# FLUID MECHANICS

### The Concept of a Fluid

From the point of view of fluid mechanics, all matter consists of only
two states, fluid and solid. The difference between the two is perfectly
obvious to the layperson, and it is an interesting exercise to ask a layperson
to put this difference into words.

The technical distinction lies with the reaction of the two to an applied shear or tangential stress. A solid can resist a shear stress by a static deflection; a fluid cannot. Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid.

The fluid moves and deforms continuously as long as the shear stress is applied. As a corollary, we can say that a fluid at rest must be in a state of zero shear stress, a state often called the hydrostatic stress condition in structural analysis. In this condition, Mohr’s circle for stress reduces to a point, and there is no shear stress on any plane cut through the element under stress.

Given this definition of a fluid, every layperson also knows that there
are two classes of fluids, liquids and gases. Again the distinction is a
technical one concerning the effect of cohesive forces. A liquid, being
composed of relatively close-packed molecules with strong cohesive forces,
tends to retain its volume and will form a free surface in a gravitational
field if unconfined from above.

Free-surface flows are dominated by gravitational effects and are studied in Chaps. 5 and 10. Since gas molecules are widely spaced with negligible cohesive forces, a gas is free to expand until it encounters confining walls. A gas has no definite volume, and when left to itself without confinement, a gas forms an atmosphere that is essentially hydrostatic.

The hydrostatic behavior of liquids and gases is
taken up in Chap. 2. Gases cannot form a free surface, and thus gas flows
are rarely concerned with gravitational effects other than buoyancy.
Figure 1.3 illustrates a solid block resting on a rigid plane and stressed
by its own weight. The solid sags into a static deflection, shown as a highly
exaggerated dashed line, resisting shear without flow.

A free-body diagram of element A on the side of the block shows that there is shear in the block along a plane cut at an angle θ through A. Since the block sides are unsupported, element A has zero stress on the left and right sides and compression stress σ = −p on the top and bottom. Mohr’s circle does not reduce to a point, and there is nonzero shear stress in the block.