Dimensionless number Schmidt

Define and interpret the following dimensionless numbers Schmidt, Prandtl, and Lewis. 

American engineers are probably more familiar with the magnitude of physical entities in U.S. customary units than in SI units. Consequently, errors made in the conversion from one set of units to the other may go undetected. The following six examples will show how to convert the elements in six dimensionless groups. Proper conversions will result in the same numerical value for the dimensionless number. The dimensionless numbers used as examples are the Reynolds, Prandtl, Nusselt, Grashof, Schmidt, and Archimedes numbers. 

The dimensionless numbers in tlris equation are the Reynolds, Schmidt and the Sherwood number, A/ sh. which is defined by this equation. Dy/g is the diffusion coefficient of the metal-transporting vapour species in the flowing gas. The Reynolds and Schmidt numbers are defined by tire equations... 

HETP = height equivalent to a theoretical plate, ft HTU = height of a transfer unit, ft L = liquid mass velocity, Ib/hr-ft m = exponent a 1.0 n = exponent 0.44 Pr = Prandtl number, dimensionless Sc = Schmidt number dimensionless U, = linear velocity of gas based on total column cross-sectional area, ft/sec... 

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = but the dependence on Sc is weak for... 

Dimensionless numbers (Reynolds number = udip/jj., Nusselt number = hd/K, Schmidt number = c, oA, etc.) are the measures of similarity. Many correlations between them (known also as scale-up correlations) have been established. The correlations are used for calculations of effective (mass- and heat-) transport coefficients, interfacial areas, power consumption, etc. 

The dynamical regimes that may be explored using this method have been described by considering the range of dimensionless numbers, such as the Reynolds number, Schmidt number, Peclet number, and the dimensionless mean free path, which are accessible in simulations. With such knowledge one may map MPC dynamics onto the dynamics of real systems or explore systems with similar characteristics. The applications of MPC dynamics to studies of fluid flow and polymeric, colloidal, and reacting systems have confirmed its utility. 

Schmidt number 3 phys chem A dimensionless number used In electrochemistry, equal to the product of the dielectric susceptibility and the dynamic viscosity of a fluid divided by the product of the fluid density, electrical conductivity, and the square of a characteristic length. Symbolized SC3. shmit. nam bar thre ) Schoeikopf s acid orgchem A dye of the following types l-naphthol-4,8-dlsulfonlc acid, l-naphthylamine-4,8-disulfonicadd,and l-naphthylamine-8-sulfonicadd may be toxic. shol.kopfs, as-3d ... 

Semenov number 1 physchem A dimensionless number used in reaction kinetics, equal to a mass transfer constant divided by a reaction rate constant. Symbolized S . Formerly known as Schmidt number 2. se-m3,n6f nom-bor won ... 

It is seen that we are comparing kinematic viscosity, thermal diffusivity, and diffu-sivity of the medium for both air and water. In air, these numbers are all of the same order of magnitude, meaning that air provides a similar resistance to the transport of momentum, heat, and mass. In fact, there are two dimensionless numbers that will tell us these ratios the Prandtl number (Pr = pCpv/kj = v/a) and the Schmidt number (Sc = v/D). The Prandtl number for air at 20°C is 0.7. The Schmidt number for air is between 0.2 and 2 for helium and hexane, respectively. The magnitude of both of these numbers are on the order of 1, meaning that whether it is momentum transport, heat transport, or mass transport that we are concerned with, the results will be on the same order once the boundary conditions have been made dimensionless. 

Both methods yield dimensionless groups, which correspond to dimensionless numbers (1), e.g.. Re, Reynolds number Fr, Froude number Nu, Nusselt number Sh, Sherwood number Sc, Schmidt number etc. (2). The classical principle of similarity can then be expressed by an equation of the form ... 

Dijfusional dimensionless numbers The Peclet, Prandtl, Schmidt, Sherwood, and Nusselt number are the most common ones. 

From our earliest example, we saw that it was advantageous to use dimensionless variables and that the characteristic quantities should be capable of being held constant. In addition, if a parametric study on the effect of varying some input quantity is to be performed, that quantity should appear in only the distinguished parameter. This is no restriction, for the others are proportional to powers of the distinguished parameter, and the proportionality constants are themselves dimensionless numbers. For example, if the viscosity is to be varied, the Reynolds and the Schmidt numbers are both functions of v, but ReSc is not so, if Sc is chosen as the dimensionless viscosity, Re = Cl Sc, where C = ReSc is independent of v. 

Schmidt number a dimensionless number, characteristic of each gas, which varies strongly with temperature and weakly with salinity, and is used to account for viscosity effects on the diffusion of gases. 

As explained earlier, with respect to the heat and mass transfer analogies, the Schmidt number is the Prandtl number analogue. Both dimensionless numbers can be appreciated as dimensionless material properties (they only contain transport media properties). For gases, the Sc number is unity, for normal liquids it is 600-1800. The refined metals and salts can have a Sc number over 10 000. 

C Wliat is the phy.sical significance of the Schmidt number How is it defined To what dimensionless number does it correspond in heat ttansfer What does a Schmidt number of 1 indicate ... 

In order to characterize mass transfer in the boundary layers, it is necessary to determine the respective mass transfer coefficients. These coefficients depend on the properties of the solutions and on the hydrodynamic conditions of the system. Such coefficient can either be obtained by experiments or be estimated with the help of empirical correlations of dimensionless numbers. The majority of the correlations referred to in the literamre for various hydrodynamic conditions have the same general form. These include Sherwood number Sh), which contains the mass transfer coefficient, as a function of the Reynolds number Re) and Schmidt number (5c) [89-91]. General mass transfer correlation can be written as... 

If these Peclet numbers are divided by the Reynolds number, the resulting dimensionless numbers are called the Pradtl number, Pr and Schmidt number. Sc, respectively. The Prandtl number (Pr) is the ratio of momentum diffusivity and thermal diffusivity. The Schmidt number (Sc) is the ratio of momentum diffusivity and mass diffusivity. These five dimensionless numbers can convey very useful information about the relative contributions of convective and molecular transport and relative magnitudes of momentum, heat and mass transfer. 

Kataoka et al. [100] foxmd that, when only the data for Re < 100 are considered, most experimental data published earlier fit the following equation using the Sherwood, Reynolds, and Schmidt dimensionless numbers... 

The introduction of different parameterizations for the turbulent viscosity parameter leads to different modifications of the correlations for the dimensionless numbers. By setting the viscous Prandtl and Schmidt number equal to unity and noting that the integral term in the denominator is simply the velocity (5.276) that can also be expressed by = = we get... 

The characteristic Nerast parameter 5, the thickness of the film around the ion exchange particle, may be converted to the mass transfer coefficient and dimensionless numbers (Reynolds, Schmidt and Sherwood) that engineers normally employ. 

Grashof number D -iPAPZ ) dimensionless number of sparger orifices or sites power number P JpO jN ), dimensionless bubble Reynolds number D fjiVdimensionless impeller Reynolds number (Dj Npjp, dimensionless Schmidt number (Pc/Pc ab) dimensionless Sherwood number (kiDy /DAB), dimensionless total pressure, N/m ... 

The product of the Reynolds and Schmidt numbers, which counts as one dimensionless number, is equivalent to the Peclet number for mass transfer, PeMx- The Peclet number represents the ratio of the convective mass transfer rate process to the diffusion rate process of component, and it appears on the left-hand side of the dimensionless mass transfer equation for component i. The remaining r dimensionless transport numbers can be treated simultaneously because they represent ratios of scaling factors for the reactant-product conversion rate due to the jth independent chemical reaction relative to the rate of diffusion of component I. Hence,... 

The Schmidt number is a dimensionless number equal to the ratio of kinematic viscosity to mass diffusivity. It is ... 

Schj.g dimensionless gas Schmidt number for H2, PgIPgDki.g Schj.l dimensionless liquid Schmidt number for H2, /Tl/PlDhi.l... 

Moreover, the mixing in the liquid-liquid system can be characterised by dimensionless numbers, such as, Sherwood number (Sh), which is the ratio of convective mass transfer to the molecular diffusion, and Schmidt niunber (Sc), which is the ratio of the viscous diffusion rate to the molecular diffusion. In addition to these, the Fourier number (Fo) can also give an idea about the dynamics of diffusive transport process. 

Reynolds number, dimensionless number of imxing stages on tray number of moles in stillpot Schmidt number, dimmsionless Sherwood number dimensionless... 

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