Page 128 - Introduction to Continuum Mechanics

Equation of Conservation of Mass 113

In cylindrical coordinates, it reads:

In spherical coordinates it reads:

For an incompressible material, the material derivative of the density is zero, and the mass
conservation of equation reduces to simply:

or, in Cartesian coordinates

in cylindrical coordinates

and in spherical coordinates

Example 3.15.1
For the velocity field of Example 3.4.2,

V- L 1 */
find the density of a material particle as a function of time.
Solution. From the mass conservation equation

Thus,