Isentropic Converging-Diverging Flow in Cross Section

Figure: Control volume inside a converging-diverging nozzle.

The important sub case in this chapter is the flow in a converging-diverging nozzle. The control volume is shown in Figure (4.4). There are two models that assume variable area flow: First is isentropic and adiabatic model. Second is isentropic and isothermal model. Clearly, the stagnation temperature, T₀, is constant through the adiabatic flow because there isn't heat transfer. Therefore, the stagnation pressure is also constant through the flow because the flow isentropic. Conversely, in mathematical terms, equation (4.9) and equation (4.11) are the same. If the right hand side is constant for one variable, it is constant for the other. In the same argument, the stagnation density is constant through the flow. Thus, knowing the Mach number or the temperature will provide all that is needed to find the other properties. The only properties that need to be connected are the cross section area and the Mach number. Examination of the relation between properties can then be carried out.