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Next: The Isothermal Process Up: Rapid evacuating of a Previous: With Fanno Flow   Index

## Filling Process

The 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 . Thus, equation (11.39) has to include the entrance Mach under the integration sign 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