3. Momentum thicknessδ(O)(动量厚度,动量损失厚度) ,= pudy. u y pua △M=0w-v △M=pUO" p8U2=p u(u-uky 0 ="= ou
3. Momentum Thickness ** ( ) （动量厚度，动量损失厚度） y d U u ( ) = − 0 2 M Uu u dy udy u 0 udy U 0 M U U ** = U u(U u)dy = − 0 ** 2 dy U u U u = = − 0 ** 1 M real = M ideal =
5.3 Momentum Integral relation for flat-plate BL (平板边界层动量积分方程) streamline P O= const p= const△z=b U Steady incompressible dddΦe1 +-ldqpout-(ddp)in] RTT CV dt dt dmv dmv [(厘m-()m(,)m=pAU·U=pbhU anm 6 out PdAuu=l pbu?dy
5.3 Momentum Integral Relation for flat-plate BL (平板边界层动量积分方程) U=const p=const Steady & incompressible 1 [( ) ( ) ] s cv out in d d d d dt dt dt = + − [( ) ( ) ] out in dmV dmV dmV dt dt dt = − RTT CV x y h U P d streamline o z = b 2 ( ) AU U bhU dt dmV i n = = = = 0 2 0 ( ) dAu u bu dy dt dmV out
dmy df )in] obu dy-pbhU/2 ann streamline P Momentum equation U ∑F=「m?- phu2° CV ∑F=D(g)→D=mbU2-mbbh Continuity:phu= pbudy=>pbhU2= pbuUdy D=pbl(U-u)hy速度积分法求阻力 0
8 Momentum equation: F D drag = − ( ) Continuity: 0 D b u U u dy ( ) = − [( ) ( ) ] out in dmV dmV dmV dt dt dt = − 2 0 2 bu dy bhU = − 2 0 2 F bu dy bhU = − = − 0 2 2 D bhU bu dy = 0 bhU budy = 0 2 bhU buUdy CV x y h U P d streamline o 速度积分法求阻力
D=pblu(U-u)dy=pbU2d1-)dy =pbu-8 D(x)=TA=bT(x)dx t, (xdx=puB 2d0 Von Ka'rma'n 1921 (1881-1963)
0 D b u U u dy ( ) = − 2 = bU 2 w d U dx = Von Ka rma n 1921 (1881-1963) = − 0 2 (1 )dy U u U u bU = x w x dx U 0 2 ( ) D(x) = w A = x b w x dx 0 ( )
0 U ud(u/l δa(y/δ)0 u=a+by+cy BC:y=0=0 Q0 y=8u≈U u。0 a=0.b= C 2yy0≤y≤6(x) Uδδ
10 0 (1 ) u u dy U U = − y ( ) x u(y) x 2 u a by cy = + + 2 2 0, , - U U a b c = = = 2 2 u y y 2 U = − 0 ( ) y x y u = = 0 0 0 u y y u U = BC: 0 ( / ) ( / ) = = y y U u U =0 w = y y u