**SUMMA****R****Y**

In this chapter the basic concepts of fluid mechanics are introduced and discussed. *Fluid mechanics *is the science that deals with the behavior of fluids at rest or in motion, and the interaction of fluids with solids or other fluids at the boundaries.

The flow of an unbounded fluid over a surface is *external flow*, and the flow in a pipe or duct is *internal flow *if the fluid is completely bounded by solid surfaces. A fluid flow is classified as being *compressible *or *incompressible*, depending on the density variation of the fluid during flow. The densities of liquids are essentially constant, and thus the flow of liquids is typically incompressible. The term *steady *implies *no change with time. *The opposite of steady is *unsteady, *or *transient. *The term *uniform *implies *no change with location *over a specified region. A flow is said to be *one-dimensional *when the velocity changes in one dimension only. A fluid in direct contact with a solid surface sticks to the surface and there is no slip. This is known as the *no-slip condition*, and it is due to the viscosity of the fluid.

At a given temperature, the pressure at which a pure sub- stance changes phase is called the *saturation pressure*. For phase-change processes between the liquid and vapor phases of a pure substance, the saturation pressure is commonly called the *vapor pressure P*υ .

The *viscosity *of a fluid is a measure of its “stickiness” or “resistance to deformation.” The tangential force per unit area is called *shear stress*, and is expressed for simple shear flow be- tween plates (one-dimensional flow) as

where m is the *dynamic *(or *absolute*) *viscosity *of the fluid, *u *is the velocity component in the flow direction, and *y *is the direction normal to flow direction. The fluids that obey this linear relationship are called *Newtonian fluids*. The ratio of dynamic viscosity to density is called the *kinematic viscosity, *υ.

For liquids, both the dynamic and kinematic viscosities are essentially independent of pressure. For gases, this is also the case for dynamic viscosity, but not for kinematic viscosity since the density of a gas is proportional to its pressure.

The pulling effect on the liquid molecules at an interface caused by the attractive forces of molecules per unit length is called *surface tension *ss. The excess pressure Ll*P *inside a spherical droplet or bubble is given by

where *P**i *and *P**o *are the pressures inside and outside the droplet or bubble. The rise or fall of a liquid in a small-diameter tube inserted into the liquid due to surface tension is called the *cap**illary effect*. The strength of the capillary effect is quantified by the *contact angle *f, defined as the angle that the tangent to the liquid surface makes with the solid surface at the point of contact*. *A liquid is said to wet the surface when f < 90°, and not to wet the surface when f > 90°. The capillary rise or drop is given by

The capillary rise is inversely proportional to the radius of the tube, and is negligible for tubes whose diameter is larger than about 1 cm.