Fundamentals of Fluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 14

heal without addition of energy into the system. This law should also be familiar from
beginning thermodynamics courses.

dS
dt $

0 ð 2 : 4 Þ

5. Conservation of Angular Momentum: Unless acted upon by an external torque, a body
rotating about an axis will continue to rotate about that axis. The mass moment of
inertia of a body is its resistance against changes in angular momentum (this is the
second mass moment of inertia with units of mass multiplied by length squared).
Moment of inertia is a state property of the material, which is related to the geometry of
the object. An example of the conservation of angular momentum is as follows: a
figure skater spinning around his or her centerline with arms outstretched will increase
his or her angular velocity by bringing his or her arms into the body. Conversely, by
stretching out his or her arms out, the angular velocity will decrease. This is due to
changes in the body's moment of inertia. Angular momentum ( - ) is defined by the cross
product between the position vector of a particle relative to the axis of rotation ( - , i.e.,
hands relative to the centerline) and the linear momentum of that particle ( - ).
Conservation of linear momentum is defined as no change in angular momentum with
time as long as the mass moment of inertia remains the same. When the mass moment
of inertia increases, the momentum decreases, and vice versa. Equation 2.5 is the
definition of angular momentum for discrete particles; for bodies, the angular
momentum must be summated over the entire mass.

-

- -

5 3 ð 2 : 5 Þ

In most of the examples we will discuss in this textbook, not all of these governing laws
will be required to solve the problem. However, they will all be applied to some extent
during the course of this textbook so that it can be realized how these laws affect different
situations in biofluid mechanics. It is also true that problem solutions may require other
relationships, such as constitutive or regulating rules, to solve the problem. However, the
five laws listed previously are always a good starting point for many biofluid mechanics
problems. For example, the ideal gas law (which is a constitutive rule), p

RT, is useful
in solving many gas flow problems that might occur in biological systems but would not

5ρ

FIGURE 2.7

The conservation of
angular momentum states that a spin-
ning body will have a particular
angular velocity. As more mass is
added to the body at a larger radius
from the axis of rotation, the angular
velocity will decrease. If the added
mass is removed, the angular velocity
will return to the original angular
velocity (angular velocity is

M M

repre-

sented by the width of the curved

arrow).