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Next: Advance Topics Up: Rapid evacuating of a Previous: Simple Semi Rigid Chamber Index
In this analysis and previous analysis the initial effect of the chamber container inertia is neglected. The analysis is based only on the mass conservation and if unsteady effects are required more terms (physical quantities) have taken into account. Further, it is assumed the ideal gas applied to the gas and this assumption isn't relaxed here.
Any continuous positive monotonic function can be expressed into a polynomial function. However, as first approximation and simplified approach can be done by a single term with a different power as
When can be any positive value including zero, 0 . The physical meaning of is that the tank is rigid. In reality the value of lays between zero to one. When is approaching to zero the chamber is approaches to a rigid tank and vis versa when the the chamber is flexible like a balloon.
There isn't a real critical value to . Yet, it is convenient for engineers to further study the point where the relationship between the reduced time and the reduced pressure are linear11.6 Value of above it will Convex and below it concave.
After carrying-out differentiation results
Again, similarly as before, variables are separated and integrated as follows
Carrying-out the integration for the initial part if exit results in
The linear condition are obtain when
That is just bellow 1 ( ) for .
Next: Advance Topics Up: Rapid evacuating of a Previous: Simple Semi Rigid Chamber Index Created by:Genick Bar-Meir, Ph.D.
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