Viscosity coefficients dynamic

It was estimated that the permeability coefficient A( = (1.4 - 4.6)xl0" m/s in the seriously weathered and fractured zone. The distribution of fractures dominates the penetrability of rock mass in the slightly weathered zone, and excavation caused unloading also plays an important role. Parameters concerned (Zhu and Zhang, 1996) are as follows the initial aperture of fractures b = 0. Imm, the dynamical viscosity coefficients of underground water ti = lOxlO m/s, the unit volume discharge s = 6.4xio m /(m s)and the bulk dense of watery = l.OxlO kg/m ... 

Where, Uj, is particle velocity (m/s), FD (u - u,) is quality drag force of particle (N/Kg), u is fluid phase velocity (m/s), (j, is fluid dynamic viscosity coefficient, p, is particle density (kg/m ), is other forces in x direction. 

Here tj is shear viscosity coefficient. For the case shown in the Fig. 9.1, jc,- = x, Xj = z, the velocity has only component and the gradient of velocity has a simple form dvjdz. Then a z = tfdvjdz. The dynamic viscosity coefficient ri is measured in Poise (g-s cm ). Sometimes one uses the so-called kinematic viscosity tj/p measured in Stokes (cm s ). The SI unit for d3mamic viscosity is Pa s (N m s). Numerically 1 Pa s =10 P. 

Scalar isotropic pressure Pg in the continuous phase approximately equals the mean fluid pressure, and particulate stresses P, are expressible through derivatives of w and scalar isotropic pressure p, in the dispersed phase in accordance with Equation 4.4. Pressure p, is a function of suspension volume concentration and of particle fluctuation temperature defined by equation of state (4.6) for particulate pseudogas. Osmotic pressure function G(())) appearing in Equation 4.6 is given by either Equation 4.8, 4.9, or by some other equation that follows from some other statistical pseudo-gas theory. Dispersed phase dynamic viscosity coefficient p, and particle fluctuation energy transfer coefficient q, that appear in Equation 4.4 also can be represented as functions of fluctuation temperature T and concentration < > in conformity with the formulae in Equations 5.5 and 5.7. Force nf of interphase interaction per unit suspension volume approximately equals the force in Equation 3.2 multiplied by the particle number concentration. Finally, coefficients and a are determined in Equation 4.11 and 4.12, respectively. 

Discussion—For gravity flow under a given hydrostatic head, the pressure head of a liquid is proportional to its density, p. For any particular viscometer, the time of flow of a fixed volume of fluid is directly proportional to its kinematic viscosity, v, where v = v/p, and ij is the dynamic viscosity coefficient. 

Calculate the dynamic viscosity coefficient rj of oxygen at normal conditions. 

The dynamic viscosity, or coefficient of viscosity, 77 of a Newtonian fluid is defined as the force per unit area necessary to maintain a unit velocity gradient at right angles to the direction of flow between two parallel planes a unit distance apart. The SI unit is pascal-second or newton-second per meter squared [N s m ]. The c.g.s. unit of viscosity is the poise [P] 1 cP = 1 mN s m . The dynamic viscosity decreases with the temperature approximately according to the equation log rj = A + BIT. Values of A and B for a large number of liquids are given by Barrer, Trans. Faraday Soc. 39 48 (1943). 

A supercritical fluid exhibits physical-chemical properties intermediate between those of liquids and gases. Mass transfer is rapid with supercritical fluids. Their dynamic viscosities are nearer to those in normal gaseous states. In the vicinity of the critical point the diffusion coefficient is more than 10 times that of a liquid. Carbon dioxide can be compressed readily to form a liquid. Under typical borehole conditions, carbon dioxide is a supercritical fluid. 

This is a statement of Newton s law of viscosity and the constant of proportionality fi is known as the coefficient of dynamic viscosity or, simply, the viscosity, of the fluid. The rate of change of the shear strain is known as the rate of (shear) strain or the shear rate. The coefficient of viscosity is a function of temperature and pressure but is independent of the shear rate y. 

Different types of liquid crystals exhibit different rheological properties [16,17]. With an increase in organization of the microstructure of the liquid crystal its consistency increases and the flow behavior becomes more viscous. The coefficient of dynamic viscosity r, although a criterion for the viscosity of ideal viscous flow behavior (Newtonian systems), is high for cubic and hexagonal liquid crystals but fairly low for lamellar ones. However, the flow characteristics are not Newtonian but plastic or pseudoplastic, respectively. 

Six viscosity coefficients required for a description of the dynamics of an incompressible, nematic liquid crystal. 

Kinematic Viscosity A coefficient defined as the ratio of the dynamic viscosity of a fluid to its density. The centistoke is the reported value of kinematic viscosity measurement. 

Transport properties play an important role in chemical reactions, electrochemistry, and liquid-liquid extraction. This concerns mainly the viscosity of ILs and fheir solutions wifh molecular solvenfs. Viscosity of ILs, typically at the level of 10-500 cP af room femperafure, is much higher than that characteristic of wafer ( /(HjO) = 0.89 cP af 298.15 K) and aqueous solutions. The high dynamic viscosity (viscosity coefficient) of ILs causes difficulties... 

In contrast to Section IV,M, where the turbulent diffusivity was employed to derive an expression for the mass transfer coefficient, in this section expression (401), which is based on a physical model, constitutes the starting point. Concerning the renewal frequency s, the following dimensional considerations can lead to useful expressions. The state of turbulence near the interface can be characterized by a characteristic velocity ua = (gSf)i/2, the dynamic viscosity rj, the surface tension a, and the density p. Therefore... 

Equation (6.3.3b) results from assuming a Poiseille flow in a filter s pore of typical radius r, i is the dynamic viscosity of the fluid. Equation (6.3.3c) is a common expression for the electro-osmotic coefficient [13], with d and , respectively, the dielectric constant of the fluid and the -potential of the pore wall. For the time being, we shall assume il> constant (independent of C(x,t)). 

Equation (2) may be used for the rate constant k of a chemical reaction or applied to the diffusion coefficient in liquid or solid phases or to the fluidity of liquids (reciprocal of dynamic viscosity) or to the specific electrical conductivity of semiconductors. 

For thermal conductivity, the SI units are W/(m K). In laminar flow, the thermal conductivity, A, and the diffiisivity, D, are constant with respect to their respective gradients. Eqn. (3.4-3) indicates that the diffusion flux of solute [mol A/(m2 s)] is proportional to the transverse concentration gradient, with D as the proportionality constant. The dimensions of D are length2/ time, and its units are m2/s in the SI. Eqn. (3.4-2) states that the heat flux [in J/ (m2.s) = W/m2] is proportional to the temperature gradient, with a constant a = A/(p cp) that is called the thermal diffusivity. Its dimensions are length2/time and its SI units are m2/s. Thus, it is not unexpected that the coefficient v = p/p has the same dimensions and units, m2/s. The coefficient v is called the kinematic viscosity, and it clearly has a more fundamental significance than the dynamic viscosity. The usual unit for kinematic viscosity is the Stokes (St) and submultiples such as the centistokes (cSt). In many viscometers, readings... 

The coefficient of viscosity is a measure of the resistance to flow exerted by a fluid. Usually, viscosity is given in units of centipoise. A centipoise is a g mass/100 sec cm. This viscosity term is called dynamic viscosity to differentiate it from kinematic viscosity, which is defined as dynamic viscosity divided by the density of the fluid. 

POISE (P). A unit of dynamic viscosity. The unit is expressed in dyne second per square centimeter The centipoise (cP) is more commonly used The formal definition of viscosity arises from the concept put forward by Newton that under conditions of parallel flow, the shearing stress is proportional to the velocity giadieut. If lire force acting on each of two planes of aiea A parallel to each oilier, moving parallel lo each other with a relative velocity V, and separated by a perpendicular distance X, be denoted by F. the shearing stress is F/A and the velocity gradient, which will be linear for a true liquid, is V/X. Thus, Ft A = q V/X, where the constant if is the viscosity coefficient or dynamic viscosity of the liquid. The poise is the CGS unit of dynamic viscosity. 

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