Mathematics, 16.12.2021 14:00 payen96151
Consider the velocity field of a fluid at time t given by F(x, y, z) = (x^3 , y^3 , z^3) . Consider the fluid flux through the surface ∂E of the closed cone E = {(x, y, z)|x^2 + y^2 = z^2 , 0 ≤ z ≤ 1} Flux = double integral ∂E F · N dS.
Use the Divergence Theorem to express the flux through ∂E
in terms of a triple integral.
Now switch to cylindrical coordinates to evaluate the triple integral
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