Gas kinematic viscosity

The side wall of the confining container is assumed to be a macroscopically homogeneous membrane with permeability Bq (in particular, Bq = 0 corresponds to the impermeable membrane i.e. the FBR). The flow rate through the membrane depends on both, permeability and the local pressure drop across the membrane (by Darcy s law). Local gas density (and pressure) is assumed to be constant at the membrane shell-side. In addition, fluid flow through the packed bed is assumed to be isothermal, nonreactive and nonturbulent, while gas kinematic viscosity is assumed to be independent on gas density. The following boundary conditions have been imposed to simulate the pressure and velocity fields in the fixed bed ... 

Figure 3.2.6 Nu versus Re for heat flux from a cooled (o) and from a heated ( ) plate to a gas [kinematic viscosity air (300 K, 1 bar) =0.15 cm s combustion gas (mean temp, of 700 K,...

The same definition of viscosity applies to oil as gas (see Section 5.2.6), but sometimes the kinematic viscosity is quoted. This is the viscosity divided by the density (u = i7p), and has a straight line relationship with temperature. 

A simplified estimate can be made by first converting the flow at actual conditions to the flow at standard conditions (i.e., at 70 F and 1 atm). The calculation basis for the linear velocity assumes a roughness coefficient of 0.0005 and a kinematic viscosity for air of 1.62 x lO fF/sec. From the ideal gas law, the following expression is developed ... 

The kinematic viscosity of a gas is a function of the pressure, and its dimension is the square of length divided by the time, its unit being m s k... 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

Experimental values of diffusivities are given in Table 10.2 for a number of gases and vapours in air at 298K and atmospheric pressure. The table also includes values of the Schmidt number Sc, the ratio of the kinematic viscosity (fx/p) to the diffusivity (D) for very low concentrations of the diffusing gas or vapour. The importance of the Schmidt number in problems involving mass transfer is discussed in Chapter 12. 

A gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm2/s, is Mowing through a pipe 0.25 nt internal diameter and 5 km long at the rate of 0.4 nt3/s and is delivered at atmospheric pressure, Calculate the pressure required to maintain this rate of flow under isothermal conditions. 

In the SI system, the theoretical unit of v is m2/s or the commonly used Stoke (St) where 1 St = 0.0001 m2/s = 100 cSt = 100 centiStoke. Similarly, 1 centiStoke = 1 cSt = 0.000001 m2/s = 0.01 Stoke = 0.01 st. The specific gravity of water at 20.2°C (68.4°F) is almost 1. The kinematic viscosity of water at 20.2°C (68.4°F) is for all practical purposes equal to 1 cSt. For a liquid, the kinematic viscosity will decrease with higher temperature. For a gas, the kinematic viscosity will increase with higher temperature. Another commonly used kinematic viscosity unit is Saybolt universal seconds (SUS), which is the efflux time required for 60 mL of petroleum product to flow through the calibrated orifice of a Saybolt universal viscometer, as described by ASTM-D88. Therefore, the relationship between dynamic viscosity and kinematic viscosity can be expressed as... 

All of the linear dimensions of the model are scaled to the corresponding dimensions of the commercial bed by the ratio of the kinematic viscosities of the gas raised to the two-thirds power. By taking the ratio of Reynolds number based on the particle diameter to Reynolds number based on the bed diameter... 

Once the model fluid and its pressure and temperature are chosen, which sets the gas density and viscosity, there is only one unique set of parameters for the model which gives similarity when using the full set of dimensionless parameters. The dependent variables, as nondimensionalized by Eq. (18), will be the same in the respective dimensionless time and spatial coordinates of the model as the commercial bed. The spatial variables are nondimensionalized by the bed diameter so that the dimensional and spatial coordinates of the model is proportional to the two-thirds power of the kinematic viscosity, as given by Eq. (69)... 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

Ka can be defined as a gas-phase transfer coefficient, independent of the liquid layer, when the boundary concentration of the gas is fixed and independent of the average gas-phase concentration. In this case, the average and local gas-phase mass-transfer coefficients for such gases as sulfur dioxide, nitrogen dioxide, and ozone can be estimated from theoretical and experimental data for deposition of diffusion-range particles. This is done by extending the theory of particle diffusion in a boundary layer to the case in which the dimensionless Schmidt number, v/D, approaches 1 v is the kinematic viscosity of the gas, and D is the molecular diffusivity of the pollutant). Bell s results in a tubular bifurcation model predict that the transfer coefficient depends directly on the... 

Gas adsorption into the liquid falling down a wetted wall column is of considerable interest. The flow of liquid down the surface of such a tube is essentially laminar if Re < 1200, where Re is defined as iu/vl, u being the volume flow rate of liquid, I the perimeter of the tube, and v the kinematic viscosity of the solvent. Under these conditions, if there are no surface forces acting, the velocity of the air-water surface of the... 

Kg, gas film coefficient A, surface area of water body 7), diffusion coefficient of compound in air W, wind velocity at 2 m above the mean water surface v, kinematic viscosity of air a, thermal diffusion coefficient of air g, acceleration of gravity thermal expansion coefficient of moist air AP, temperature difference between water surface and 2 m height APv virtual temperature difference between water surface and 2 m height. 

L T ), and v is the kinematic viscosity ofthe hquid (L" T ). Ihe dimensionless groups include N/v) = Reynolds number (Re) d N /g) = Froude number (Fr) and (Q/N d = aeration number (Na), which is proportional to the ratio of the superficial gas velocity with respect to the tank cross section to the impeller tip speed. 

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