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Chapter 3
Summary Flow of gases through tubes and orifices
This chapter is about the flow of gases through tubes and orifices. Evacuation of a vacuum vessel by pumping requires the vessel to be somehow connected to the pump. This connection, usually consisting of valves and pipelines, will always result in some resistance for the gas on its way from vessel to pump. Obviously, for an unobstructed gas flow it will be important to keep this resistance as low as possible. A good understanding of the various gas flow types is essential to be able to determine the correct dimensions of the different necessary system components. In some cases, the proper operation of a vacuum system is undermined by a mismatch between successive vacuum components. Formulas for the laminar and molecular conductances of orifices and tubes of different dimensions are derived by application of the relevant thermodynamic and flow laws. In relation to the operation of vapour stream pumps (see chapter 4), special attention is paid to the supersonic flow through a Laval nozzle and the occurence of a choked gas flow and shock wave. The chapter is concluded with the definition of the concept ‘pumping speed’ and some calculation examples in a simple vacuum system.
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Contents Flow of gases through tubes and orifices
3.1 Introduction 101
3.2 Thermodynamic laws 104
3.2.1 First law of thermodynamics 104
3.2.2 Second law of thermodynamics; isentropic process 107
3.2.3 Equation of state 107
3.3 Overview of flow laws 109
3.3.1 Continuity equation 109
3.3.2 Bernoulli’s law 111
3.3.3 Conservation of momentum 115
3.4 Supersonic flow through a nozzle or aperture 116
3.5 The shock wave 123
3.6 Laminar flow 129
3.7 ‘Choked’ gas flow in a tube 133
3.8 Molecular flow 134
3.8.1 Molecular flow through an orifice 135
3.8.2 Molecular flow in a (cylindrical) tube 136
3.9 Definition of the concept of ‘conductance’ 139
3.10 Conductance in case of a supersonic flow 140
3.11 Conductance in case of a laminar flow 141
3:12 Conductance in the case of a choked flow 144
3.13 Conductance in case of a molecular flow 144
3:14 Conductance in the transition domain between viscous and molecular flow 152
3.15 Conductance of complex vacuum components 153
3:16 Pumping speed 153
17.3 Calculation examples in a simple vacuum system 155
exercises
