Derive an expression for \(D \boldsymbol{v} / D t\) in spherical coordinates. Follow the same procedure as for cylindrical coordinates. Some unit vectors have derivatives. The components in Table 3.2 would be obtained.

Table 3.2. The convection operator (v system; componentwise equations . V) in a spherical coordinate av vo avr r component Vr + + ar 0 v avr rsine - ave component Vr + + ar vo avo > component Vr + + ve ave r 20 rsine vo avo VrVo Vevo r VrVO + cote r + + cot 0 ar r ae rsine r r