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i
In part b, the velocity ﬁeld is the same: v = vˆ but the area vector S = Aθ n. Where
i
ˆ. The ﬂux is v · S = vAθ cos θ = vA.
n is at an angle θ with i
Flux v · S of a vector v over an area S is magnitude of the area times the component
of v along the normal direction. In part b), the area increases, but component of the
velocity, normal to the area, decreases by the same factor. The ﬂux is the same.
Problem 3: Rain
We can solve this problem in a similar way to problem 2, i.e. the volumetric ﬂow rate of
the rain = ﬂux = product of the surface area and the dot product of the rain velocity and
unit normal to the...
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 Spring '06
 PANTANO
 Math, Multivariable Calculus, Dot Product

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