Basic study of leaks through a contactless seal
 

I am working on an IC engine project and I have to determine the leaks through a contactless seal. Abradable seals are commonly used in jet engines to seal between the turbine blades and the stator. The principle is repeated here in a different context.
The situation can be schematized as follows: determine the flow of gas passing through the opening of a seal without contacts of FIG. 1 (file attached) :

We have :
• a half cylinder in red, so a 2D arc (1),
• a plan in blue, a line in 2D (2),
• Between the two, the gap (3) with width e
• In hatched red, gases under pressure (4),
• In hatched blue, underneath, the outside atmosphere (5).
It is desirable that the values of the following variables be modifiable, by declaring them, for example, in a file:
r, arc radius (1), 10mm
e the width of the joint, 0.1 mm, length 40mm
The burned gases (4): pressure 80 bar, temperature 1273 ° C (for 1 / 600th of a second, but this is not important since we are interested in instantaneous flow only)
Atmosphere (5): 1 bar, 273 ° C.
Please contact me and tell me your conditions and delay
Thanks
William