On the weakly compressible/incompressible limit applied to falling jets
Date Issued
2010
Abstract
We consider the flow of a fluid falling from a vertical pipe, hitting a horizontal plate and flowing
sideways.
First the steady two-dimensional and irrotational flow of an inviscid and incompressible fluid is
considered. A parametric study shows that the flow can either leave the pipe tangentially or detach
from the edge of the pipe. Two dimensionless numbers come into play: the Froude number and the
aspect ratio between the falling altitude and the pipe width. When the flow leaves tangentially, it
can either be diverted immediately by the plate or experience squeezing before being diverted. The
profile of the pressure exerted on the plate is computed and discussed.
Then the same problem is revisited with the inclusion of compressibility effects, both for the
falling liquid and for the gas surrounding it. An additional dimensionless number comes into play,
namely the Mach number.
Finally, an asymptotic analysis in the limit of the Mach number going to 0 is provided.
sideways.
First the steady two-dimensional and irrotational flow of an inviscid and incompressible fluid is
considered. A parametric study shows that the flow can either leave the pipe tangentially or detach
from the edge of the pipe. Two dimensionless numbers come into play: the Froude number and the
aspect ratio between the falling altitude and the pipe width. When the flow leaves tangentially, it
can either be diverted immediately by the plate or experience squeezing before being diverted. The
profile of the pressure exerted on the plate is computed and discussed.
Then the same problem is revisited with the inclusion of compressibility effects, both for the
falling liquid and for the gas surrounding it. An additional dimensionless number comes into play,
namely the Mach number.
Finally, an asymptotic analysis in the limit of the Mach number going to 0 is provided.
Subjects