Drag forces

In a particle-fluid flow, the particle velocity Vp generally differs from the fluid velocity V. The slip velocity, V — Vp, leads to unbalanced pressure distribution as well as viscous stresses on the particle surface, which yield a resulting force known as the drag force. The drag force of a single particle in a uniform flow field can be generally 

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The linear dependence of C witii temperahire agrees well with experiment, but the pre-factor can differ by a factor of two or more from the free electron value. The origin of the difference is thought to arise from several factors the electrons are not tndy free, they interact with each other and with the crystal lattice, and the dynamical behaviour the electrons interacting witii the lattice results in an effective mass which differs from the free electron mass. For example, as the electron moves tlirough tiie lattice, the lattice can distort and exert a dragging force. 

Some empirical equations to predict cyclone pressure drop have been proposed (165,166). One (166) rehably predicts pressure drop under clean air flow for a cyclone having the API model dimensions. Somewhat surprisingly, pressure drop decreases with increasing dust loading. One reasonable explanation for this phenomenon is that dust particles approaching the cyclone wall break up the boundary layer film (much like spoiler knobs on an airplane wing) and reduce drag forces. 

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

If the particle is at a given radius from the center of rotation, the plasma now has to apply an inward drag force, E, on the cell to maintain the position of the particle ... 

When this inward drag force, is exceeded by the plasma, the particle moves inward with the plasma. The inward velocity the plasma needs to exceed in order to drag the particle inward is called the critical velocity, U, of the particle ... 

Viscous Drag. The velocity, v, with which a particle can move through a Hquid in response to an external force is limited by the viscosity, Tj, of the Hquid. At low velocity or creeping flow (77 < 1), the viscous drag force is /drag — SirTf- Dv. The Reynolds number (R ) is deterrnined from... 

A single particle settling in a gravity field is subjected primarily to drag force, gravity force, Ta-g-, and buoyancy, which have to be in... 

Pneumatic classification can be partitioned conveniently into coarse, ie, fine products above 95% < 100 pm intermediate, ie, fine products ranging between 95% < 100 and 30 pm and fine, ie, fine products below 95% < 30 pm. Pneumatic classification, like hydraulic classification, balances the force of gravity with drag forces (counter flow) in order to bring about a separation. 

Based on such analyses, the Reynolds and Weber numbers are considered the most important dimensionless groups describing the spray characteristics. The Reynolds number. Re, represents the ratio of inertial forces to viscous drag forces. 

These equations assume that there is no drag force at the gas/liquid interface, such as would be produced by gas flow. For a flat surface inclined at an angle 0 with the horizontal, the preceding equations may be modified by replacing g by g sin 0. For films falhng inside vertical tubes with film thickness up to and including the full pipe radius, see Jackson AlChE1, 231-240 [1955]). 

Whenever relative motion exists between a particle and a surrounding fluid, the fluid will exert a drag upon the particle. In steady flow, the drag force on the particle is... 

The drag force is exerted in a direction parallel to the fluid velocity. Equation (6-227) defines the drag coefficient. For some sohd bodies, such as aerofoils, a hft force component perpendicular to the liquid velocity is also exerted. For free-falling particles, hft forces are generally not important. However, even spherical particles experience lift forces in shear flows near solid surfaces. 

A particle falling under the action of gravity will accelerate until the drag force balances gravitational force, after which it falls at a constant terminal or free-settling velocity given by... 

Fluidized This is an expanded condition in which the sohds particles are supported by drag forces caused by the gas phase passing through the interstices among the particles at some critical velocity. It is an unstable condition in that the superficial gas velocity upward is less than the terminal setting velocity of the solids particles the gas... 

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