Unformatted text preview: ero. Thus the work done along this path from A to C
is negative.
b) F is not conservative. Consider if we traveled from A to C via point B instead– the
work done along this path is positive (why?), so the work cannot be path–independent.
Problem 2: Flux through a Pipe
a) Assuming that the ﬂuid velocity is the same over the entire crosssection, the volumetric
ﬂow rate is then 5 m/s × 3 m2 = 15 m3 /s.
Why? Consider a column of ﬂuid of area A = 3 m2 and width v = 5 m, as shown in
the part (a) of ﬁgure below. This is the amount of liquid that will ﬂow through A in
1 second. The volume of this liquid is vA = 15 m3 , a...
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 Spring '06
 PANTANO
 Math, Multivariable Calculus, Dot Product

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