Turbulence lecture 33

Turbulence lecture - Turbulence Lecture 33 Now multiply 2 by y n and integrate w.r.t y between 0 integrate by parts a couple of times Final Result

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Turbulence Lecture 33 Now multiply 2 by and integrate w.r.t y between n y 0& δ , integrate by parts a couple of times. Final Result 11 2 21 00 0 1 1 U 1 U1 1 1 1U U 1 U UU U mm y m mn n m y m nm n U U y dy y dy dy nx m U x nU U yd y y d y U mx xU δδ ++ + +− ∞∞ + + −+    ∂∂   −− +   +∂ +    ∫∫ i i + 0 0 U U m n m m n U ydy U U y y τ ρ −= Moment of Momentum Equation Let 0, n=1 If 0, you get Momentum Integral Equation. m = == Result 2 0 1 U 1 U y y y U d y d y xx 0 d y −+− + = ∫∫ ∫ i Last term is shear stress integral. Development of shear stress integral. 0 0 1 If 0, 1 then By parts let ; . 1 I y d y mdn mn ndm m y dn dy dm dy y Iy y = =− = = 0 1 dy dy 1
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Energy Integral Equation 2 3 0 Let 1, 0 1 Then U 1 2U U mn dU U U dy dx δ ∞∞ ==    −− =    0 U U dy y τ ρ
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This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.

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Turbulence lecture - Turbulence Lecture 33 Now multiply 2 by y n and integrate w.r.t y between 0 integrate by parts a couple of times Final Result

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