Drag force on a particle

Dimensional analysis (see drag force on a sphere example) yields CD =/ (Re). If we ensure that the value of Re is the same from prototype to model, then we will have dynamic similarity, and therefore Cd must have the same value from model to prototype. 

1 Problem. Calculate the drag force exerted on a spherical particle, diameter 25 mm, as it moves through water at 2 m s-1. 

2 Solution. It is often convenient to tabulate the calculations, showing clearly the values of the variables for prototype and model in separate columns. The solution to this problem is given in Table 2. 

If we have dynamic similarity, i.e. Re = constant, then CD must be constant between model (M) and prototype (P) 

13 Achievements. Calculation of drag force on prototype based upon graphical experimental model data. 

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It is seen therefore that, in the absence of any entirely satisfactory theoretical approach or reliable experimental data, it is necessary to adopt a highly pragmatic approach to the estimation of the drag force on a particle in a non-Newtonian fluid. 

In a concentrated suspension, the drag force on a particle will be a function of its velocity up relative to the liquid and will be influenced by the concentration of particles that is, it will be a function of the voidage e of the suspension. 

I drag force on a particle due to passing air g acceleration due to gravity... 

Table 2 Solution, drag force on a particle problem...

Ed and Foo are the values of drag force on a particle in a fluidized bed and on a particle in an infinite medium, respectively. is the dimensionless distance (x/dp) between the particles. The following equations were derived for the elastic wave velocity ... 

The aerodynamic diameter dj, is the diameter of spheres of unit density po, which reach the same velocity as nonspherical particles of density p in the air stream Cd Re) is calculated for calibration particles of diameter dp, and Cd(i e, cp) is calculated for particles with diameter dv and sphericity 9. Sphericity is defined as the ratio of the surface area of a sphere with equivalent volume to the actual surface area of the particle determined, for example, by means of specific surface area measurements (24). The aerodynamic shape factor X is defined as the ratio of the drag force on a particle to the drag force on the particle volume-equivalent sphere at the same velocity. For the Stokesian flow regime and spherical particles (9 = 1, X drag... 

Up to this point, we have considered the drag force on a particle moving at a steady velocity u00 through a quiescent fluid. Recall that this case is equivalent to the flow of a... 

Up to this point, we have considered the drag force on a particle moving at a steady velocity through a quiescent fluid. Recall that this case is equivalent to the flow of a fluid at velocity oo past the stationary particle. The motion of the particle, however, arises in the first place because of the action of some external force on the particle such as gravity. The drag force arises as soon as there is a difference between the velocity of the particle and that of the fluid. The basis of the description of the behavior of a particle in a fluid is an equation of motion. To derive the equation of motion for a particle of mass nip, let us begin with a force balance on the particle, which we write in vector form as... 

Numerous experimental and theoretical investigations have been made of the isothermal drag force on a particle in the noncontinuum regime. Much of the work is summarized in several references [2.5-7]. As will be evident in this discussion, there exists even now no satisfactory comprehensive description of this phenomenon. 

Determine the drag force on a particle 0.1 iim in diameter settling in air at standard conditions. The particle is sand. 

Due to the lack of information about the drag force on a particle in a cloud moving with a carrier gas, the proposal of Wen Yu [11] will be adopted in the present work. They give the drag force for a single particle as. 

Derive, by dimensional analysis, the standard equation for the drag force on a particle in relative motion to a fluid ... 

For larger particles and/or higher velocities, leading to a value of the particle Reynolds number Re = 2YpUpztP,/p) > 0.1, the drag force on a particle (relation (3.1.64)) is described using a drag coefficient Cp ... 

The drag force on a particle placed at r = Tmin = fo + follows from equations (6.208) and... 

In Chapter 3, expressions for the drag force on a particle in a bed of particles were obtained from the relations for unrecoverable pressure loss AP. These apply quite generally, regardless of how the particles are supported. They will now be applied to particles in a fluidized bed. 

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