Particulate Emission Control - Mathematics and Statistics for the Environment - page 495

For d p = 400 µm:

033 .

400
25 000

32 2 . × 144 14 . × 0 0569 .

K = × = 14 4 .

( )

2

, × 12

− 5

141 . × 10

Now select appropriate law. The numerical value of K determines the appropriate law:

• K < 3.3, Stokes' law range
• 3.3 < K < 43.6, intermediate law range
• 43.6 < K < 2360, Newton's law range

• For d p = 0.4 µm, the flow regime is laminar.
• For d p = 40 µm, the flow regime is also laminar.
• For d p = 400 µm, the flow regime is the transition regime.

For d p = 0.4 µm:

= () =

2

[ ]

2

gp pp

32 2 . × 144 14 . × ( 0.4/25,400 ) × 12

− 5

v =× 31510 . ft/s

( )

− 5

18 µ

18 × 14110 . ×

For d p = 40 µm:

= () =

2

[ ]

2

gp pp

32 2 . × 144 14 . × ( 40/25,400 ) × 12

− 5

v =× 31510 . ft/s

( )

18 µ

− 5

18 × 14110 . ×

For d p = 400 µm (use transition regime equation):

()()
()

114 . 0 71 .

071 .

[ ]

114 .

0 153 . gd p

071 . 071 .

0 153 32 2 . ( .) × ( 400/25,400 ) × 12 × ( 14 4414 . )

p p

v = = = 890 . ft/s

( )

029 . 043 .

043 .

() µ p

− 5 029 .

14110 . × × ( . 0 0569 ) a

For d p = 40 µm:

Distance = Time × Velocity = 30 × 0.315 = 9.45 ft

For d p = 400 µm:

Distance = Time × Velocity = 30 × 8.90 = 267 ft

For d p = 0.4 µm without Cunningham correction factor:

Distance = Time × Velocity = 30 × (3.15 × 10 -5 ) = 94.5 × 10 -5 = 94.5 × 10 -5 ft

For d p = 0.4 µm with Cunningham correction factor, the velocity term must be corrected. For our
purposes, assume particle diameter = 0.5 micron and temperature = 212°F to find the C f value. Thus,
C f is approximately equal to 1.446, and

Corrected velocity = vC f = 3.15 × 10 -5 (1.446) = 4.55 × 10 -5 ft/s

Distance = 30(4.55 × 10 -5 ) = 1.365 × 10 -3 ft