page_title: Isentropic nozzle flow
section_title: Converging nozzle
hierarchical_section_title: Isentropic nozzle flow / Flow analysis / Supersonic flow / Converging nozzle
caption_attribution_description: English: A converging-diverging nozzle with reservoir pressure fixed.
context_page_description: Isentropic nozzle flow describes the movement of a gas or fluid through a narrowing opening without an increase or decrease in entropy.
context_section_description: Consider a converging nozzle connecting a reservoir with a receiver. If the reservoir pressure is held constant and the receiver pressure reduced, the Mach number at the exit of the nozzle will increase until Me=1 is reached, indicated by the left curve in figure 2. After Me =1 is reached at the nozzle exit for , the condition of choked flow occurs and the velocity throughout the nozzle cannot change with further decreases in. This is due to the fact that pressure changes downstream of the exit cannot travel upstream to cause changes in the flow conditions.
  The right curve of Fig2. represents the case when the reservoir pressure is increased and the receiver pressure is held constant. When , the condition of choked flow also occurs; but Eq indicates that the mass flux will continue to increase as  is increased. This is the case when a gas line ruptures.
  It is interesting that the exit pressure  is able to be greater than the receiver pressure . Nature allows this by providing the streamlines of a gas the ability to make a sudden change of direction at the exit and expand to a much greater area resulting in a reduction of the pressure from  to . The case of a converging-diverging nozzle allows a supersonic flow to occur, providing the receiver pressure is sufficiently low. This is shown in Fig. 9.6 assuming a constant reservoir pressure with a decreasing receiver pressure. If the receiver pressure is equal to the reservoir pressure, no flow occurs, represented by curve . If pr is slightly less than p_0, the flow is subsonic throughout, with a minimum pressure at the throat, represented by curve B. As the pressure is reduced still further, a pressure is reached that result in M =1 at the throat with subsonic flow throughout the remainder of the nozzle.
  There is another receiver pressure substantially below that of curve C that also results in isentropic flow throughout the nozzle, represented by curve D; after the throat the flow is supersonic. Pressures in the receiver in between those of curve C and curve D result in non-isentropic flow (a shock wave occurs in the flow) and will be considered in the next section. If pr is below that of curve D, the exit pressure pe is greater than pr. Once again, for receiver pressures below that of curve C, the mass flux remains constant since the conditions at the throat remain unchanged. It may appear that the supersonic flow will tend to separate from the nozzle, but just the opposite is true. A supersonic flow can turn very sharp angles, since nature provides expansion fans that do not exist in subsonic flows. To avoid separation in subsonic nozzles, the expansion angle should not exceed 10°. For larger angles, vanes are used so that the angle between the vanes does not exceed 10°.
caption: Figure : A converging-diverging nozzle with reservoir pressure fixed.
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