Question

Q1 13 Points Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x,y,z) € R3 : x2 + y2 <z<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) +23, 2cz cos(x2) + y,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Please select file(s) Select file(s) Q1.2 8 Points Compute the flux through the filter (SS, F.ñds). Please select file(s) Select file(s) Q1.3 2 Points Is there more water entering the filter or leaving it? O Entering Same O Leaving

Answer 1

filter ve {(6952): Oxleges zsi} (842 (03(y) +23, 272 COD (x) +y3,07 4 wator How af (X,9,2) = 0 ham gin we ZEI 4 622 5x2xyz the surface of content cone ... 225x² + y2 i haure Hence, اسرا 2 7 Z z/ antes x?ty²=1, 2=1 انا the shahed region io required volume. which is purt of filter. Я X 2 :: surface to closed we can apply guers diuryonce therm, which state that ☆ fonds JSS divf du. / where diu f cente ( 2y 2 (03 y2 + x3) + (2x2 (m) (x ?) ty3) +0 3x² + 3y² N S U hau 020 Z z r » f finds a JJS a (x²ty?) du using cylend indrical cordinate system, we flexe jo si je 3 r. Ydz dy dre 2 12 11 373. (1-2) drda (3) [to-t.) 720 pus 27 br 2 GT 31 To To 127

N - . flux is tue So this implics that more flux is leaning and less to entering. 3rd option is correct. 3)