ABSTRACT
The Navier–Stokes equations for a general fluid mechanics problem were stated in this chapter. Turbulence is an important area of study in fluid mechanics because most flows with which are familiar are turbulent flows. A set of differential equations to describe fluid motion can be derived for the general case. If the continuity and momentum equations are written for all three principal directions, and the fluid is Newtonian with constant properties of density and viscosity, a set of differential equations results. The momentum equation written for each principal direction gives what are called the Navier–Stokes equations. The equations that have just written are easily applied to various laminar flow problems to obtain the descriptive differential equation. Plane Couette flow is flow through a two-dimensional channel that has one wall moving. Graphical solution methods allow a quick and easy determination of instantaneous time-dependent velocity profiles.
