Suppose we have the open surface S, the upper hemisphere (with no bottom): z = f (x, y) = /1 – x² – y². If the fluid velocity field is F (x, y, z) = (y, –x, z²), then evaluate the polar double integral that is equivalent to: Net Upward Flux = // (F î) dS = ||(-Mfz– Nfy+P) dA, S R where în is the unit upward normal to S, and the region R is the projection of S down onto the xy-plane.
Suppose we have the open surface S, the upper hemisphere (with no bottom): z = f (x, y) = /1 – x² – y². If the fluid velocity field is F (x, y, z) = (y, –x, z²), then evaluate the polar double integral that is equivalent to: Net Upward Flux = // (F î) dS = ||(-Mfz– Nfy+P) dA, S R where în is the unit upward normal to S, and the region R is the projection of S down onto the xy-plane.
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Transcribed Image Text:Net Upward Flux.
Suppose we have the open surface S, the upper hemisphere (with no bottom):
z = f (x, y) = /1 – x² – y?.
If the fluid velocity field is F (x, y, z) = (y, –x, z2), then evaluate the polar double integral
that is equivalent to:
-
Net Upward Flux =
(F.î) dS =
(-M fr – Nfy + P) dA,
S
R
where în is the unit upward normal to S, and the region R is the projection of S down onto
the xy-plane.
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