Relation between diameter

In practice it is stiU necessary to read the diameter of the Brinell impressions with a caUbrated microscope however, the computations to derive the Brinell hardness number are uimecessary for standard loads and indentors. Table 1 of ASTM ElO (2) contains the tabulated relation between indentation diameter and hardness number. 

In Figure 13 the relation between the intrinsic coercivity and the particle diameter dis given. The figure is based on a described model (35). The maximum is found around the critical particle diameter. In general the particle diameter and size is not very well defined. For the multidomain particles (d > ) the is smaller than the intrinsic anisotropy field of the particle. Nucleation effects cause a decrease in as the increases. This behavior is... 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

Based on the practical history of scale-up, most fermentation processes for alcohol and organic acid production have followed the concepts of geometric similarity and constant power per unit volume. From the above concept, and as a strong basis for translation of process criteria, only physical properties of the process were considered in the scale-up calculation. For power consumption in an agitated vessel, there is a fixed relation between impeller speed, N, and impeller diameter, l)t. The constant power per unit volume, for a mechanical agitated vessel is given by ... 

The relation between c and / and X (defined by equation 5.1) is shown in Figure 5.4, where it is seen that separate curves are given according to the nature of the flow of the two phases. This relation was developed from studies on the flow in small tubes of up to 25 mm diameter with water, oils, and hydrocarbons using air at a pressure of up to 400 kN/m . For mass flowrates per unit area of U and G for the liquid and gas, respectively, Reynolds numbers Rei L d/fii ) and Rec(G d/fia) may be used as criteria for defining the flow regime values less than 1000 to 2000, however, do not necessarily imply that the fluid is in truly laminar flow. Later experimental work showed that the total pressure has an influence and data presented by Gr1H ITH(i9) may be consulted where... 

The relation between cost per unit length C of a pipeline installation and its diameter d is given by ... 

From a dimensional analysis, obtain a relation between the power and the four variables. The power consumption is found, experimentally, to be proportional to the square of the speed of rotation. By what factor would the power be expected to increase if the impeller diameter were doubled ... 

An agitated tank with a standard Rushton impeller is required to disperse gas in a solution of properties similar to those of water. The tank will be 3 m diameter (1 m diameter impeller), A power level of 0.8 kW/m3 is chosen. Assuming fully turbnlent conditions and feat the presence of fee gas does not significantly affect the relation between fee Power and Reynolds numbers ... 

Now, we show the relation between the ratio of 8 to Tq, 8/ro and the volume fraction of carbon black (p in Table 18.1, when the diameter of the hard particle (including carbon black, the GH layer and a little more contribution from the cross-links at the surface of particle) is tq and the distance between the hard particles is 8. In the carbon black-filled rubber (ip g 0.23-0.25), the fact that the stress of the filled system is 10-15 times larger than that of the unfilled rubber as shown in Figure 18.1 indicates that more than 90% of the stress of the system is supported by the supernetwork and the remainder of the stress results from the matrix rubber. In the present calculation, however, we can ignore the contribution from the matrix mbber. 

Relation between flame speed Vj and maximum tangential velocity in an axially decaying vortex flow in a tube for various mixtures (tube diameter 31mm, the mean axial velocity 3m/s). (From Ishizuka, S., Combust. Flame, 82,176,1990.)... 

Figure 2.5 illustrates the state of affairs, and shows that heterogeneous material may be characterized by an inhomogeneous (C) or homogeneous (D) concentration function dependent on the relation between the total variation of concentration and the uncertainty of measurement on the one hand and the sample amount (or microprobe diameter in case of distribution-analytical investigations) on the other. 

Before we discuss the relation between ultimate fibre strength and degree of polymerisation (zn or DP), we first show that this model in fact describes the relation between the composite strength and the aspect ratio of the rod. In the case of a monodisperse distribution, i.e. all rods or chains have the same diameter 2r and the same length a, the ultimate strength as a function of the aspect ratio fr= a(2r) 1 is given by... 

The relation between bed voidage e and fluid velocity uc for particulate fluidisation of uniform particles which are small compared with the diameter of the containing vessel is given by ... 

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