18 What is pressure?

The first of the forces affecting momentum concentration that we will consider is the pressure gradient force – it is almost always an important contributor to the force balance in a fluid. We will consider this force in the next section, but first we will look in more detail at pressure.

First, recall the normal force from your first quarter physics class.  This is one of two fundamental contact forces between two objects. The normal force is the contact force that is perpendicular to the surface of contact. Remember that contact forces come in pairs that are equal and opposite (Newton’s third law), each representing the force from one of the two objects on the other.

In a fluid, there are countless water parcels moving together. Pressure is the name given to the magnitude of the normal contact force pair between adjacent fluid parcels, defined per unit area of the contact surface. It is a scalar field, P(x,y,z,t).

Key Takeaways

From the point of view of a water parcel, the normal contact force due to its neighbors is always directed inward. Pressure, Pis a scalar field that represents the magnitude of the contact force.

Pascal’s Law states that if there is a pressure change at the boundary of an enclosed fluid, that change is transmitted (via the normal contact forces between water parcels) to every other point in the fluid. This transference happens very quickly, for laboratory scales it is effectively instantaneous. Remember that pressure is a scalar field, so Pascal’s Law means that any addition or subtraction from the value of pressure at the boundary of the fluid is added or subtracted from all points in the fluid.