Question

Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) € R3 : Vx2 + y2 <2<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) + x3,2xz cos(x?) + y3,0) 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. ndS). 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

Griun boundors ir = {(ng, 2) E R': Duty 2 221} To immersed by water a flow given by F (nege) = (24 COSLY") + n², 2n2 cos(22) 45 (0) To Draw sketch of the fillter in given points Z1 ✓ FE,E,F) 72 2 = Vatyr. = {242 zos(°J+x?, 20260560) +yiso) To compert ter filter though tlum ss. E nas: s From Goow farmela $ Fiñan Sain Fau of divergene div> v DE OF ា ។ +OF, 3 SS (24 g) dudy dz 22 dn Z 211 = 3nt3y to 351 % v dvdo dz = 3 (nay) 70.000

TO talie M. TUOSO y = reino 361 By Car San Jose 3 [ount Sixt az g (ny) an 2CVQ 6) - & 3x 1 it Jozdz GOSOring = rino nye9 : 7x21 x 2 %). =Y 3 xx l xl er leaving