Liquid flow density

It was revealed that the fact that liquid flows densities and viscosities change doesn t influence on reaction torch front formation is also very important (Fig. 4.2,4.3). The rise of density of flows at the expense of reduction of low bound of ratios Vi / V2 required for the formation of plan front and constancy of ratios Vi / V2 required for formation of low bound of torch front leads to the narrowing of ineffective torch regime region formation. The last fact widens possibilities of tubular turbulent apparatus exploitation in optimal quasi-plug-flow regime (quasi-isothermal regime) (Fig. 4.4). 

Moreover the effect of chemical reaction rate constant and also of some physical parameters of liquid flows (density, viscosity) on conditions of characteristic macroscopic fronts formation in turbulent flows limited by impenetrable wall allows supposing the various nature of reaction and mixing fronts formation. In the first case kinetic and diffusion process parameters are determinant, and in the second - preliminary convective and turbulent transfer. The influence of density and viscosity of liquid flows, i.e. parameters determining hydrodynamic regime of liquid flows in tubular canals on conditions of reaction and mixing plan front formation shows the important role of hydrodynamic constituent also in general case under corresponding macrostructures formation. 

These observations can be explained by the influence of the liquid flow density and viscosity on the turbulence level, defined in the first approximation by the Reynolds Number (Re). In particular, an increase of the density value for the reactant flow in motion, leads to an increase of the Re values, i.e., the hydrodynamic similarity of the system changes. In order to form the quasi-plug flow mode in the reactor after a change in the reactant density, it is necessary to reach the previous Re values, which may be possible due to a decrease in the linear rate of the liquid motion V, or due to a decrease of the reactor diameter D, and increase of the system viscosity. The hydrodynamic similarity of the system and the quasi-plug flow mode are reached due to the decrease of the V1/V2 ratio (a decrease of the axial flow rate). In much the same way, it is possible to explain the influence of viscosity on the conditions of plane front formation. 

Moreover, the influence of the chemical reaction rate constant and some other physical parameters of the liquid flow (density, viscosity) on the conditions of macroscopic front formation in turbulent flows, allow us to make an assumption about the differences in the nature of the reaction front and mixing front formation. In the first case, the key parameters of the process are the kinetic and diffusion parameters in the second case, however, the key parameters of the process are the convective and turbulent transfer. The influence of density and viscosity, i.e., the parameters which define the hydrodynamic motion mode of the liquid flow in the tubular channels, on the... 

Porter (I968) and Stanek et al. (1965) applied this homogeneous diffusional picture to the radial spreading of rivulets and replaced the liquid flow density by a rivulet density. However, Lespinasse (1962) pointed out that this diffusional picture is unable to account for the occurrence of liquid flow preferential paths stable in time (see also Berner et al., 1978). 

Lateral distribution of the li- Lateral distripution of the quid flow density liquid flow density... 

When a gas or liquid flows over a surface, the pressure at the surface is reduced according to the formula shown in equation (1), in which d is the density and v is the linear flow velocity of the moving stream. 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

Kj= thermal conductivity of gas film surrounding the droplet, Btu/(h ft )(°F ft), evaluated at the average between diyer gas and drop temperature V = volume of diyer chamber, rP At = temperature driving force (under terminal conditions described above), °F D, = maximum drop diameter, ft to, = weight rate of liquid flow, Ib/h p, = density of hquid, Ib/ft ... 

Gf = liquid-flow rate (weight/cross-sectional area) p = liquid density... 

Mobile-Bed Scrubbers Mobile-bed scrubbers (Fig. 17-51) are constructed with one or more beds of low-density spheres that are free to move between upper and lower retaining grids. The spheres are commonly 1.0 in (2.5 cm) or more in diameter and made from rubber or a plastic such as polypropylene. The plastic spheres may be solid or hollow. Gas and liquid flows are countercurrent, and the spherical packings are flmdized by the upward-flowing gas. The movement of... 

Density gradients to stabilize flow have been employed by Philpot IT> Yin.s. Faraday Soc., 36, 38 (1940)] and Mel [ j. Phys. Chem., 31,559 (1959)]. Mel s Staflo apparatus [J. Phys. Chem., 31, 559 (1959)] has liquid flow in the horizontal direction, with layers of increasing density downward produced by sucrose concentrations increasing to 7.5 percent. The solute mixture to be separated is introduced in one such layer. Operation at low electrolyte concentrations, low voltage gradients, and low flow rates presents no cooling problem. 

The term three-phase fluidization requires some explanation, as it can be used to describe a variety of rather different operations. The three phases are gas, liquid and particulate solids, although other variations such as two immiscible liquids and particulate solids may exist in special applications. As in the case of a fixed-bed operation, both co-current and counter- current gas-liquid flow are permissible and, for each of these, both bubble flow, in which the liquid is the continuous phase and the gas dispersed, and trickle flow, in which the gas forms a continuous phase and the liquid is more or less dispersed, takes place. A well established device for countercurrent trickle flow, in which low-density solid spheres are fluidized by an upward current of gas and irrigated by a downward flow of liquid, is variously known as the turbulent bed, mobile bed and fluidized packing contactor, or the turbulent contact absorber when it is specifically used for gas absorption and/or dust removal. Still another variation is a three-phase spouted bed contactor. 

The above is valid for a liquid flow, when the effect of compressibility can be ignored when calculating gas flows with small pressure differences. For instance, in ventilating duct work, air is not compressed, so the density is considered as constant. In HVAC technology a unit of pressure frequently used for convenience is a water column millimeter, 1 mm H.O=10Pa. 

Hughmark and Pressburg (H14) studied holdup and pressure drop for cocurrent gas-liquid flow, and correlated holdup with a function of gas and liquid flow rates, surface tension, densities of gas and liquid, viscosities of gas and liquid, and total mass velocity. 

An organic liquid flows across a distillation tray and over a weir at the rate of 15 kg/s. The weir is 2 m long tmcl the liquid density is 650 kg/m3. What is the height of liquid flowing over the weir ... 

Inertial force is associated with the reluctance of a body to change its state of rest or motion. Considering a mass m of liquid flowing with a linear velocity u through an area A during the time interval dr then dm = puA dr where p is the fluid density. The inertial force F, = (mass x acceleration) or ... 

In Table 6.7, C is the Martinelli-Chisholm constant, / is the friction factor, /f is the friction factor based on local liquid flow rate, / is the friction factor based on total flow rate as a liquid, G is the mass velocity in the micro-channel, L is the length of micro-channel, P is the pressure, AP is the pressure drop, Ptp,a is the acceleration component of two-phase pressure drop, APtp f is the frictional component of two-phase pressure drop, v is the specific volume, JCe is the thermodynamic equilibrium quality, Xvt is the Martinelli parameter based on laminar liquid-turbulent vapor flow, Xvv is the Martinelli parameter based on laminar liquid-laminar vapor flow, a is the void fraction, ji is the viscosity, p is the density, is the two-phase frictional... 

Fig.2 and Fig.3 show the typical liquid velocity and gas hold up distribution in the ALR. From the figures, one notices that the cyclohexane circulates in the ALR under the density difference between the riser and the downcomer. An apparent large vortex appears near the air sparger when the circulating liquid flows fi om the downcomer to the riser at the bottom. In the riser, liquid velocity near the draft-tube is much larger than that near the reactor wall, the latter moved somewhat downward. The gas holdup is nonuniform in the reactor, most gas exists in the riser while only a little appears in the dowmcomer. 

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