Spherical polar coordinates (r, θ, φ) are defined in Fig. P4.12. The cartesian transformations are
x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ
Do not show that the Cartesian incompressible continuity relation (4.12a) can be transformed to the spherical polar form What is the most general form of υ r when the flow is purely radial, that is, υθ and υφ are zero?

Transcribed Image Text:

(1's sin θ) + r dr rsin θ (e r constant