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Next: The Isothermal Process Up: Rapid evacuating of a Previous: With Fanno Flow Index Filling ProcessThe governing equation is For a choked flow the entrance Mach number to the tube is at its maximum, 
and therefore
.
The solution of equation (11.37) is obtained
by noticing that 
is not a function of time
and by variable separation
results in
direct integration of equation (11.38) results in It has to be realized that this is a reversed function. Nevertheless, with today computer this should not be a problem and easily can be drawn as shown here in Figure (11.5). The Figure shows that when the modified reduced pressure equal to one the reduced time is zero. The reduced time increases with decrease of the pressure in the tank.
At some point the flow becomes
chokeless flow (unless the back pressure is a complete vacuum).
The transition point is denoted here as
Next: The Isothermal Process Up: Rapid evacuating of a Previous: With Fanno Flow Index Created by:Genick Bar-Meir, Ph.D. On: 2007-11-21 If you want the whole book or parts in pdf or other formats, then click here. You also can get the best and the largest gas dynamics tables in the world. About Potto Project
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![$\displaystyle {d \bar{P} \over d \bar{t}} - k \bar{M} f[M] \bar{P} ^{3k -1 \over 2k} = 0$](img1266.png)
![$\displaystyle \int _{0}^{\bar{t}} {d\bar{t}} = \int _{1}^{\bar{P}} {d\bar{P} \o...
...ver {k \bar{M} f[M]}} \int _{1}^{\bar{P}} {{\bar{P}^{1-3k \over 2k}} d\bar{P} }$](img1268.png)
![$\displaystyle \bar{t} = {2 \over (k-1) \bar{M} f[M]} \left[ \bar{P}^{1 -k \over 2k} -1 \right]$](img1269.png)
.
Thus, equation (![$\displaystyle \bar{t} -\bar{t}_{chT} = \int _{P_{chT}}^{\bar{P}} {1 \over {k \bar{M} f[M]}} {{\bar{P}^{1-3k \over 2k}} d\bar{P} }$](img1273.png)