Velocity Profile

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

2023
Views:

314

Pages:

2
Author:

Pemuda H

L-T Transition -0.2 Cf = 0.046 UD V for a pipe 0=4(r) 2πr dr fully developed (velocity profile doesn't change) u = U(r)rdr Sordr = average velocity Uc = 0.8 Cf = 0.046 ((2R)) -0.2 = 0.04 ÜR-0.2 = 2 Cf = 0.04 (R)-02-> Cuc = 0.027 (CR)-0.2 Cfuc Uc Prandtl-Karman Hypothesis (4.2.3.2) Can replace Uc with low and R with S UR-0.2 ( 27( Cf = 0.027 ne [6, 10] ↓ ↓ → typically use n = 7 low Re high Re * = So (1-te) dy = 50[1-(*)*]dy=850[1-()*]5() 00 /- YE [0,6] te [0, 1] 5** s So² (1-t) dt = s (t-*+1 t² +1)188=8(1- 22 1+1 ue (1-tue) dy = Sole (1-1 0= = (n+1)(n+2) 7 0 = 872 72 =-=0.027() = 0.027 (100)-0.2. dx 2 Y de dx = 0.017 2 (4)-0.2 de -0.2 -0.2 0.0085 dx 012 12 0.0085 400-0.2-02 Y 2 -0.2 (1.2) (0.0085) Rex 72 12 = 0.022 Rex x 8 = 0.23 Rex x Thermal Boundary Layer (4.3) 214 wax + vay ray(1) ap → flat plate: x=0 GOAL: wax+ K 1 vay = PCP ay Took A too-large Temperature gradient may crack the flat plate You can also draw the gradient as Q = Wsis + Sp (h+ + gê) (in) do k+y(kdy PV (h+u²+v²)dx + 2 zy [pv (n+u²+v²)dx]dy 2 ay dy puth+udy 1 + x [puch+²²+x3dy]dx Toy+dx pv (h+ -pushed Assumptions: 9"=-k 1) Neglect velocity flux in y-direction 2) Neglect h in the x-direction WsTx dx.u + Tx dx.u + a 24 (xudx) dy Conduction: Convection: W Q=hfA (Tw-Too)→ = mk thermal conductivity, heat convection coefficient 9" = - key →heat flux Tw