalitvianski Nov 9 '14 at 11:13
• It doesnt match the definition of vector en.wikipedia.org/wiki/Vector_space – Wolphram jonny Nov 9 '14 at 11:15
• possible duplicate of Define Pressure at A point. Why is it a Scalar? – Kyle Kanos Nov 9 '14 at 16:06
• Thanks all the answers (@Nikos M.) and assistance , However I am still unclear as to why dynamic pressure is not thought of to be a force acting in a specific direction (perhaps vector is not the right term ?) – Quentin Chester Nov 10 '14 at 0:49

## 1 Answer

As mentioned in comments the dynamic pressure is the equivalent of the kinetic energy in fluid dynamics.

It is dynamic since it can change with time (like kinetic energy) and also like kinetic energy it is an invariant under coordinate transformations (e.g rotations) as such it is a scalar and not a vector (just like energy which also depends on velocity in similar manner).

quoting from related answer:

A fluid does not sustain shear, and this is true whether it is still or moving, by the principle of relativity. This means that if you put fluid between two plates, and squeeze, the force per-unit-area with which you squeeze (the local flow of momentum in the direction perpendicular to the plates) is equal to the force per unit area pushing outward at the edge of the plates. The flow of momentum is the same in all directions.

This means it is isotropic, in other words invariant under rotations (and other coordinate transformations), thus it is a scalar quantity (a vector is not invariant under rotations)

• Thanks all the answers ( @Vladimir Kalitvianski @) and assistance , However I am still unclear as to why dynamic pressure (at any instant) is not thought of to be a force acting in a specific direction (perhaps vector is not the right term ?) – Quentin Chester Nov 10 '14 at 2:50
• @QuentinChester, really it is just a matter of definition, a quantity of the characteristics you mention can indeed be defined, but dynamic pressure is what is stated above as equivalent to kinetic energy – Nikos M. Nov 10 '14 at 7:38