These are the two variables with which you have to deal when solving
1D compressible flow problems.
I found this problem in a text book:
This reads like "Kadenacy" to me.Isentropic Back Flow. A duct of constant cross section is
filled with air ( gamma = 1.4) that is isentropically compressed from
atmospheric pressure, and the right end of the duct is suddenly
opened to the atmosphere. What fraction of the initial mass
in the duct is discharged, and how does the pressure at the
closed end vary with time? (Note: assume p/p0 is 2.83)
The author solved it using pencil, paper, triangles and a calculator (a graphicalThe fact that a sudden discharge of air or gas from a previously
pressurized container left a depression within the container has been known
since before the turn of the century and was often referred to as the
'Kadenacy effect'.
method). I am altering his method somewhat by using a little bit of pencil, paper
and calculator and a lot of a spreadsheet and a CAD program. You learn by doing.
Ideally, consider a thin membrane covering the open end of a half open tube. This
membrane is ruptured at time, t=0.
A centered expansion wave (a.k.a. fan) exists at the now open (right) end.
It begins to propagate toward the left approaching the closed end of the
tube. The head is shown in the diagram as being reflected as an
expansion (or rarefaction) wave when it reaches the closed end.
The rest will follow suit in time, but they must first traverse a region
occupied with other waves.
Of course, this is just the beginning to the solution.
-fde