What causes a fluid to move? Fluids will begin to move when a nonzero resultant force acts on them. For example, when the pressure in one location is higher than in another location, the fluid will tend to move toward the region of lower pressure. Such pressure differences play a major role in establishing weather patterns, for example. Gravity can also cause a fluid to move: liquids flow downhill, trading their potential energy for kinetic energy of motion. Similarly, temperature differences will cause one part of a fluid to have a lower density compared to another part, and the lighter fluid will tend to rise.
There is also friction. When one layer of fluid moves with respect to an adjacent layer, a viscous shear stress develops which tends to speed up the flow in the slower layer and slow down the speed of the faster layer (see Section 1.6). Sometimes we consider fluids where the viscosity is zero. These inviscid fluids do not exist in nature because all real fluids are viscous, but we can often use this approximation when the effects of viscosity are small. However, we must be careful, because neglecting viscosity can sometimes lead to spectacularly wrong answers (see, for instance, Section 6.9).
Forces due to stress differences are called surface forces because they are proportional to the total surface area over which they act. For instance, if a constant shear stress τ acts over an area A, the resultant shear force is equal to τ A, so that the force is proportional to the area. In contrast, the acceleration due to gravity g acting on a fluid mass m introduces a force that is proportional to the mass of the fluid, mg, and it is called a body force. We must also include forces exerted by solid surfaces. This becomes clear when we think of a jet of water hitting a flat plate — there is a force exerted on the plate by the water, and by Newton’s third law the plate exerts an equal but opposite force on the water (which acts to change the direction of motion of the fluid and therefore changes its momentum).
Other forces may also be important. For instance, if the fluid is electrically charged it can be made to move by applying a magnetic field, and Coriolis forces can be important in a rotating flow (they are another crucial factor in forming our weather patterns — see Chapter 13). Mostly, however, we will only consider the forces due to pressure differences, viscous stress differences, solid surfaces, and gravity.