Application of Navier Stokes Equation in Problems | Swansea University

Academic year

2023
Author

Jake Tomson
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Application of Navia Strokes Equation in problem A liquid developed laminal film of thickness flows down and inclined in a (h) steady Deduce fully the expression for the liquid velocity profile gloce Codening Any the to equations momentum equn. of (N.San) Issued g 15° T as + ov + ow - I 02 oy of 0 O ST. of + 4.34 02 ty 04 oy + w 04 of 2000 ox + ig. 2 + 0 2 2 2 to act 0x2 O say 2 S 0 0 s( or of + u. av Ox + V. tw ou of = ap Boy f 3 ay 2 2 2 Me [ a + au for 022 0 O oy2 S[ 4.3W Ox +v.20 as t.w.36 DW and 10 + + = a oz 93 sg of of 2 27 2 4 r the w + dw ax2 DLE considering 1 , ou = ao =0 ax of W=0 a =0 V=O oy

: 2) 1) Incompresible steady developed Read) with 3) 4) Fully No Variation developed in the 8 direction, 2 taky equet 2 0 = Pgx + to 8ye on 5 3 tabs. exad 6 ap = sgy O = - op + Pgy ) by og 4 take equat total equation is zew, taby 5 2 fe au = Pg, + (Some 2 oy2 54 - Sgx = du 2 og" L = M 2 (gx gone) dy2 (Constant) a ( all these are constant). have 2 terms if we du = He. game some values. ay2 Cose the dy he

fu A dj - - I du. Ay the tci dy u= Ay' + Gyt + C2 u = - y' + Cry + C2 2 pgs 2H Bourday Conditions: (3) du = 0 at yeh dy U=0 @ y-o (4) I and 2 Substhuary (3) and (4) in G= ig Sno Ne xh c,=0 = 2 U= - 8g sincy " 2te t 1 xh 4