Page 222 - 48Fundamentals of Compressible Fluid Mechanics

184 CHAPTER 11. EVACUATING AND FILLING A SEMI RIGID CHAMBERS

more complicate. Combination of gas
compressibility in the chamber and flow
out or through a tube post a special in-
terest and these next two Chapters are dealing with these topics. In the first Chap-
ter models where the chamber volume is controlled or a function of the pressure
are discussed. In the second Chapter models where the chamber’s volume is a
function of external forces are presented (see Figure 11.1).

11.1 Governing Equations and Assumptions

The process of filing or evacuating a semi flexible (semi rigid) chamber through a
tube is very common in engineering. For example, most car today equipped with
an airbag. For instance, the models in this Chapter are suitable for study of the
filling the airbag or filling bicycle with air. The analysis is extended to include a
semi rigid tank. The term semi rigid tank referred to a tank that the volume is either
completely rigid or is a function of the chamber’s pressure.
As it was shown in this book the most appropriate model for the flow in
the tube for a relatively fast situation is Fanno Flow. The Isothermal model is more
appropriate for cases where the tube is relatively long in–which a significant heat
transfer occurs keeping the temperature almost constant. As it was shown in Chap-
, should be larger than . Yet Isothermal flow model is
used as to limiting case.

ter 9 the resistance,
fanno model fanno model
reduced for relativly short tube for relativly short tube
connection 1 2 1 2

Isothermal model

Isothermal model

for a relativly long tube for a relativly long tube
The connection is through a narrow passage A schematic of a direct connection
Fig. 11.2: A schematic of two possible connections of the tube to a single chamber

The Rayleigh flow model requires
that a constant heat transfer supplied either "!$#&% ')( * +
by chemical reactions or otherwise. This ,.- / 0
author isn’t familiar with situations in which
Control volume for the evacuating case
Rayleigh flow model is applicable. And
therefore, at this stage, no discussion is of-
fered here.
Fanno flow model is the most ap- 1"2$3&4 5)6 7 8 9.: ;
propriate in the case where the filling and
To put the dimensionless evacuating is relatively fast. In case the the Control volume for the filling case
analysis to discuss what is
fast enough. than the
Fig. 11.3: A schematic of the control vol-
Isothermal flow is appropriate model. Yet
umes used in this model
filling is relatively slow (long
as it was stated before, here Isothermal flow