Page 449 - Introduction to Continuum Mechanics

Integrals over a Control Volume and Integrals over a Material Volume 433

where v is the velocity field.
Solution. Let P be the total power, then

T*
But Tn • v = n • T v (definition of transpose of a tensor). Thus,

Application of the divergence theorem gives

Now,

Thus,

7.3 Integrals over a Control Volume and Integrals over a Material Volume
Consider first a one-dimensional problem in which the motion of a continuum, in Cartesian
coordinates, is given by

and the density field is given by

The integral