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.