Let x, y, and z be measured in meters, and suppose thatF(x, y, z) = yi + z j + 3xk is
Chapter 15, Problem 30(choose chapter or problem)
Let \(x, y\), and \(z\) be measured in meters, and suppose that \(F(x, y, z) = 2xi − 3y j + zk\) is the velocity vector (in m/s) of a fluid particle at the point \((x, y, z)\) in a steady-state incompressible fluid flow.
(a) Find the net volume of fluid that passes in the upward direction through the hemisphere \(z=\sqrt{9-x^{2}-y^{2}}\) in 1 s.
(b) Assuming that the fluid has a mass density of \(1060 \mathrm{~kg} / \mathrm{m}^{3}\), find the net mass of fluid that passes in the upward direction through the surface in part (a) in 1 s.
Equation Transcription:
Text Transcription:
x, y
z
F(x, y, z) = 2xi-3y j + zk
z =square root 9-x^2-y^2
1060 kg/m^3
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