The velocity vector field of a fluid (in meters per seco
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The velocity vector field of a fluid (in meters per second) is F = x2 + y2, 0, z2 Let W be the region between the hemis
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The velocity vector field of a fluid (in meters per second) is F = x2 + y2, 0, z2 Let W be the region between the hemisphere S = & (x, y, z) : x2 + y2 + z2 = 1, x, y,z ? 0 ' and the disk D = & (x, y, 0) : x2 + y2 ? 1 ' in the xy-plane. Recall that the flow rate of a fluid across a surface is equal to the flux of F through the surface. (a) Show that the flow rate across D is zero. (b) Use the Divergence Theorem to show that the flow rate across S, oriented with outward-pointing normal, is equal to W div(F)dV . Then compute this triple integral.
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