Euler equations for axisymmetric flow For the flow field and coordinate system o

Question

Euler equations for axisymmetric flow For the flow field and coordinate system of Exercise 2.1, show that the Euler equations (inviscid momentum equations) take the form Navier-Stokes equations for two-dimensional axisymmetric flow Show that the strain rates and vorticity for an axisymmetric viscous flow like that described in Exercise 2.1 are given by Hint: Note that the azimuthal strain rate is not zero. The easiest way to determine it is to recognize that = 0 must be equivalent to the continuity equation. Show that the Navier-Stokes equations for axisymmetric flow are given by Euler equations for two-dimensional flow in polar coordinates For the two-dimensional flow described in Exercise 2.2, show that the Euler equations (inviscid momentum equations) take the form Hints: (i) The momentum components perpendicular to and entering and leaving the side faces of the elemental control volume have small components in the radial direction that must be taken into account; likewise (ii) the pressure forces acting on these faces have small radial components.

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