Page 106 - Introduction to Continuum Mechanics

Material Derivative 91

we have

Also, since

so that

therefore,

Thus,

i.e.,

We note that in this example, even though at any spatial position (except the origin ), the
velocity is observed to be changing with time, but the actual velocity of a particular particle is
a constant, with zero acceleration.
(b)Since

therefore,

so that

Thus,