Page 226 - 48Fundamentals of Compressible Fluid Mechanics

188 CHAPTER 11. EVACUATING AND FILLING A SEMI RIGID CHAMBERS

The ratios can be expressed in term of the reduced pressure as followed:

(11.15)

>
and > > > >

(11.16)
>
So equation (11.13) is simplified into three different forms:

>

>

: <

> >*
(11.17)
>
> >
> >*
>*

>

>

Equation (11.17) is a general equation for evacuating or filling for isentropic pro-
> >*

>
>
> >

>*
>*
>

cess in the chamber. It should be point out that, in this stage, the model in the tube
>

>

could be either Fanno flow or Isothermal flow. The situations where the chamber
>
>

>*
>*
undergoes isentropic process but the the flow in the tube is Isothermal are limited.
Nevertheless, the application of this model provide some kind of a limit where to
expect when some heat transfer occurs. Note the temperature in the tube entrance

can be above or below the surrounding temperature. Simplified calculations of the
entrance Mach number are described in the advance topics section.
11.2.2 Isothermal Process in the Chamber
11.2.3 A Note on the entrance Mach number
and the ratio

is
The value of Mach number, is a function of the resistance,

different from in some situations. As it was shown before, once the flow became
. These

statements are correct for both Fanno flow and the Isothermal flow models. The
choked the Mach number, is only a function of the resistance,
method outlined in Chapters 8 and 9 is appropriate for solving for entrance Mach
of pressure in the tank to the back pressure, . The exit pressure,
number, .

Two equations must be solved for the Mach numbers at the duct entrance
and exit when the flow is in a chockless condition. These equations are combina-
tions of the momentum and energy equations in terms of the Mach numbers. The

characteristic equations for Fanno flow (9.50), are
(11.18)

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