Chapter 3
The Equations of Change for Isothermal
Systems
ChE 771: Advanced Transport Phenomena
Dr Rami Jumah
Department of Chemical Engineering
Jordan University of Science and Technology

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Outline
Perspectives of Fluid Motion
Types of Time Derivatives
The Equation of Continuity (The Mass Balance)
The Equation of Motion (The Momentum Balance)
Common Simplifications of the Equation of Motion
The Equations of Change and Solving Steady-State
Problems with One Independent Variable
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Introduction
It is tedious to set up a shell balance for each problem that
one encounters.
The shell balance method cannot be applied to all flows,
such as flows with curved streamlines.
What we need is a general mass balance and a general
momentum balance that can be applied to any problem.
The two main equations that we derive are called the
equation of
continuity
(for
the mass balance
) and the
equation of motion
(for the
momentum balance
).
The term
“
equation of change
”
may be used to describe
how any physical quantity changes with time and position.

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Perspectives of Fluid Motion
Eulerian Perspective:
the flow as seen at fixed locations in space, or
over fixed volumes of
space, the observer is fixed in space (the
perspective of most analysis).
In the Eulerian description of fluid flow, a finite volume called a flow
domain or control volume is defined, through which fluid flows in and
out.
Lagrangian Perspective
:
the flow as seen by the fluid material, the observer
moving with the particle with the same velocity as the fluid particle (the
perspective of the laws of motion)
Lagrangian analysis is analogous to the (closed) system analysis; namely, we
follow a mass of fixed identity.
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fixed observer measuring
velocity of wind
10 km/h
observer in a balloon
0 km/h