Page 234 - 48Fundamentals of Compressible Fluid Mechanics

196 CHAPTER 11. EVACUATING AND FILLING A SEMI RIGID CHAMBERS

(11.48)

Notice that when ( : > equation (11.49) reduced to equation (11.43).

< E

>
After carrying–out differentiation results
>
>*
(11.49)

E
Again, similarly as before, variables are separated and integrated as fol-
(
E

%
>

lows
>

>
>

>*

(11.50)

B

Carrying–out the integration for the initial part if exit results in

E

(

>
>
>
*

(11.51)

The linear condition are obtain when E >

E E

>
>* (
(11.52)

E
That is just bellow 1 ( ( 1+ ) for .
(
E

E E

), 9-)
11.5 Advance Topics
is very large for small values of the entrance Mach number which
(

requires keeping many digits in the calculation. For small values of the Mach num-
The term
bers, equation (??) can be approximated as
(11.53)

and equation (??) as O B
E

U
O B
U
(11.54)

The solution of the last two equations yields U O B

*
U
O B

(11.55)

& B
E