Ideal nozzles

Ideal (Frictionless) Flow in Nozzles The flow path in well-formed nozzles follows smoothly along the nozzle contour without separating from the wall. The effects of small imperfections and small frictional losses are accounted for by correcting the ideal nozzle flow by an empirically determined coefficient of mscharge. The acceleration of a fluid initially at rest to flowing conditions in an ideal nozzle is given by ... 

Total pressure deerease in the nozzle and outlet diffuser are only from frietional losses. In an ideal nozzle or diffuser the total pressure drop is zero. Isentropie effieieney is defined as the ratio of the aetual work to the isen-tropie enthalpy deerease, whieh is the expansion from the inlet total pressure to the outlet total pressure... 

This method employs a theoretical critical mass flow based on an ideal nozzle and isothermal flow condition. For a pure gas, the mass flow can be determined from one equation ... 

Equation (9-45) represents flow through an ideal nozzle, i.e., an isentropic constriction. 

The subscript s denotes an isentropic path for ideal nozzle flow. For ideal gas with Pok = constant, substitution of this isentropic expansion law into Eq. (23-98) yields the following critical pressure ratio PJP and critical flow rate Gc ... 

With the P-v relation given by Eq. (23-103), Eq. (23-98) can be integrated to give a generalized equation for flow through an ideal nozzle... 

The gas flow through the control valve as a whole will be very close to adiabatic, and, as just noted, the expansion as far as the valve throat will incur only a small frictional loss, implying a process that is approximately isentropic. Accordingly we may substitute the ratio of the gas s specific heats, y = Cp/c,. for the polytropic index, n, in the flow equations (5.25) and (5.26) derived for an ideal nozzle in Chapter 5. Combining those two equations gives the mass flow, W, as ... 

Equation (9.2) holds at low valve pressure ratios, when flow is choked and where the value of Cg comes from manufacturer s experimental data. But from our model of the valve as an ideal nozzle undergoing isentropic, choked flow, equation (9.5) should also apply. Since the two equations should give the same flow, it follows that the SI limiting gas conductance Cg must be given by... 

To evaluate the effect of a less-than-ideal nozzle on velocity, we rewrite equation (14.1), as... 

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