Adiabatic Frictionless Nozzle Flow

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

Convergent/Divergent Nozzles (De Laval Nozzles) During frictionless adiabatic one-dimensional flow with changing cross-sectional area A the following relations are obeyed ... 

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... 

Chapter 5 presented a mathematical model for adiabatic flow through a frictionless nozzle, and we shall use some of that chapter s results. It will be helpful for our present purpose if we derive the Mach number at station 2 , where the Mach number, M, is defined as the ratio of the velocity to the local speed of sound. Recalling equation (5.47), the Mach number at station 2 will be ... 

Sizing coefficient for adiabatic frictionless flow of real gases through nozzles ... 

The adiabatic flow of an ideal gas flowing through a frictionless conduit or a constriction (such as an orifice nozzle, or valve) can be analyzed as follows. The total energy balance is... 

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

Very little energy is lost to friction in the convergent part of any nozzle, and so we may write down the velocity at station 2 by using equation (5.22), setting n = y for frictionless, adiabatic flow ... 

Figure 8.3 is a plot of AM versus Ji for steady, one-dimensional, frictionless, adiabatic flow of a perfect gas. It is, in effect, a design guide for a supersonic nozzle If we wish the Mach number to increase linearly with distance in steady, isentropic flow of a perfect gas, then the cross-sectional area-distance relation must be exactly the curve in Fig. 8.3, This is the diagram for a converging-diverging nozzle, a type of nozzle commonly referred to as a de Laval nozzle after its inventor, who used it in the first practical steam turbine [11]-...

As we have assumed the flow to be frictionless, these considerations are limited to short well-formed nozzles. Then one may apply the adiabatic gas laws... 

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