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Next: The ``Simple'' General Case Up: Rapid evacuating of a Previous: The Isothermal Process Index Simple Semi Rigid ChamberA simple relation of semi rigid chamber when the volume of the chamber is linearly related to the pressure as where 
is a constant that represent the physics.
This situation occurs at least in small ranges for airbag balloon etc.
The physical explanation when it occurs beyond the scope of this
book.
Nevertheless, a general solution is easily can be obtained similarly
to rigid tank.
Substituting equation (11.42) into yields
Carrying differentiation result in Similarly as before, the variables are separated as The equation (11.45) integrated to obtain the form The physical meaning that the pressure remains larger thorough evacuating process, as results in faster reduction of the gas from the chamber.
Next: The ``Simple'' General Case Up: Rapid evacuating of a Previous: The Isothermal Process 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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![$\displaystyle {d \over d \bar{t}} \left( \bar{P}^{1 + k \over k} \right) - \bar{P}^{k +1 \over 2k} \bar{M} f[M] = 0$](img1278.png)
![$\displaystyle {1 + k \over k} \bar{P}^{1 \over k} {d \bar{P} \over d \bar{t}} - \bar{P}^{k +1 \over 2k} \bar{M} f[M] = 0$](img1279.png)
![$\displaystyle \int_0^{\bar{t}} dt = {k \over 1+k} \int _{1}^{\bar{P}} {\bar{P}^{k - 1 \over 2k} d\bar{P} \over \bar{M} f[M]}$](img1280.png)
![$\displaystyle \bar{t} = {2k^2 \over \bar{M} f[M] (3k - 1) (1+k)} \left[ 1 - \bar{P}^{3k -1 \over 2k} \right]$](img1281.png)