Industrial Air Quality and Ventilation

89Air Injection in Chutes

© 2010 Taylor & Francis Group, LLC

For the forward ow, Equation 3.40 will appear as:

d

P

dx

D

v

k

vvvv

dx

m

=− +

−−

λρψβ ρ

2

2

21

1212

2

22

*

()

; (3.53)

for the reverse ow:

d

P

v

D

k

vv

dx

m

=− +

+













λρψβ ρ

2

2

21

12

2

2

22

*

()

. (3.54)

By integrating Equations 3.53 and 3.54 along the tube length, we obtain, respectively:

PP

x

D

v

k

vvvv

dx

m

x

−=−+

−−

∫

0

2

2

21

1212

2

0

22

λρψβ ρ

*

()

, (3.55)

PP

x

D

v

k

vv

dx

m

x

−=−+

+

∫

0

2

2

21

12

2

2

0

22

λρψβ ρ

*

()

. (3.56)

For the rst part, the integral represents the air pressure drop at a tube section of

x length that results from the fall of material. We refer to this pressure drop value

as the induction pressure [49, 70]. If there is no directional ai ...