Flow through Variable-Area Conduits

Flow through a given nozzle is controlled by fixing the reservoir and receiver pressures. For a given flow through a specific nozzle, a unique pressure exists at each point along the axis of the nozzle. The relation is conveniently shown as a plot of p/po versus L, where pg is the reservoir pressure and p the pressure at point 

If Pr and po are equal, no flow occurs and the pressure distribution is represented by the line aa. If the receiver pressure is slightly below the reservoir pressure, flow occurs and a pressure distribution such as that shown by line abc 

Variation of pressure ratio with distance from nozzle inlet. 

The reason for this is as follows when the velocity in the throat is sonic and the cross-sectional area of the conduit is constant, sound waves cannot move upstream into the throat and the gas in the throat has no way of receiving a message from downstream. Further reduction of the receiver pressure cannot be transmitted into the throat. 

The area below line adghf is not accessible to any kind of adiabatic flow. Isentropic flow is confined to the subsonic area adea a and the single line dghf. 

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In faa, some flow-measuring devices make use of Equation (8.12) to determine the volume flow rate of a fluid by first measuring the fluid s average velocity and the cross-sectional area of the flow. Finally, note that in Chapter 9 we will explain another closely defined variable, mass flow rate of a flowing material, which provides a measure of time rate of mass flow through pipes or other carrying conduits. 

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