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Next: Isothermal Nozzle (T=constant) Up: Nozzle Flow With External Previous: Nozzle Flow With External Index
The energy equation for isentropic nozzle provides
Utilizing equation (4.27) when leads to
For the isentropic process when the at any point of the flow. The equation (7.2) becomes
The continuity equation as developed earlier (mass conservation equation isn't effected by the gravity)
Substituting from equation 7.3, into equation (7.2) moving to the right hand side, and diving by yields
Rearranging equation (7.5) yields
And further rearranging yields
Equation (7.7) can be rearranged as
Equation (7.8) dimensionless form by utilizing and is the nozzle length
And the final form of equation (7.9) is
The term is considered to be very small ( %) for ``standard'' situations. The dimensionless number, sometimes referred as Ozer number determines whether gravity should be considered in the calculations. Nevertheless, one should be aware of value of Ozer number for large magnetic fields (astronomy) and low temperature, In such cases, the gravity effect can be considerable.
As it was shown before the transition must occur when . Consequently, two zones must be treated separately. First, here the Mach number is discussed and not the pressure as in the previous chapter. For (the subsonic branch) the term is positive and the treads determined by gravity and the area function.
For the case of (the supersonic branch) the term is negative and therefore
For the border case , the denominator , is zero either or
And the is indeterminate. As it was shown in chapter (4) the flow is chocked ( ) only when
It should be noticed that when is zero, e.g. horizontal flow, the equation (7.11) reduced into that was developed previously.
The ability to manipulate the location provides a mean to increase/decrease the flow rate. Yet this ability since Ozer number is relatively very small.
This condition means that the critical point can occurs in several locations that satisfies equation (7.11). Further, the critical point, sonic point is If is a positive function, the critical point happen at converging part of the nozzle (before the throat) and if is a negative function the critical point is diverging part of the throat. For example consider the gravity, a flow in a nozzle vertically the critical point will be above the throat.
Next: Isothermal Nozzle (T=constant) Up: Nozzle Flow With External Previous: Nozzle Flow With External Index Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21 include("aboutPottoProject.php"); ?>