"Reactor particle-size and velocity calculation, with no trial-and-error" by Miguel Larocca, May 10, 2005

Input Data: Because three different flow regimes are involved in the calculations of particle

size and settling velocity, a trial-and-error calculation is normally required for

Fluid Density rf = 0.06 lb/ft3

evaluate the particle diameter at a given velocity, or evaluate the particle

Fluid Viscosity m = 0.0149 cp velocity at a given diameter. In this spreadsheet the trial-and-eror procedure

Particle Density rp = 82.00 lb/ft3

is eliminated by using equations derived from correlations readily available

in the literature.

Input only one and calculate the other :

References:

Particle Diameter dp = 79.7 micron (1) Theodore L., Buonicore A.J., "Air Pollution Control Equipment" CRC Press

Particle Velocity vp = 1.0 ft/s Boca Raton, Florida, 1976.

(2) Larocca M., Chemical Engineering, March 2, 1987.

Determining Particle Velocity : Determining Particle Diameter :

Law Constant K = 3.04 Law Constant

The System is under Regime The System is under

Particle Velocity is vp = 1.00 ft/s Particle Diameter is

Stoke's Law

"Reactor particle-size and velocity calculation, with no trial-and-error" by Miguel Larocca, May 10, 2005

Because three different flow regimes are involved in the calculations of particle

size and settling velocity, a trial-and-error calculation is normally required for

evaluate the particle diameter at a given velocity, or evaluate the particle

velocity at a given diameter. In this spreadsheet the trial-and-eror procedure

is eliminated by using equations derived from correlations readily available

(1) Theodore L., Buonicore A.J., "Air Pollution Control Equipment" CRC Press

Boca Raton, Florida, 1976.

(2) Larocca M., Chemical Engineering, March 2, 1987.

Determining Particle Diameter :

W = 0.37

Regime

dp = 79.7 micron

Stoke's Law

Determining Particle Velocity Determining Particle Diameter

Adimensional Constants K = dp ( gρpρf / μ2 )

1/3W = ρ ( v

3 / gρpμ )

0.5

Stoke's Regime v = gdp2ρp / 18μ dp = ( 18vμ / gρp )

0.5

K < 3.3 W < 0.471

Intermediate Regime v = 0.153g0.71

dp1.14

ρp0.71

/ μ0.43

ρ0.29

dp = { vμ0.43

ρ0.29

/ 0.153(gρp)0.71

}1/1.14

43.6 > K > 3.3 38.9 > W > 0.471

Newton's Regime v = 1.74 ( gdpρp / ρ )0.5

dp = v2ρ / gρp1.74

2

K > 43.6 W > 38.9

Determining Particle Diameter

W = ρ ( v3 / gρpμ )

0.5

dp = ( 18vμ / gρp )0.5

W < 0.471

dp = { vμ0.43

ρ0.29

/ 0.153(gρp)0.71

}1/1.14

38.9 > W > 0.471

dp = v2ρ / gρp1.74

2