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Homework answers / question archive / Show by direct differentiation that the divergence of the vorticity vector is zero

Show by direct differentiation that the divergence of the vorticity vector is zero. ∇ · ω = 0 13. Derive expressions for the components of the curl operator in cylindrical polar coordinates. Using these relations, find the vorticity field for the flow described by the following velocity field: vθ = Ar + B/r where A and B are constants. This field is a general representation of the “torsional flow” and occurs in many practical situations. What is the direction of the vorticity vector? What is the magnitude? A free vortex can be considered to be a special case of the torsional flow of the above problem with the constant A equal to zero. Show that the vorticity field is zero for a free vortex. A rigid-body type of rotational motion is described by vθ = Ar Why is it called a rigid-body type of motion? Find the vorticity for this flow.