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Pressure: Scalar or Vector?

Yesterday, I distributed IB physics past paper questions that came mainly from first chapter  – “Physics and physical measurements” to my 11-graders. One of the questions had started a debate whether the pressure is a scalar or vector quantity. Actually they should have remembered this discussion from their IGCSE physics classes because it is common discussion topic when I am teaching pressure for IGCSE and IB.

They learn that pressure is defined as “force per unit area” where force is a vector and area is a scalar quantity. They also know that vector when divided by scalar yields a vector, they naturally conclude that pressure is a vector quantity. But pressure is a scalar quantity and it is a little hard to explain. Let me try my best:

There are two ways in which the concept of pressure is used, the pressure in a fluid (liquid or gas), and the pressure of one solid surface against another. In the case of liquids and gasses the pressure, measured or calculated, is equal in all directions, and therefore has no direction, making it a scalar.

In the case of one solid against another, for example, a tire against the road surface, the tire exerts a downward force ( downward vector) against an area of roadway (upward vector). If we divide the magnitude of the force (a scalar) by the magnitude of the area (a scalar) we get a quantity (scalar) which we call “pressure”. As a mathematical ratio (F/A) it is non-directional just as pi is non-directional or electrical resistance is non-directional.



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