MOMENTUM ANALYSIS
OF FLOW SYSTEMS
W
hen dealing with engineering problems, it is desirable to obtain fast
and accurate solutions at minimal cost. Most engineering problems,
including those associated with fluid flow, can be analyzed using
one of three basic approaches: differential, experimental, and control volume.
In
differential approaches
, the problem is formulated accurately using differ
ential quantities, but the solution of the resulting differential equations is
difficult, usually requiring the use of numerical methods with extensive
computer codes.
Experimental approaches
complemented with dimensional
analysis are highly accurate, but they are typically timeconsuming and
expensive. The
finite control volume approach
described in this chapter is
remarkably fast and simple and usually gives answers that are sufficiently
accurate for most engineering purposes. Therefore, despite the approxima
tions involved, the basic finite control volume analysis performed with paper
and pencil has always been an indispensable tool for engineers.
In Chap. 5, the control volume mass and energy analysis of fluid flow
systems was presented. In this chapter, we present the finite control volume
momentum analysis of fluid flow problems. First we give an overview of
Newton’s laws and the conservation relations for linear and angular momen
tum. Then using the Reynolds transport theorem, we develop the linear
momentum and angular momentum equations for control volumes and use
them to determine the forces and torques associated with fluid flow.
167
CHAPTER
6
OBJECTIVES
When you finish reading this chapter, you
should be able to
■
Identify the various kinds of
forces and moments acting on
a control volume
■
Use control volume analysis to
determine the forces associated
with fluid flow
■
Use control volume analysis to
determine the moments caused
by fluid flow and the torque
transmitted
The design of many machines, such as this
helicopter, requires use of the equations
of conservation of mass and energy, and the
linear momentum and angular momentum
equations.
Photograph by John M. Cimbala.
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6–1
■
NEWTON’S LAWS
Newton’s laws are relations between motions of bodies and the forces act
ing on them. Newton’s first law states that
a body at rest remains at rest,
and a body in motion remains in motion at the same velocity in a straight
path when the net force acting on it is zero
. Therefore, a body tends to pre
serve its state of inertia. Newton’s second law states that
the acceleration of
a body is proportional to the net force acting on it and is inversely propor
tional to its mass.
Newton’s third law states that
when a body exerts a force
on a second body, the second body exerts an equal and opposite force on
the first
. Therefore, the direction of an exposed reaction force depends on
the body taken as the system.
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 Fall '10
 Dr.Ra’fatAlWaked
 Angular Momentum, Force

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