Bezwymiarowy współczynnik strat λ

Korzystając z prawa Maigena-Paisenlliego Q=π∆pR4/(8µl)

Q=vśr*F

vśr=Q/F

F=π* R2

π ⋅ p

∆ ⋅ R 4

8 ⋅ µ ⋅ l

p

∆ ⋅ R 2

v =

=

śr

π ⋅ R 2

8 ⋅ µ ⋅ l

v

v = max śr

2

p

∆

2

p

∆

v max =

⋅ R ⋅2 =

⋅ R 2

8 ⋅ µ ⋅ l

4 ⋅ µ ⋅ l

v ⋅ µ ⋅ = ∆ ⋅ 2

ś

l

p R

r

v ⋅8⋅ µ ⋅

⋅32µ ⋅

ś

l

vś

l

p

r

r

∆ =

=

d 2

d 2

( )

2

v ⋅8⋅ µ ⋅

⋅8⋅ µ ⋅

⋅32µ ⋅

ś

l

vś

l

vś

l

r

r

r

Re =

=

=

R 2

d 2

d 2

( )

2

v ⋅

ś

d

r

Re =

λ

µ = ni ⋅ g v ⋅ 32ν ⋅ ⋅

2 ⋅64ν ⋅ ⋅

2 ⋅64⋅ ⋅

ś

g l

vś

g l

vś

g l

p

r

r

r

∆ =

=

=

d 2

v ⋅ 2 ⋅

2 R ⋅

e

ś

d d

d

r

Porównując ten wzór ze wzorem na straty Darcy’ego 2

l

ρ ⋅

∆ p = λ ⋅

vśr

d

2

2

v

g

l

l

v

śr

⋅ ⋅64

2

ρ ⋅ ś

64

r

⇒

= λ −

λ =

2 Re⋅ d

d

2

Re