Derive an expression for \(D \boldsymbol{v} / D t\) in cylindrical coordinates.

Define the nabla operator in cylindrical coordinates and let it be dotted with a vector. Expand and use the chain rule, taking care to differentiate some of the unit vectors. The components in Table 3.1 would be obtained.

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Table 3.1. The convection operator (v.) in a cylindrical coordinate system; componentwise equations r component component z component avr vo avr avr v Vr + ar r ae az ave vo ave Vr + + V + ar rae az r avz vg av: avz Vr + +- ar az