Page 104 - Introduction to Continuum Mechanics

Material Derivative 89

(C) Spherical Coordinates (r,0,0)- With
v = v r(r,0,0)e r+v0(r,0,0)e0+V0(r,0,0)e^

and, [seeEq. (2D3.17)]

we have,

Example 3.4.1
(a) Find the velocity field associated with the motion of a rigid body rotating with angular
velocity ft> = (oe 3 in Cartesian and in cylindrical coordinates.
(b) Using the velocity field of part (a), evaluate the acceleration field.
Solution, (a) For a rigid body rotation

In Cartesian coordinates

i.e.,

In cylindrical coordinates