1. Mass Flow Rate M 1 Flow rate out of a tank depends on tank temperature, pressure and size of throat.

2. Mass Flow Rate For a Diatomic Gas (e.g.,Air): Mass flow/unit area M 1

3. Mach #-Area Relation Values of A/A* tabulated over a range of Mach #s) M=1 A* A Two values for M at A One subsonic, One supersonic. Solution depends on  p.

4. Mach #-Area Relation If the M = 1 at throat the flow is chocked. For each value of A/A* there are two solutions, one subsonic, the other supersonic. If M=1 at the smallest cross-sectional area the mass flow rate is largest. If M A*), pretend. If A reduced below A*, decreases.

5. Converging Nozzle Flow Steady, adiabatic, reversible, no work flow If backpressure p B = p atm : no flow As p B is lowered: flow Assume here p B = p e Eventually p B so low, (pe/p 0 =.528), M e = 1 Nozzle chocked; lowering p B no longer changes conditions in nozzle (message of lower p B cannot pass through sonic throat). Here p B no longer equal p e (see later) pBpB PeMePeMe p 0 =p atm

6. Converging Nozzle Flow If nozzle chocked, flow rate fixed for given upstream stagnation pressure and temperature. Use as flow-meter (chocked orifice meter). Assumed flow from atmosphere to partially evacuated vessel; similar from pressurized vessel to atmosphere or lower pressure vessel