13.3:
Pressure of Fluids
Ever wondered how a fluid flows from one point to another?
To understand this, consider a fluid of constant density at rest. If a force is applied parallel to the surface of the fluid, then to accommodate this force, the fluid is set into motion.
In contrast, if a normal force is applied on the fluid's surface, an equal and opposite force develops in the fluid as a reaction. This normal force exerted by the fluid per unit area is called pressure. The SI unit of pressure is pascal.
Pressure is always normal to any surface in contact with the fluid and so is a scalar quantity. In comparison, force has a specific direction and is a vector quantity.
The pressure at a depth h from the fluid's surface is the sum of atmospheric pressure and pressure due to the fluid's weight.
When we substitute the equivalent expressions for weight, mass, and volume, we get the pressure due to the fluid's weight as the product of density, acceleration due to gravity, and h.
13.3:
Pressure of Fluids
There are many examples of pressure in fluids in everyday life, such as in relation to blood (high or low blood pressure) and in relation to weather (high- and low-pressure weather systems). A given force can have a significantly different effect, depending on the area over which the force is exerted. For instance, a force applied to an area of 1 mm2 has a pressure that is 100 times greater than the same force applied to an area of 1 cm2. That's why a sharp needle is able to poke through skin when a small force is exerted, but applying the same force with a finger does not puncture the skin.
Pressure is very important when discussing fluids. An important characteristic of fluids is that there is no significant resistance to the component of the force applied parallel to the surface of the fluid. The molecules of the fluid simply flow to accommodate the horizontal force. A force applied perpendicular to the surface compresses or expands the fluid. For instance, if one tries to compress a fluid, a reaction force develops at each point inside the fluid in the outward direction, balancing the force applied on the molecules at the boundary. The pressure at any point in a static fluid depends only on the depth at that point.
Pressure in a fluid near Earth varies with depth due to the weight of the fluid above a particular level. Hence, in a swimming pool, the density is approximately constant, and the water at the bottom is compressed very little by the weight of the water on top. On the other hand, traveling up in the atmosphere is quite a different situation, as the density of the air begins to change significantly just a short distance above the Earth's surface. Furthermore, fluid pressure, being a scalar quantity, has no direction, whereas the forces due to pressure have well-defined directions—they are always exerted perpendicular to any surface. The reason for this is that fluids cannot withstand or exert shearing forces. Thus, in a static fluid enclosed in a tank, the force exerted on the walls of the tank is exerted perpendicular to the inner surface. Likewise, pressure is exerted perpendicular to the surfaces of any object within the fluid.
This text is adapted from Openstax, University Physics Volume 1, Section 14.1: Fluids, Density, and Pressure.