Equations dimensional

Various other non-ideal-gas-type two-dimensional equations of state have been proposed, generally by analogy with gases. Volmer and Mahnert [128,... 

The data could be expressed equally well in terms of F versus P, or in the form of the conventional adsorption isotherm plot, as shown in Fig. Ill-18. The appearance of these isotherms is discussed in Section X-6A. The Gibbs equation thus provides a connection between adsorption isotherms and two-dimensional equations of state. For example, Eq. III-57 corresponds to the adsorption isotherm... 

B. Adsorption Isotherms from Two-Dimensional Equations of State... 

Show what two-dimensional equation of state corresponds to the isotherm ... 

Representation of Heat-Transfer Film Coefficients There are two general methods of expressing film coefficients (1) dimensionless relations and (2) dimensional equations. 

The dimensional equations are usually expansions of the dimensionless expressions in which the terms are in more convenient units and in which all numerical factors are grouped together into a single numerical constant. In some instances, the combined physical properties are represented as a linear function of temperature, and the dimension equation resolves into an equation containing only one or two variables. 

Simplified Dimensional Equations Equation (5-32) is a dimensionless equation, and any consistent set of units may be used. Simphfied dimensional equations have been derived for air, water, and organic hquids by rearranging Eq. (5-32) into the following form by collecting the fluid properties into a single factor ... 

For the turbulent flow of water in layer form down the walls of vertical tubes the dimensional equation of McAdams, Drew, and Bays [Trans. Am. Soc. Mech. Eng., 62, 627 (1940)] is recommended ... 

The following dimensional equations may be used for any liquid flowing in layer form down vertical surfaces ... 

Dimensional Equations for Various Conditions For gases at ordinary pressures and temperatures based on c[L/k = 0.78 and [L =... 

The following dimensional equations (5-73 to 5-77) are based on flow normal to a bank of staggered tubes without leakage. Multiply the values obtained for h by 0.6 for normal leakage and, in addition, by 0.79 for in-line (not staggered) tube arrangement. 

Equation 12-25 is a dimensional equation, therefore, the dimensions given in the parameters must be used. 

Buckingham, E., 1914. On physically similar systems illustrations of the use of dimensional equations. Physics Review, 4, 335-376. 

The one-dimensional equation describing the variation of igniter energy content ... 

The one-dimensional equation for the steady state becomes, for this case ... 

Any consistent set of units may be used. For the few dimensional equations, the appropriate units are given in the text. 

Below the system of quasi-one-dimensional equations considered in the previous chapter used to determine the position of meniscus in a heated micro-channel and estimate the effect of capillary, inertia and gravity forces on the velocity, temperature and pressure distributions within domains are filled with pure liquid or vapor. The possible regimes of flow corresponding to steady or unsteady motion of the liquid determine the physical properties of fluid and intensity of heat transfer. 

In this section we present the system of quasi-one-dimensional equations, describing the unsteady flow in the heated capillary tube. They are valid for flows with weakly curved meniscus when the ratio of its depth to curvature radius is sufficiently small. The detailed description of a quasi-one-dimensional model of capillary flow with distinct meniscus, as well as the estimation conditions of its application for calculation of thermohydrodynamic characteristics of two-phase flow in a heated capillary are presented in the works by Peles et al. (2000,2001) and Yarin et al. (2002). In this model the set of equations including the mass, momentum and energy balances is ... 

Such an approximation is the result of a natural generalization of homogeneous conservative schemes from Chapter 3 for one-dimensional equations to the multidimensional case. These schemes can be obtained by means of the integro-interpolational method without any difficulties. 

Furthermore, to problem (5) there corresponds the first chain of one-dimensional equations by reducing either (5) or... 

The simple pore structure shown in Figure 2.69 allows the use of some simplified models for mass transfer in the porous medium coupled with chemical reaction kinetics. An overview of corresponding modeling approaches is given in [194]. The reaction-diffusion dynamics inside a pore can be approximated by a one-dimensional equation... 

Step 5 Write the dimensional equations for each of the remaining variables. Then substitute the results of step 4 for the dimensions in terms of the reference variables ... 

There is no general correlation available to date to predict the steady state attrition rates for various materials. Zenz and Kelleher (1980) gave a simple correlation to predict steady-state attrition rates for FCC catalyst and glass beads. This is an empirical dimensional equation as given by ... 

The method of combination of variables requires that a suitable combination ofy and t can be found. Dimensionally, equation 10.19 can be written as... 

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