Schlichting jet is a steady, laminar, round jet, emerging into a stationary fluid of the same kind with very high Reynolds number.
The problem was formulated and solved by Hermann Schlichting in 1933,[1] who also formulated the corresponding planar Bickley jet problem in the same paper.
[2] The Landau-Squire jet from a point source is an exact solution of Navier-Stokes equations, which is valid for all Reynolds number, reduces to Schlichting jet solution at high Reynolds number, for distances far away from the jet origin.
Consider an axisymmetric jet emerging from an orifice, located at the origin of a cylindrical polar coordinates
being the radial distance from the axis of symmetry.
Since the jet is in constant pressure, the momentum flux in the
direction is constant and equal to the momentum flux at the origin, where
is called as the kinematic momentum flux.
The boundary conditions are The Reynolds number of the jet, is a large number for the Schlichting jet.
A self-similar solution exist for the problem posed.
can be evaluated from the momentum condition, Thus the solution is Unlike the momentum flux, the volume flow rate in the
is not constant, but increases due to slow entrainment of the outer fluid by the jet, increases linearly with distance along the axis.
[3] Schlichting jet for the compressible fluid has been solved by M.Z.
[5] Similarly, Schlichting jet with swirling motion is studied by H.