Inżynieria procesowa – najważniejsze wzory 



 L. Zander 

                           

Materiały ziarniste 

Rozdział układów niejednorodnych 

w

s

w

w

V

V

V

V

V

+

=

=

ε

 

τ

d

F

dV

u

⋅

=

 

L

P

K

d

F

dV

⋅

=

⋅

η

∆

τ

 

(

)

C

V

2

K

d

dV

+

=

τ

 

0

0

1

1

x

G

x

G

e

⋅

⋅

=

η

 

Przepływ płynów 

τ

⋅

=

⋅

⋅

+

k

V

C

V

2

2

 

G = U · 

ρ 

S

w

G

⋅

=

 

S

u

U

⋅

=

 

2

2

18

1

d

r

u

u

F

s

o

η

ρ

⋅

⋅

=

 

g

a

Fr

=

 

r

a

2

ω

=

 

const

g

u

g

p

z

=

+

⋅

+

2

2

1

1

1

ρ

 

2

18

1

d

g

u

s

η

ρ

ρ −

=

 

N

⋅

=

π

ω 2

 

2

2

1

1

0

0

x

G

x

G

x

G

⋅

+

⋅

=

⋅

 

h

g

P

⋅

⋅

=

ρ

 

Procesy cieplne 

υ

η

η

ρ

d

u

d

w

d

u

Re

⋅

=

⋅

=

⋅

⋅

=

 

n

n

B

B

A

A

c

x

...

c

x

c

x

c

⋅

+

+

⋅

+

⋅

=

 

r

t

c

i

±

⋅

=

 

t

c

m

q

∆

⋅

⋅

=

 

)

C

·

kg

/(

kJ

,

c

SS

°

≈ 76

1

)

C

·

kg

/(

kJ

,

c

w

°

= 19

4

 

A

A

A

i

G

Q

∆

=

 

κ

S

d

e

⋅

=

4

 



























−

=

2

1

R

r

u

u

max

 

A

A

A

A

t

c

G

Q

∆

=

 

B

B

B

B

t

c

G

Q

∆

=

 

 

L

Pd

U

η

∆

π

128

4

=

 

2

32

d

Lu

P

η

∆

=

 

F

Q

q

F

=

 

L

Q

q

L

=

 

t

R

1

Q

∆

⋅

=

 

F

s

R

⋅

=

λ

 

ρ

λ

∆

2

2

u

d

L

P

=

 

t

F

s

Q

∆

λ

⋅

⋅

=

 

(

)

∑

=

+

−

⋅

=

n

i

i

i

n

s

t

t

F

Q

1

1

1

λ

 

1

2

1

2

d

d

ln

d

d

d

m

−

=

 

L

d

F

m

m

⋅

⋅

=

π

 

Re

64

=

λ

 

25

0

3164

0

,

Re

,

=

λ

 

mn

n

n

m

m

n

F

s

F

s

F

s

t

t

Q

λ

λ

λ

+

⋅⋅

⋅

+

+

−

=

+

2

2

2

1

1

1

1

1

 

t

F

Q

∆

α

⋅

⋅

=

 

ρ

ξ

∆

2

2

u

P

⋅

=

 

ρ

2

2

u

P

d

=

 

λ

α

d

Nu

⋅

=

 

λ

α

h

Nu

⋅

=

 

λ

η

ν

p

c

a

Pr

⋅

=

=

 

ρ

λ

p

c

a

=

 

Procesy hydromechaniczne 

B

A

Pr

Re

C

Nu

⋅

⋅

=

 

i

i

Pr

Gr

C

Nu

⋅

⋅

=

 

Mieszanie 

2

2

3

η

ρ

∆

β

⋅

⋅

⋅

⋅

=

g

t

h

Gr

4

0

8

0

023

0

,

,

Pr

Re

,

Nu

⋅

⋅

=

 

t

F

k

Q

∆

⋅

⋅

=

n

X

I

i

∑

=

 

p

x

X

i

i

=

 

2

1

1

1

1

α

λ

α

+

+

=

∑

s

k

∑

⋅

+

⋅

+

⋅

−

=

B

B

m

A

A

B

A

F

F

s

F

t

t

Q

α

λ

α

1

1

 

η

ρ

⋅

⋅

=

2

d

N

Re

m

 

g

d

N

Fr

m

⋅

=

2

 

(

)

B

A

m

t

t

F

k

Q

−

⋅

⋅

=

 

m

t

F

k

Q

∆

⋅

⋅

=

 

2

1

2

1

t

t

ln

t

t

t

m

∆

∆

∆

∆

∆

−

=

 

W

R

L

+

=

 

ρ

5

3

d

N

P

Ne

m

=

 

1

0

b

R

b

L

⋅

=

⋅

 













−

=

1

0

b

b

1

L

W

 

n

1

W

G

1

=

 

Fluidyzacja 

(

)















−

−

=

0

3

0

2

2

0

1

200

ε

ε

ηϕ

ρ

ρ

g

d

u

F

s

z

 

(

)

(

)

n

W

G

str

1

W

W

0

1

L

t

c

"

i

Q

t

c

"

i

W

t

t

Lc

G

−

+

−

+

−

=

 

(

)

n

W

G

1

W

W

t

c

"

i

t

c

"

i

W

G

−

−

=

 

Parametry powietrza wilgotnego i suszenie 

A

B

i

Y

i

i

⋅

+

=

 

Ar

,

Ar

Re

max

61

0

18

+

=

 

B

A

m

m

Y

=

 

Y

622

,

0

Y

P

p

A

+

⋅

=

 

AS

A

p

p

=

ϕ

 

(

)

t

c

r

Y

t

c

i

A

o

B

⋅

+

+

⋅

=

(

)

F

F

F

s

z

d

g

Ar

η

ρ

ρ

ρ −

⋅

=

3

 

AS

AS

S

p

P

p

622

,

0

Y

−

=

273

273

t

18

Y

29

1

4

,

22

v

+













+

=

 

1

2

A

B

Y

Y

1

w

w

−

=

ε

ε

−

−

=

1

1

0

0

h

h

 

(

)

0

1

A

B

A

i

i

w

w

w

Q

q

−

=

=

2

2

1

1

A

x

1

x

x

G

w

−

−

=

 

x

1

x

X

−

=