Page 231 - 48Fundamentals of Compressible Fluid Mechanics

11.4. RAPID EVACUATING OF A RIGID TANK 193

(11.40) has to include the entrance Mach under the integration sign as

(11.36)

For practical purposes if the flow is choked for more than 30% of the charecteristic

>* E
time the choking equation can be used for the whole range, unless extra long
@
>
>
>*
>
time or extra low pressure is calculated/needed. Further, when the flow became

chockless the entrance Mach number does not change much from the choking
condition.

Again, for the special cases where the choked equation is not applicable
the integration has to be separated into zones: choked and chockless flow regions.
And in the choke region the calculations can use the choking formula and numerical
calculations for the rest.
Example 11.2:
A chamber with volume of 0.1[ . ] is filled with air at pressure of 10[Bar]. The
chamber is connected with a rubber tube with and length of

SOLUTION 9 ,

9
The first parameter that calculated is
11.4.2 Filling process 9
The governing equation is

(11.37)

For a choked flow the entrance Mach number to the tube is at its maximum,

E
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 N

>*

?PO
>

(11.38)

>

B
direct integration of equation (11.40) results in > >

>
>

>*
>

>
(11.39)

> E

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 11.6. The Figure shows that when the modified reduced pressure
E