Drag coefficient Newton

Fig. 14. Drag coefficient for terminal settling velocity correlation (single particle) where A represents Stokes law B, intermediate law and C, Newton s...

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

The aerodynamic force varies approximately as the square of the flow velocity. This fact was established in the seventeenth centui y—experimentally by Edme Marione in France and Christiaan ITuygens in Holland, and theoretically by Issac Newton. Taking advantage of this fact, dimensionless lift and drag coefficients, and Cj, respectively, are defined as... 

Dust venting nomographs, 514-520 Calculations, 513-517 Dust, mist calculations, 226-236 Brownian movement, 226. 236 Drag coefficients, chart, 235 Intermediate law, 226 Newton s law, 226, 228... 

A glass sphere, of diameter 6 mm and density 2600 kg/m3, falls through a layer of oil of density 900 kg/m3 into water. If the oil layer is sufficiently deep for the particle to have reached its free falling velocity in the oil, how far will it have penetrated into the water before its velocity is only 1 per cent above its free falling velocity in water It may be assumed that the force on the particle is given by Newton s law and that the particle drag coefficient R /pu2 = 0.22. 

As the Reynolds number increases further, vortex shedding takes place (Figure 1.13) in what is known as the Newton region, in the range 500 < Re <2 X where the drag coefficient has a value of approximately 0.44. Consequently equation 1.28 gives the drag force as... 

Archimedes number Bingham number Bingham Reynolds number Blake number Bond number Capillary number Cauchy number Cavitation number Dean number Deborah number Drag coefficient Elasticity number Euler number Fanning friction factor Froude number Densometric Froude number Hedstrom number Hodgson number Mach number Newton number Ohnesorge number Peclet number Pipeline parameter... 

Subsequent workers found that this equation had to be modified by introducing a coefficient, which we call the drag coefficient Cj. This coefficient is not a constant equal to ij, as Newton believed, but varies with varying conditions, as we will see. Introducing it and dividing both sides of Eq. 6.52 by the cross-sectional area of the sphere, we find... 

The situation where the particle Reynolds rmmber is greater than 0.2 requires a solution to a force balance equation where the drag force is ejqrressed by Newton s law (above) and is con licated by the interrelation between the drag coefficient and the settling velocity through the Reynolds number. 

For other shapes of particles, drag coefficients will differ from those given in Fig. 14.3-1 and data are given in Fig. 3.1-2 and elsewhere(B2, L2, PI). In the turbulent Newton s law region above a Reynolds number of about 1000 to 2.0 x 10, the drag coefficient is approximately constant at Cj, = 0.44. 

The macroapproach uses Newton s second law initially for a single particle system and then expands to a multiparticle system. Some of the concepts of a single-phase friction factor will be employed in the multiparticle system analysis. In addition to the acceleration and drag forces, the gravity and electrostatic forces should be considered in gas solid analysis. The variation of the drag coefficient with the kind of particle and condition of flow is important in the analysis. The terminal veloeity of the partiele is often used as another way to charaeterize partieles, and the larger the value of the terminal velocity, the greater the size and/or density of the particle. 

Equation 3-13 is often called Newton s law. In the regime of Newton s law. the drag coefficient of a sphere is approximately 0.44, as shown in Figure 3-2, Newton s law applies to turbulent flow regimes. 

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