Compressible flows ideal nozzle

Moving on to compressible flow, it is first of all necessary to explain the physics of flow through an ideal, frictionless nozzle. Chapter S shows how the behaviour of such a nozzle may be derived from the differential form of the equation for energy conservation under a variety of constraint conditions constant specific volume, isothermal, isentropic and polytropic. The conditions for sonic flow are introduced, and the various flow formulae are compared. Chapter 6 uses the results of the previous chapter in deriving the equations for frictionally resisted, steady-state, compressible flow through a pipe under adiabatic conditions, physically the most likely case on... 

Using the formula for one-dimensional compressible flow presented in Section IV.B, we calculated the pressure, temperature, and velocity profiles describing the subsonic adiabatic expansion of pure carbon dioxide inside the orifice and the capillary up to the nozzle exit (i.e., point 2 in Figures 3 and 5). Both the Bender (38) and Camahan-Starling-van der Waals (39) equations of state were used to calculate the necessary PvT properties for CO2, and results using either of the two equations were essentially identical. Downstream of the nozzle exit, we calculated the pressures and temperatures on the upstream and downstream sides of the Mach disk by using the formulas of Ashkenas and Sherman (36) (see Section V). These formulas assume an ideal gas with y = 1.286, close to the value of CO2 at ambient conditions. We should remember, however. 

When the fluid flowing through the valve is a compressible gas or a vapor, then the design must consider whether critical flow is achieved in the nozzle of the valve. The critical flow rate is the maximum flow rate that can be achieved and corresponds to a sonic velocity at the nozzle. If critical flow occurs, then the pressure at the nozzle exit cannot fall below the critical flow pressure Pcf, even if a lower pressure exists downstream. The critical flow pressure can be estimated from the upstream pressure for an ideal gas using the equation... 

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