Page 228 - 48Fundamentals of Compressible Fluid Mechanics

190 CHAPTER 11. EVACUATING AND FILLING A SEMI RIGID CHAMBERS

Equation (11.23) can be integrated as

(11.24)

B
The integration limits are obtained by simply using the definitions of reduced pres-

> . After the integration, equation (11.24) and

*
rearrangement becomes >* >*
'

(11.25)
>*
sure, at
and

E

Example 11.1: > % * >
A chamber is connected to a main line with pressure line with a diaphragm and
*
nozzle. The initial pressure at the chamber is 9
, and the volume is . .
Calculate time it requires that the pressure to reach 5[Bar] for two different noz-
] when diaphragm is erupted. Assumed the
stagnation temperature at the main line is the ambient of ) .

SOLUTION

The characteristic time is
zles throat area of 0.001, and 0.1 [
(11.26)

And for smaller area $ $ $ )(

?PO
=)$
$
*
N

?PO
)$
N

9
The time is * )(
9
>

*
(11.27)

Substituting values into equation (11.27) results *

N > E
?PO

* *
%
(11.28)

E

11.3.1.1 Filling/evacuating the chamber under upchucked condition

$
*

(
%
The flow in the nozzle can became upchucked and it can be analytically solved.
*
Owczarek [1964] found that analytical solution which described here.