Let (mathcal{T}) be the triangular region with vertices ((1,0,0),(0,1,0)), and ((0,0,1)) oriented with upward-pointing normal vector (Figure
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Let \(\mathcal{T}\) be the triangular region with vertices \((1,0,0),(0,1,0)\), and \((0,0,1)\) oriented with upward-pointing normal vector (Figure 16). Assume distances are in meters.
A fluid flows with constant velocity field \(\mathbf{v}=2 \mathbf{k}\) (meters per second). Calculate:
(a) the flow rate through \(\mathcal{T}\).
(b) the flow rate through the projection of \(\mathcal{T}\) onto the \(x y\)-plane [the triangle with vertices \((0,0,0),(1,0,0)\), and \((0,1,0)]\).
Transcribed Image Text:
X (1,0,0) (0, 0, 1) v = 2k (0, 1, 0) -y
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The equation of the plane through the three vertices is xyz1 hence the upwardpointing normal vector ...View the full answer
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