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Unformatted text preview: te is the same as in a). Here are two ways to see it:
1) Since the amount of ﬂuid coming in from the left side of the pipe remains the same,
the amount that comes out from the right side should also be unchanged regardless of
the shape of the cut. (Conservation of mass, with constant density)
2) Consider a slanted column of ﬂuid of area Aθ and width v , as shown in the part (b)
of ﬁgure above. This is the amount of liquid that will ﬂow through Aθ in 1 second.
The volume of this liquid is vAθ cos θ (area time the height perpendicular to area).
Note that Aθ = A/ cos θ. This is easy to see if the pipe had an rectangular cr...
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