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next up previous index
Next: Rigid Tank with Nozzle Up: General Model and Non-dimensioned Previous: Isothermal Process in The   Index

A Note on the Entrance Mach number

The value of Mach number, $ M_1$ is a function of the resistance, $ \frac{4fL}{D}$ and the ratio of pressure in the tank to the back pressure, $ P_B/P_1$ . The exit pressure, $ P_2$ is different from $ P_B$ in some situations. As it was shown before, once the flow became choked the Mach number, $ M_1$ is only a function of the resistance, $ \frac{4fL}{D}$ . These statements are correct for both Fanno flow and the Isothermal flow models. The method outlined in Chapters 8 and 9 is appropriate for solving for entrance Mach number, $ M_1$ .

Two equations must be solved for the Mach numbers at the duct entrance and exit when the flow is in a chokeless condition. These equations are combinations of the momentum and energy equations in terms of the Mach numbers. The characteristic equations for Fanno flow (9.50), are


and
where $ \frac{4fL}{D}$ is defined by equation (9.49).

The solution of equations (11.18) and (11.19) for given $ \frac{4fL}{D}$ and $ {P_{exit}} \over {P_{0}(t)}$ yields the entrance and exit Mach numbers. See advance topic about approximate solution for large resistance, $ \frac{4fL}{D}$ or small entrance Mach number, $ M_{1}$ .


next up previous index
Next: Rigid Tank with Nozzle Up: General Model and Non-dimensioned Previous: Isothermal Process in The   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21


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