Momentum Thickness

University:
Duke University
Course:
PHYSICS 814 | Introduction to Fluid Mechanics
Academic year:

2023
Views:

296

Pages:

2
Author:

Pemuda H

s* = Son (1+e) dy nd (usually say h=8) = So" (1+ pove) dy if compressible h Pu = A-Solue-wdy s ue = So (ue-u) dy = (ue-u) = * is a measure of the mass flow rate lost Momentum Thickness (4.2.1.2.3) = pu ue (1-pelle) dy measure of the momentum loss Shape Factor (4.2.1.2.4) H= Momentum Integral Method (4.21.3) Solu + v ]dy = Soue dy + por dy au ax au vay D nege. compared to oxy=0 P(Tex(n)=x(0)) nhau x+y=0v=-Sony dy 2x ax dle Soh (Ue-u) dy = Sx x [u (ue-u)]dy (ue-u)] dy + dx. →8*= So (1-ue)dy → Son the (1-ve) dy d dx ←← = dile shou (2)+dxo We le Ue-u due le-u Ue 2 do dile le dx + 2Ue dx + due dx Ue 5* = P do dx + de due (20+) = Tow dx dx dle + Ue dx (2+ H) I went from 2 PDE's to 1 ODE If you have a flat plate: Ue=const Blasius Solution (Look in Notes) dx = pur LOOK FOR NOTES! Incompressible flow over a flat plate- Blasius Solution (4.2.2.1) ff" + 2511-0 Rex 8 = 5 le f = f'=0n=0. 5=1.72 2.59 do + due o x 0=0.664ue dx de (2+H) pur 0 do dx = pur puz x=x0.664= 0.664 Rex = ½ c of local skin friction coefficient = 2 pue Cp=&o apdx Thwaite's Integral Momentum Method (4.2.2.2) do dx (2+1)= pu 20 ()+[(2+H)-0] θ TE Thwaite's Coefficient T=(H-1)+0.225 (())=(c)→(de(F) (x) 0.45 x 5 = +0.45