Page 463 - Introduction to Continuum Mechanics

Moving Frames 447

That is, the force per unit width on the fluid by the plate is acting to the left with a magnitude

7.7 Moving Frames
There are certain problems, for which the use of a control volume fixed with respect to a
frame moving relative to an inertial frame, is advantageous. For this purpose, we derive the
momentum principle valid for a frame moving relative to an inertial frame.

Fig. 7.6

Let FI and FI be two frames of references. Let r denote the position vector of a
differential mass dm in a continuum relative to FI and let x denote the position vector relative
to p2 (see Fig. 7.6). Then the velocity of dm relative to FI is

and the velocity relative to F 2 is