Velocity fluid

By assuming a reasonable fluid velocity, together with fluid physical properties, standard heat transfer correlations can be used. 

The field unit for permeability is the Darcy (D) or millidarcy (mD). For clastic oil reservoirs, a good permeability would be greater than 0.1 D (100 mD), while a poor permeability would be less than 0.01 D (10 mD). For practical purposes, the millidarcy is commonly used (1 mD = 10" m ). For gas reservoirs 1 mD would be a reasonable permeability because the viscosity of gas is much lower than that of oil, this permeability would yield an acceptable flowrate for the same pressure gradient. Typical fluid velocities in the reservoir are less than one metre per day. 

Here the thennal diflfiisivity Dj. = tc/fp Cp. These two equations couple only to the longitudinal part T = V-iJ of the fluid velocity. From equation (A3.3.17) it is easy to see diat T satisfies... 

By using the relationship between the fluid current and its veloeity field, J = Pv, a quantum fluid velocity field of... 

Here f denotes the fraction of molecules diffusely scattered at the surface and I is the mean free path. If distance is measured on a scale whose unit is comparable with the dimensions of the flow channel and is some suitable characteristic fluid velocity, such as the center-line velocity, then dv/dx v and f <<1. Provided a significant proportion of incident molecules are scattered diffusely at the wall, so that f is not too small, it then follows from (4.8) that G l, and hence from (4.7) that V v° at the wall. Consequently a good approximation to the correct boundary condition is obtained by setting v = 0 at the wall. ... 

At Che opposite limit, where Che density Is high enough for mean free paths to be short con ared with pore diameters, the problem can be treated by continuum mechanics. In the simplest ease of a straight tube of circular cross-section, the fluid velocity field can easily be obtained by Integrating Che Nsvler-Stokes equations If an appropriate boundary condition at Che... 

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

Meters can be further divided into three subgroups depending on whether fluid velocity, the volumetric flow rate, or the mass flow rate is measured. The emphasis herein is on common flow meters. Devices of a highly specialized nature, such as biomedical flow meters, are beyond the scope of this article. 

Gup and Vane Anemometers. A number of flow meter designs use a rotating element kept in motion by the kinetic energy of the flowing stream such that the speed is a measure of fluid velocity. In general, these meters, if used to measure wind velocity, are called anemometers if used for open-channel Hquids, current meters and if used for closed pipes, turbine flow meters. 

Measurement by Thermal Effects. When a fine wire heated electrically is exposed to a flowing gas, it is cooled and its resistance is changed. The hot-wire anemometer makes use of this principle to measure both the average velocity and the turbulent fluctuations in the flowing stream. The fluid velocity, L, is related to the current, /, and the resistances, R, of the wire at wire, and gas, g, temperatures via... 

Convection Heat Transfer. Convective heat transfer occurs when heat is transferred from a soHd surface to a moving fluid owing to the temperature difference between the soHd and fluid. Convective heat transfer depends on several factors, such as temperature difference between soHd and fluid, fluid velocity, fluid thermal conductivity, turbulence level of the moving fluid, surface roughness of the soHd surface, etc. Owing to the complex nature of convective heat transfer, experimental tests are often needed to determine the convective heat-transfer performance of a given system. Such experimental data are often presented in the form of dimensionless correlations. 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

The first bracketed term represents the pressure difference between the inlet and oudet no22les resulting from the difference in fluid velocity, acceleration or momentum, and the second bracketed term represents the pressure difference between the inlet and outlet no22les from the difference in elevation. 

The bulk fluid velocity method relates a blending quaUty Chemscale number to a quaUtative description of mixing (Table 3). The value of is equal to one-sixth of the bulk fluid velocity defined by pumping rate divided by cross-sectional area of the tank (4). 

Cavitation. The subject of cavitation in pumps is of great importance. When the Hquid static pressure is reduced below its vapor pressure, vaporization takes place. This may happen because (/) the main stream fluid velocity is too high, so that static pressure becomes lower than vapor pressure (2) localized velocity increases and static pressure drops on account of vane curvature effect, especially near the inlets (J) pressure drops across the valve or is reduced by friction in front of the pump or (4) temperature increases, giving a corresponding vapor pressure increase. 

A number of analytical solutions have been derived for iC as a function of channel dimensions and fluid velocity (30). In practice, the fit between theory and data for K is poor except in idealized cases. Most processes exhibit either higher fluxes, presumably caused by physical dismption of the gel layer from the nonideal hydrodynamic conditions, or lower fluxes caused by fouling (31). In addition, iCis a function of the fluid composition. 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

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