First Principles - Sustainable Design: The Science of Sustainability and Green Engineering - page 59

A couple is formed by two equal and parallel forces that have noncollinear lines
of actions that are opposite in sense. The moment of a couple is determined from
the product of the force and the minimum distance between the two forces. Like
the moment in a point of space, the equation for the moment of a couple is M

=
Fd. Thus, couples are common in all mechanical devices, including windmills,
pumps, and engines.

Environmental Dynamics

Dynamics is the general area of physics concerned with moving objects. It includes
kinematics and kinetics. Kinematics is concerned with the study of a body in
motion independent of forces acting on the body. That is, kinematics is the
branch of mechanics concerned with the motion of bodies with reference to force
or mass. This is accomplished by studying the geometry of motion irrespective
of what is causing the motion. Therefore, kinematics relates position, velocity,
acceleration, and time.
Hydrodynamics is the important branch of environmental mechanics that is
concerned with deformable bodies. It is concerned with the motion of fluids.
Therefore, it is an important underlying aspect of contaminant transport and
movements of fluids, and considers fluid properties such as compressibility and
viscosity. These are key to understanding water distribution and treatment systems,
flows in pipes, and the design of pumps and fluid exchange systems.
Kinetics is the study of motion and the forces that cause motion. This includes
analyzing force and mass as they relate to translational motion. Kinetics also
considers the relationship between torque and moment of inertia for rotational
motion.
A key concept for environmental dynamics is that of linear momentum , which
is the product of mass and velocity. A body's momentum is conserved unless an
external force acts on a body. Kinetics is based on Newton's first law of motion ,
which states that a body will remain in a state of rest or will continue to move
with constant velocity unless an unbalanced external force acts on it. Stated as the
law of conservation of momentum , linear momentum is unchanged if no unbalanced
forces act on a body. Or, if the resultant external force acting on a body is zero,
the linear momentum of the body is constant.
Kinetics is also based on Newton's second law of motion , which states that the
acceleration of a body is directly proportional to the force acting on that body
and inversely proportional to the body's mass. The direction of acceleration is the
same as the force of direction. The equation for the second law is

d p
dt

=

F (2.9)

where p is the momentum.