Page 232 - 48Fundamentals of Compressible Fluid Mechanics

194 CHAPTER 11. EVACUATING AND FILLING A SEMI RIGID CHAMBERS

Fig. 11.6: The reduce time as a function of the modified reduced pressure

equal to one the reduced time is zero. The reduced time increases with decrease
of the pressure in the tank.
At some point the flow became chockless flow (unless the back pressure is
a complete vacuum). The transition point is denoted here as $ . Thus, equation
(11.40) has to include the entrance Mach under the integration sign as

(11.40)

>* E

@
>
>*
11.4.3 The Isothermal Process > >

For Isothermal process, the relative temperature, . The combination of the
isentropic tank and Isothermal flow in the tube is different from Fanno flow in that

. This model is reasonably appropriated

when the chamber is insulated and not flat while the tube is relatively long and the
>
process is relatively long.
It has to be remembered that the chamber can undergo isothermal pro-

the chocking condition occurs at
cess. For the double isothermal (chamber and tube) the equation (11.6) reduced
into
(11.41)
6

N > >*
@

@
> > " ?PO
>
"

11.4.4 Simple Semi Rigid Chamber

"

>*
*
A simple relation of semi rigid chamber when the volume of the chamber is linearly
related to the pressure as
(11.42)

where, is a constant that represent the physics. This situation occurs at least
* , *
in small ranges for airbag balloon etc. The physical explanation when it occurs
beyond the scope of this book. Nevertheless, a general solution is easily can be
obtained similarly to rigid tank. Substituting equation (11.42) into yields
(11.43)

: < E

>

>
>
>*