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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Particle density, ρp		g/cc
Fluid density, ρ		g/cc
Fluid viscosity, μ		g/cm.s
Particle effective diameter, dp		μm (microns)

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OUTPUT   VARIABLES   &   GRAPHS

Variables	Values	Units
♦  K-factor
♦  Flow-regime
♦  Settling velocity, vt		cm/s

Velocity Of Particle In Motion In A Fluid

Processes for the collection and recovery of particles in a fluid stream are based on the movement of particle in the fluid stream. An important characteristic of particle movement is the settling or terminal velocity. This is the constant velocity reached when all forces (gravity, bouyancy, drag, etc) acting on the particle balance. To computer the settling velocity, one must first determine the applicable flow-regime via the K-factor:

     K = d_p[gρ_pρ_g/μ²]^1/3

For K < 3.3, flow-regime is laminar and Stoke's law applies:

     v_t= gd_p²ρ_p/18μ

For 3.3 <= K < 43.6, flow-regime is transitional and the Intermediate law applies:

     v_t= 1.53g^0.71d_p^1.14ρ_p^0.71/ μ^0.43ρ_g^0.43

For K > 43.6, flow-regime is turbulent and Newton's law applies:

     v_t= 1.74√[gd_pρ_p/ρ_g]

where
     v_t= settling velocity
     d_p= effective diameter of particle
     ρ_p= density of particle
     ρ_g= density of fluid
     μ_p= fluid viscosity
     g = acceleration due to gravity = 981 cm/sec₂

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Theodore L; Nanotechnology,: Basic Calculations For Engineers And Scientists; John Wiley & Sons, New Jersey, 2006