Page 227 - 48Fundamentals of Compressible Fluid Mechanics

11.3. RIGID TANK WITH NOZZLE 189

and

(11.19)

E
*

is defined by equation (9.49).

yields

where

the entrance and exit Mach numbers. See advance topic about approximate solu-
The solution of equations (11.18) and (11.19) for given
or small entrance Mach number, . and & B

tion for large resistance,
11.3 Rigid Tank with Nozzle
The most simplest possible combination is discussed here before going trough the
more complex cases A chamber is filled or evacuated by a nozzle. The gas in the
chamber assumed to go an isentropic processes and flow is bounded in nozzle
5
between isentropic flow and isothermal flow . Here, it also will be assumed that
the flow in the nozzle is either adiabatic or isothermal.
11.3.1 Adiabatic Isentropic Nozzle Attached
The mass flow out is given by either by Fliegner’s equation (4.47) or simply use
and equation (11.17) becomes
!
(11.20)
$

>*
It was utilized that and > is simplified as . It can be noticed
definition

that the characteristic time defined in equation (11.5) reduced into:

>

>

>*
>
>
>
(11.21)

Also it can be noticed that equation (11.12) simplified into

@

*
"

(11.22)

E
Equation (11.20) can be simplified as % *

(11.23)

5 This work is suggested by Donald Katze the point out that this issue appeared in Shapiro’s Book
Vol 1, Chapter 4, p. 111 as a question 4.31.

%
:) <
>*