(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b)

(5) 74 Re, bondar laer (Prandtl) Re z ω z = x

(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b)

(5) 76 l V x ) 1/ 1 ( 1 1 1 δ δ = x Re x p V x t V l l (1-1) 1/ 1 δ δ δ δ = x Re p V x t V l l (1- ) 1 1 = x V l (1-3) t V t = l v V Re l = (1-4) V 1 / = V x δ δ l / δ = δ l

(5) 77 δ 1 x1 1 v = x v δ 1 1 δ 1 x 1 x v 1 v δ v δ x v δ x v 1 δ v δ v 1 δ

(5) 78 Re 1 Re δ v l l (1-5) δ p δ 1 p = v x ρ x (1-6) p = (1-7) = x (1-8) 1 p = (1-9) ρ x x =, = ( = ) ( x) ( ) (1-1) p = λρ (1-11) x λ λ 1/ l

(5) 79 v x

(5) 8 x η ψ, ψ = f n (η) (1-1) 1/ η = = R x (1-13) vx / x x R x = v ψ ( x, ) = v x f ( η) (1-14) ψ n ψ ψ η = = = f ( η) η ψ 1 v = = { ηf ( η) f ( η) } x x η η = = f ( η) x η x x η = = f ( η) η vx η = ( η) = f η vx vx (1-15) f ( η)

(5) 81 / 1 x /

(5) 8 1 p = v x ρ x = v (1-16) x f ff = (1-17) η f f (1-18) η f v =.865 (1-19) x

(5) 83 l 1-5 f, f, f 7 = Rx 1/ x 6 5 4 3 = Rx 1/ x 6 5 4 3 1 1..4.6.8 1. (a).4.8 (b) R x 1/

(5) 84 δ(x) = f ( η) =. 99 (11-1) η η δ = 5. vx = 5.xR 1/ x (11- ) = [ ) ] q ( d (11-3) * δ * δ = * δ = q (11-4) 1 d * δ (displacement thickness) vx x * δ = 1.73 = 1. 73 1/ R x (11-5)

(5) 85.99 () d

[ ] (5) 86 ρ d ρ θ (momentm thickness) θ = 1 d (11-6) vx x θ =.664 =.664 1/ R x (11-7) l D l D = µ dx =.664 µρl = D( l) C f =, ( A = bl) (1/ ) ρa (11-8) 1. 38 C f = (11-9) R l R l = l / v Rl Rl

(5) 87 l (Dail-Harleman, Addison-Wesle )

(5) 88 d p / d x (adverse pressre gradient) (separation) p = const. ρ PA A = ρ PC PB 1 = ρ ρ PB = ρ ( ) B C B = P C ρ C (11-1) (11-11) E = p ρ A A = p ρ B B E A B = p C ρ C E A C (11-1)

(5) 89 (a) (b) (c) A A B B C C D D

(5) 9 C p pb pc B = EB C (11-13) p = ρ ρ 1 C B ( B C ) B C ρ E (11-14) d p / d x =, ( = ) (bondar laer control)

(5) 91 = = h x h h h h h 1 p d d v d d t x = ν ρ x (1-1) h h d = d x h d v = x (1- ) h 1 p = d d d ρ x t x (1-3) τ µ / ( / ) = h = ( ) = µ τ ν = = (1-4) ρ ρ = h h h v d = d d x (1-5) h h = d d x x h h h = h 1 p τ d d d d (1-6) t x x ρ x ρ δx h h dδx δx d vδx t x =

(5) 9

(5) 93 x x δx h ( ) d [ ] d τ ( ) ( ) d = (1-7) t x x ρ h x d a da db a f ( x, α) dx = f ( a, α) f ( b, α) b fdx dα dα dα b α (1-8) ( δ * ) * τ ( θ ) δ = t x x ρ (1-9) = : = = : =, =

(5) 94 B v d x = D δx x A C x

(5) 95 d/dx t dθ ( x) τ ( x) = d x ρ (1-1) θ (x) τ ( x) = f (η ) (1-11) η = / δ ( x) 1 θ = ( )d = δ ( x) f (1 f )dη α1δ ( x) = (1-1) α = 1 f ( 1 f ) dη (1-13) τ ν ( / ) ν = ν = = β1 ρ δ η δ = η = (1-14) β1 = f () (1-15) * δ f * δ = α δ ( x) (1-16) α ( 1 f ) η (1-17) = 1 d dδ β1 ν δ = d x α1 (1-18) x =, δ = δ ( x) = β1 νx α1 (1-19) * δ * β1 νx δ = α α1 (1- )

(5) 96 θ = α1 β1 νx α1 (1-1) D(l) C f ( = D( l) /{ bl( ρ / )}) α1β1 x τ ( x) = µ x ν (1- ) 3 D ( l) = b α 1β1 µρl (1-3) C f α 1β1 = l / ν (1-4)

(5) 97 f ( η) = η ( < η < 1) (1-5) f ( ) = f ( 1) = 1 f (1) = = 1 ( < η < 1) f ( η) = ( η = 1) (1-6) 1 1 α 1 = η(1 η)dη = 6 1 1 α = (1 η)dη = (1-7) β 1 = f () = 1 * νx δ = 1. 73 (1-8) C f ν = 1.155 (1-9) l

(5) 98 3

(5) 99 3 4 f ( η) = A A1η Aη A3η A4η (1-3) = : = ( f () = ) 1 d p d = : v = = ( f () = ) ρ d x d x = δ : = ( f (1) = 1) = δ : = ( f (1) = ) = δ : = ( f (1) = ) (1-31) A =, A1 =, A =, A3 =, A4 = 1 (1-3) 3 4 f ( η ) = η η η (1-33) 1 1 1 7 367 37 α f (1 f )dη = d d = 1 f η f η 1 63 315 β 1 = f () = (1-34) 1 1 3 α = (1 f )dη = 1 d = f η 1 = x = * 3 315 δ 1. 751 1 37 (1-35) C f = 4 37 ν 315 l (1-36)

(5) 1 1-1

(5) 11 Re = D / ν = D ν Re C 3 5 16. 1 < Re < 1 C

(5) 1

(5) 13 = v = v v (13-1) w = w w, v, w, v, w = v = v (13- ) w = ρ v d A ρ v d A τ = ρv (13-3) σxx τx τxz ρ ρv ρw τx σ τz = ρv ρvv ρvw τzx τz σ zz ρw ρwv ρww (13-4) p = p p ρ ρ µ ρ v w p v w = Fx t x z x x z ρ v ρ µ ρ v v v w v p v v vw = F v t x z x z (13-5) ρ w ρ µ ρ w v w w w p w vw w = Fz w t x z z x z

(5) 14

(5) 15 ρνd /d ρ v = ρν T d /d (13-6) ν ν T T ν d v l (13-7) d d d ρ v = ρl d d (13-8) d ν T = l d l l = k (13-9) ρv = ρk d d d d (13-1)

(5) 16 τ ρ τ / ρ 14-1 * = * η η * = 14- ν ( ) * = fn 14-3 * ν max ( ) = fn 14-4 * a

(5) 17 l E (a) l E (b) (Dail-Harleman, Addison-Wesle)

(5) 18 d τ τ = µ 14-5 d ( ) * = 14-6 * ν τ l = k τ τ τ = τ = const. l = k τ d = ( k) d ρ * = τ / ρ d * = d k 14-7 ( ) 1 = ln C1 * k 14-8 ( ) 1 * = ln AS * k ν 14-9 AS k =.4 AS ( ) * = 5.75log1 * ν 14-1

(5) 19 log S ( ) (a)

(5) 11 * 4 < < ν 4 < * < 14-11 ν * < ν = a max 1 * a = ln AS * k ν 14-1 max ( ) 1 a = ln * k 14-13

(5) 111

(5) 11 ν ks ( ) = f n 14-14 * ks ( ) 1 = ln Ar 14-15 * k ks Ar ks Ar ( ) = 5.75log1 14-16 * k S ks

(5) 113 k S * ν * ks /ν k S δ S k S / δ S * ks /ν δ S / k S * ks /ν δ S / k S * ks /ν δ S / k S * ks /ν ( ) 1 * ks = ln A 14-17 * k ks ν A * ks /ν A = A ln( * k S / ν ) 14-18 1 / n ( ) = 14-19 max a 5 Re 1 n 5 Re > 1 n n = log1 Re 14-1 n

(5) 114 * * = 1 ln As x ν * = 1 ln Ar x ks = * * S s a δ S A (Schlichting, McGraw-Hill)

(5) 115 L ( p1 p )( π ) τ ( π L) = a a ( p1 p )( π ) ( τ π L) p1 p a d p τ = = 14-1 L d x τ D = a a d p D d p τ = = 14- d x 4 d x f = Q /( π ) D p1 p L = f D 1 ρ a 14-3 d p 1 1 f = / ρ d x D 14-4 (14-1) τ * f = 8 = 8 ρ 14-5 max ( ) 1 a = ln ( ) = π ( a ) d * k πa ( max ) π a a = ln ( a )d * k πa = k = 3.75πa ( 1 ξ ) a 1 ln dξ ξ ( ξ = / a) 14-6 = max 3. 75 * 14-7

(5) 116 p 1 p max 1 * a = ln A S * k ν max 1 * a = ln 1. 75 14-8 k ν * ( ) 1 (14-1) (14-15) = ln Ar * k ks a = A max *.5ln r ks 14-9 / * a =.5ln 4. 75 * k S 14-3 f 1 a =.log1 f. 8 14-31 f ν 1 ks =.log1 1. 14 f D 14-3 f k S / D f =.3164 Re / 4 Re = 14-33.37 f =.3.1Re Re = 14-34

{ log ( Re ). } f = 1/ f Re = 1 8 (5) 117 14-35 64/Re, (7-1) ( ) (14-1) f n (Re), (14-31) (14-16) f n (k s /D), (14-3) ( ) ( ) ( ) ( ) ( )

(5) 118 Re C 4 Re C 4

(5) 119

(5) 1 x p p = = x (15-1) τ t x v ρ (15- ) v v = x (15-3) τ ρv = ρl ε = l d d d d d d (15-4) x b τ ρε = (15-5) ( ε = kb 1 max min) (15-6) ε R ε b ( ) max min R ε = ε 1 = = const (15-7) k 1

- (5) 11 min v =ε x (15-8) ε = kb 1 max (15-9) x = s S b S x max x max ( x) = S f1( x/ s) m bx ( ) = bs f ( x/ s) = bs( x/ s) (15-1)

(5) 1

(5) 13 η φ( x, ) η = bx ( ) (15-11) Ψ( x, ) = f( x) ψ ( η ) P f ( x) = bss( x/ s) (15-1) dp / dx = J = ρ = ρ = ρb S = const ( x, )d b( x) S ( x / s) ( x, η)dη P m { ψ ( η) } dη (15-13) ε S s ( ψ ) ψψ ψ = b S S (15-14) = : / =, v = : η = : ψ =, ψ = 1 (15-15) : ψ b S b ε σ = = S S 4k1 = s s S (15-16) η ψ ( η) = tanhη (15-17)

(5) 14 z z z e e z e e z z z z z cosh sinh tanh cosh sinh = = =

S, v 3 J S = ρσs 3 J = ( 1 tanh η) ρσx 3 Jσ v = { η( 1 tanh η) tanhη} 4 ρx = 1 η σ x (5) 15 (15-18) σ σ = 1/ 767. (15-19) b 1 / b b 1 1 1 tanh / = b b = 115. b 1 / (15- ) ε = kb 115. σ = b1 4 =. 37b 1 max / max 1 / max (15-1)

(5) 16 (form drag), pressre drag (frictional drag)

(5) 17 (a) (b) (c) L R D

(5) 18 D D f D p D = D f D p ρ ρ ρ (16-1) = C f A C p A = CD A C f C p C D A da p wda da pda pdacos da wda wda sin D p = p cosθda (16- ) A D τ sinθda (16-3) f = A w C D

(5) 19 da w da w da sin pda 16-1 (Re =1 4 1 6 ) (Re =1 4 1 6 ) C D 6 9 1.161. 1.5 1.55 1.98.5..3 [ (1976) 4-4 p.8 3] 16- (Re =1 4 1 6 ) C D C D sting spport.47 separation 1.17.38 1.17.4 1.4 3 4.59 1.38 cbe.8 cbe 1.5 6.5 )

(5) 13 d Red/ν (16-4) Re Re Re Re áá Re áá Re Re Re

(5) 131

(5) 13 p D C D = (16-5) 1 ρ d D Re 1 Re 1 Re 1 5 C D 11. D 5 Re 1 6 5

(5) 133 1-1 - -3 3 6 9 1 15 18 Re < 4 1 5 4 1 5 < Re < 3 1 6 Re > 3 1 6

(5) 134 x x x x x t l l tt Y(T) l (t) Y ( T ) = T l ( t) dt 17-1) t tt (17- ) Y ( T ) = T l ( T ξ) dξ 17-3) T dy l ( T ) = dt 17-4) C l Y CY(C/) l Y(C/) F C = ( ly ) 17-5) = l Y 17-6) l Y T ( T ) Y ( T ) = ( T ) ( T ξ) dξ 17-7) l l l l (T) ( T ) Y ( T ) ( T ) ( T ξ) dξ 17-8) l = T l l

(5) 135 v l (t) Y (t) v l (o)

(5) 136 l (T)Y(T) l Y dy 1 dy ly = Y = dt dt 17-9) (ensemble mean) l ( T ) Y( T ) 1 dy T = l Y = = l ( T ) l ( T ξ) dξ dt 17-1) 1 d Y T = l Rl ( ξ ) dξ dt 17-11) R ξ ) = ( T ) ( T ξ) / 17-1) l ( l l l R l () Y T η Y = R ( ξ ) dξ dη 17-13) l l one particle analsis

(5) 137 C C C Y Y C C

(5) 138 R l, R l 1 T R 1 dy K = = l T, dt ( T ) 17-14) Y = l T, ( T ) 17-15) T T Rl ( ξ ) dξ = const = T* 17-16) 1 dy K = = l T* ( = const), ( T >> T* ) dt 17-17) Y = l T T, ( T >> T ) 17-18) * * T * ( ξ ) = exp ξ / T 17-19) ( ) R l * 1 dy T K = = l T* 1 exp dt T* 17- ) T T Y = T l * 1 exp T* T* R l () T TT * T x Tx/ TT * xt * x l T * T *

(5) 139 5.. D=T 1. D.5..1.1..5 1.. 5. 1 T a b c

(5) 14 ( ) Re 9/4 = = = z w w v x w w z p F z w w w v x w t w z w v v x v v p F z v w v v x v t v z w v x x p F z w v x t z x ρ µ ρ ρ ρ µ ρ ρ ρ µ ρ ρ 18-1) τ ρv = d /d ρν v T /d d ρν ρ = (18- ) T ν T ν K ε ν µ K C T = (18-3) µ C T ν K K- µ C

(5) 141 LES(large edd simlation) LES DNS(direct nmerical simlation) DNS

(5) 14 present work;, R 8, R 65, R 39, R 5 slope -5/3 others;, R (Grant, et al., 196), R 1(, 1995), R 318(Karakin et al., 1991) NASA, R 15 (Saddoghi & Veeravalli, 1994), R 85 (Coantic & Favre, 1974), R 41 (Sanborn & Marshall, 1965), R 38 (beroi & Fremth, 1969), R 13 (Champagne, 197), R 54 (Kistler & Vrebalovich, 1966), R 7, R 37 (Comte-Bellot & Corrsin, 1971) Saddoghi & Veeravalli(1994) (Flohr, 1999)