The intensity of pressure at a point in a fluid is defined as the normal force acting per unit area at that point, i.e. p = F/A as the area shrinks toward the point. The word normal is essential: pressure acts perpendicular to any surface it touches.

A key idea from fluid statics is Pascal's Law, which states that in a fluid at rest the pressure at a point is the same in all directions — it does not depend on the orientation of the surface on which it is measured. This is why pressure is treated as a scalar quantity (a single magnitude) rather than a vector, even though the force it produces on a chosen surface is a vector directed normal to that surface.

Why the correct definition is 'normal force per unit area at a point, scalar and independent of direction': It captures both the defining ratio (force ÷ area, taken normal to the surface) and the directional property established by Pascal's Law for a fluid at a point.

Why the other statements are wrong:

• The claim that pressure includes both normal and shear stresses acting simultaneously is incorrect for pressure: in a static fluid the shear stress is zero (fluids at rest cannot sustain shear), so pressure involves only the normal component.
• The statement that it is a total normal force acting uniformly over a surface, independent of area and location is wrong because pressure is force per unit area, and it does vary with depth and position — it is not independent of location.
• The claim that pressure varies significantly with direction even in a static fluid directly contradicts Pascal's Law, which shows it is the same in every direction at a point.

Therefore the correct description is normal force per unit area at a point in the fluid, a scalar intensity independent of direction.