Let (mathbf{v}=z mathbf{k}) be the velocity field (in meters per second) of a fluid in (mathbf{R}^{3}). Calculate
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Let \(\mathbf{v}=z \mathbf{k}\) be the velocity field (in meters per second) of a fluid in \(\mathbf{R}^{3}\). Calculate the flow rate (in cubic meters per second) through the upper hemisphere \((z \geq 0)\) of the sphere \(x^{2}+y^{2}+z^{2}=1\).
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We use the spherical coordinates xcos theta sin phi quad ysin theta sin phi quad zcos ...View the full answer
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