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CFD

CD

CD =CD(Re)

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n

Qi i= 1, 2, . . . , n

F(Q1, Q2, . . . , Qn) = 0,

F

Qi

m

F(1, 2, . . . , m) = 0.

p = n m Qi

Q Qj Qk Ql

i=Qxj Q

yjQ

zl Qi i= n 3.

x , y, z

[i] = [Qxj ] [Q

yj ] [Q

zl ] [Qi].

n

n

p

p

n

p

p

Qi

Qi = Qj = Qk =U Ql =D

=xUyDz

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= UD

=Re1

=xUyDz 1

= UD

= Re

x,y,z

SI

MLT

m kg M

L m L

t s T

A m2 L2

V m3 L3

U m/s LT1

a m/s2 LT2

F N MLT1

M Nm ML2T2

E

W J ML2T2

P W ML2T3

kg/m3 ML3

m kg/s MT1

V m3/s LT1

p

Pa ML1T2

Sij s1 T1

rad

rad/s T1

Pa s ML1T1

m2/s L2T1

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p= f(U,,,L,D).

D [mm] L [m] V [m3/h] p [Pa] [kg/m3] [Pa s]

2.92 104

2.92 104

2.92 104

1 103

1 103

1 103

1.56 103

1.56 103

1.56 103

p

L

n = 6

F(p, U, , , L, D) = 0

p

=M L1T2

U

=LT1

=M L3

=M L1T1

L

=L

D

=L

{MLT}

m = n p = 6 3 = 3

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pU

,,D

p=xyDz p, U=

abDc U, L = deDf L

p

M0L0T0 = (ML3)x (ML1T1)y Lz ML1T2

x + y+ 1 = 03x y+ z 1 = 0y 2 = 0

x= 1y= 2z= 2

,

p =D2 p

2

U

M0L0T0 = (ML3)a (ML1T1)b Lc LT1

a+ b= 03a b+ c 1 = 0b 1 = 0

a= 1b= 1c= 1

,

U= UD

=

UD

=Re

L

M0L0T0 = (ML3)e (ML1T1)f Lg L

e + f= 03e f+ g+ 1 = 0b= 0

e= 0f= 0

g= 1,

L= L

D

F1(p, U, L) = 0 F1D2 p

2

, Re, L

D = 0

D2 p

2 =F

Re,

L

D

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D L V p 104 U 104Re 109p L/D

[mm] [m] [m3/h] [Pa] [kg/m3] [Pa s] m/s

2.92

2.471 3.732

2.92

4.942 17.78

2.92

8.236 56.46

10

1.765 0.8303

10 3.53 4.192

10

15.6

15.6

log p log Re

L/D

L/D

log p log Re

1e+06

1e+07

1e+08

1e+09

1e+10

1e+11

10000 100000

logRe

log

p

log

(p

/L

)

p Re p/L Re

L

D= 200

0.155Re1.75

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D3 p

2L =f(Re)

p L

log

pL

= 1.75log Re 0.8097,

pL

= 0.155 Re1.75 D3 p

2L = 0.155 Re1.75

D3 p

2L = 0.155

UD

1.75

p U1.75

U

D

FDU2D2

=f

UD

w

U

D

wU2

=f

UD

,

L

D

P

V

D

P

3D5 =f

V

D3,D2

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D

U

H/L

H L N

D

U =f

N,

H

L

Re 1

U

L

Cc c

FD/(0.5U2A)

d

FD = 3Ud Cc

FD = const U L; Cc= FDU L

= const;

Cc= 3

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m

Um = U

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50km/h

350N

35 m

11 m/s

1 m

p0m= 0.2kPa