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Derivation of Material Acceleration
(Section 41, Çengel and Cimbala)
Recall the
chain rule
: If
f
is a function of two variables,
t
and some variable
s
which is
itself also a function of
t
, then we take the total derivative of
f
with respect to
t
as
follows:
df
f dt
f ds
f
f ds
dt
t dt
s dt
t
s dt
∂
∂∂
∂
=+=
+
∂
∂
Now let’s apply this chain rule to the time derivative of the fluid particle’s velocity:
Thus, the acceleration of a fluid particle is calculated using the chain rule as follows:
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This note was uploaded on 07/23/2008 for the course ME 33 taught by Professor Cimbala during the Fall '05 term at Pennsylvania State University, University Park.
 Fall '05
 CIMBALA

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