(point) A fluid has density 5 and velocity field = ~yi + xj + Szk: Find the rate of flow (the flux of density times velocity) outward through the sphere x2 + y2 + 22 = 16. Hint: Apply the divergence theorem to the local mass flux vector field (the density times the velocity vector field) , and use the fact that the density is constant
Added by Ivan R.
Step 1
Step 1: Compute the divergence of the density times velocity vector field, which is given by \( \nabla \cdot (\rho \mathbf{v}) = \nabla \cdot (5\mathbf{i} + x\mathbf{j} + 5z\mathbf{k}) \). Show more…
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