Actual diameter, definition

Actual diameter, definition, 348 Aggregates, binary decane-surfactant mixture, 257-58 Aggregation number,... 

Sometimes a diameter is defined in terms of particle settling velocity. All particles having similar settling velocities are considered to be the same size, regardless of their actual size, composition, or shape. Two such definitions which are most common are... 

These tests also point out to alternatives for improving the capacity cost indicator cases B and B4 have the same column diameter (0.2 m), practically the same energy requirement and still the capacity is higher in case B4. This suggests that the largest liquid and vapor flows in the column could be used in the cost indicator definition, rather than the actual individual stage flow values. 

Chung and Wen (1968) and Wen and Fan (1975) have proposed a dimensionless equation using the dependency of the dispersion coefficient on the (particle) Reynolds number Re (Eq. 6.169) for fixed and expanded beds. It is an empirical correlation based on published experimental data and correlations from other authors that covers a wide range of Re. Owing to two different definitions of the Reynolds number, the actual appearance varies in the literature. Since the particle diameter dp, is the characteristic value of the packing, Eq. 6.168 based on the (particle) Peclet number Pe (Eq. 6.170) is used here ... 

The surface excess can be defined in various ways. Actually, there is no true dividing plane, but rather an AW interface that is not sharp, since molecules have a finite size and moreover exhibit Brownian motion. Flence the interface extends over a layer of some molecular diameters. In the derivation of Eq. (10.2), the position of the dividing plane has been chosen so that the surface excess of the solvent is zero. In Figure 10.5 the concentration of the solute is depicted as a function of the distance from the dividing plane (z). In Figure 10.5a, there is no adsorption the two hatched areas on either side of the dividing plane are equal. (Because of the definition... 

The second virial coefficient f3i is actually the excluded volume of the at molecule to another rod with orientation a3. According to the definition, the exclusion volume is the volume occupied by one molecule in which the mass centers of other molecules are not allowed to touch. For cylindrical rods with length L and diameter I). the exclusion volume is schematically shown in Figure 2.2. In this figure the two particular cases are depicted, i.e., two cylinders are parallel or perpendicular to each other, fti is dependent on the shape of the rigid rods. The expression for cylinders can be approximately expressed by... 

For purposes of comparison it is convenient to calculate the static hold-up, ox)erating hold-up and total hold-up per theoretical or practical plate. The total hold-up varies with the load, but the literature gives little definite information on this relationship. For an Oldershaw sieve-plate column with a diameter of 28 mm, containing 30 actual plates, Collins and Lantz [200] published the values shown in B. 92. The total hold-up lies between 43 and 60 ml, depending on the load, so that it can be taken to be 1.4—2.00 ml for each actual plate and 2.5—3.5 ml for each theoretical plate. According to measurements of the author s, the total hold-up of packed columns is about the same, as wHl also be. seen from Fig. 96, which indicates... 

Although in the foregoing discussion the molecule was pictured as an elastic sphere, the result retains a good deal of its value even if this simple representation is entirely abandoned and the molecule is regarded, for example, as a mere centre of force which repels similar centres when they approach too closely. What the above calculations have really yielded is information about the average distance between the molecular centres at which transfers of momentum occur. For many purposes this constitutes quite a reasonable definition of the diameter. Ambiguity is, however, avoided if collision diameter. In actual fact it corresponds fairly closely to the molecular magnitudes determined by the methods of X-ray and electron diffraction. 

Actually, the wall shear stresses found in a cylindrical tube are not really material parameters at all, because their dependence on geometry limits their applicability to cylindrical-tube flow. For cylindrical tubes of similar geometry and a constant length/diameter ratio, the wall shear stresses determined according to equation 2 are identical. Other shapes, however, such as cones (die) or auger chaimels demand a different, more suitable approach, with equation 2 modified to accommodate the corresponding geometric boundary conditions. Nonetheless, the waU shear stress remains superior to the coefficient of friction as a useful material parameter, because it yields a correct, practical, near-system definition of a compound s material properties, as explained above. 

Microscopic analysis of received suspensions showed that particles of BaS04 posses pronounced anisometry (they represent sticks with length-to-diameter ratio about 4, that explains the sigmoid shape of sedimentation curves with extreme) (Fig. 5.19). At the initial moment of sedimentation the rotation of stick-shaped particles is possible, that determines additional resistance to sedimentation proceeding (analogously to viscosity increase) and slowing down of rate of deposition accumulation. Moreover, at free precipitation particles of spherical form are oriented in movement direction in that way to create maximum resistance to movement. This also reduces the precipitation rate of solid particles in liquid and embarrasses the definition of their actual sizes. In this connection, equivalent radius re (radius of spherical particle precipitating with the same rate) was determined by results of sedimentation analysis. 

The discrete formulation is based on the modelling of the nodes (both demand and supply) in the network as horizontal lines in a two dimensional discrete space. The position of each line is represented by (x,y). The y value specifies the head at the node. The length of a horizontal line in this discrete space represents the amount of water through the node, irrespective of the actual location along the x-axis. Transportation of water from one node to another occurs when the lines corresponding to the two nodes overlap (in terms of the x co-ordinates) provided a connection between the two nodes is allowed. The definition of the network is actually a superstructure of allowable pipe connections, pipe diameters and distances between nodes. 

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