A fluid has density 860 kg/m3 and flows with velocity v = z i + y2 j + x2 k, where x, y, and z are measured in meters and the co
mponents of v in meters per second. Find the rate of flow outward through the cylinder x2 + y2 = 25, 0 ≤ z ≤ 1.
1 answer:
You can use the divergence theorem:

has divergence

Then the rate of flow out of the cylinder (call it <em>R</em>) is

(by divergence theorem)

(after converting to cylindrical coordinates)
whose value is 0.
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