This volume is known as the control volume. The equation is applied on a number of fluids. These are the Compressible Newtonian fluids, incompressible Newtonian fluids and Non-Newtonian fluids (Gresho 414). These equations are the benchmark for viscous fluids and are derived by relating the Law of Motion by Newton to a fluid. It is important to note the aspects of the Compressible, Incompressible, and Non-Newtonian fluids.
The definition of compressibility is important in understanding what compressible fluids are. Compressibility refers to the decline in volume of the fluid because of outside forces exerted on it. It is imperative to note that, there are three basic assumptions that guide the application of these derivative functions to a number of fluids. The derivative function is shown below
Application of the above assumptions will lead to a generic equation that has a number of elements. Important elements to note are two distinct proportionality constants that categorically denote that stress is determined linearly by stress rates. These constants are viscosity and the second coefficient of viscosity. The value of the second coefficient of viscosity generates a viscous stimulus that leads to volume change. However, the value is hard to ascertain in compressible fluids and is habitually negligible. It is stipulated that almost all fluids can be compressible to a certain extent. That is, variations in temperature and/or pressure will lead to variations in density. The influence of outside pressure will force a compressible fluid to diminish its volume. In this regard, the numerical extent of compressibility is denoted as the relative variation in volume of the fluid due to change in pressure. Gases are greatly compressible as opposed to fluids. There are two types of compressibility. Adiabatic compressibility refers to