Fluid Flow Basic Equations

FLUID FLOW BASIC EQUATIONS (A.) Pitot tube... 

Newman, J., 52-4 Newtonian fluid flow, basic equations for, 60-2 Newtonian mechanics, 51-7 NGOMSL (natural GOMS... 

Incompressible Fluids The basic equation of flow in a stream-tube is the Bernoulli equation (D. BemouUi, see box), which is given for steady-state conditions and an incompressible fluid with internal friction by ... 

When adsorption occurs in a vessel where adsorbents are in contact with a flowing fluid, the basic equations must be modified so that Eq. (S-S) is involved. Suzuki and Chihara (1982) provide a detailed discussion on the topic the results are summarized as follows When the concentration of the inlet fluid, Cm, is constant, then the solutions obtained in Section 5.2.3 and 5.2.4 are applicable by equating... 

In the basic heat transfer equation it is necessary to use the log mean temperature difference. In Equation 2-4 it was assumed that the two fluids are flowing counter-current to each other. Depending upon the configuration of the exchanger, this may not be true. That is, the way in which the fluid flows through the exchanger affects LMTD. The correction factor is a function of the number of tube passes and the number of shell passes. 

Pressure drop on the tube-side of a shell and tube exchanger is made up of the friction loss in the tubes and losses due to sudden contractions and expansions and flow reversals experienced by the tube-side fluid. The friction loss may be estimated by the methods outlined in Section 3.4.3 from which the basic equation for isothermal flow is given by equation 3.18 which can be written as ... 

Figure 26.9 illustrates Darcy s law, the basic equation used to describe the flow of fluids through porous materials. In Darcy s law, the coefficient k, hydraulic conductivity, is often called the coefficient of permeability by civil engineers. 

This is the basic equation from which the frictional pressure drop may be calculated. It is valid for all types of fluid and for both laminar and turbulent flow. However, the value of / to be used does depend on these conditions. 

When considering flow of a liquid in contact with a solid surface, a basic understanding of the hydrodynamic behavior at the interface is required. This begins with the Navier-Stokes equation for constant-viscosity, incompressible fluid flow, such that Sp/Sf = 0,... 

Any fluid flow situation is described completely by momentum, mass, and energy balances. We have thus far looked at only simplified forms of the relevant balance equations for our simple models, as is done implicitly in aU engineering courses. It is interesting to go back to the basic equations and see how these simple approximations arise. We need to examine the full equations to determine the errors we are making in describing real reactors with... 

Conservation Laws. The fundamental conservation laws of physics can be used to obtain the basic equations of fluid motion, the equations of continuity (mass conservation), of flow (momentum conservation), of... 

Equations (5.139) to (5.142) are the basic equations for a gas-solid flow. More detailed information on both the fluid-particle interacting force Fa and the total stresses T and Tp must be specified before these equations can be solved. One approach to formulate the fluid-particle interacting force FA is to decompose the total stress into a component E representing the macroscopic variations in the fluid stress tensor on a scale that is large compared to the particle spacing, and a component e representing the effect of detailed variations of the point stress tensor as the fluid flows around the particle [Anderson and... 

The basic hydrodynamic equations are the Navier-Stokes equations [51]. These equations are listed in their general form in Appendix C. The combination of these equations, for example, with Darcy s law, the fluid flow in crossflow filtration in tubular or capillary membranes can be described [52]. In most cases of enzyme or microbial membrane reactors where enzymes are immobilized within the membrane matrix or in a thin layer at the matrix/shell interface or the live cells are inoculated into the shell, a cake layer is not formed on the membrane surface. The concentration-polarization layer can exist but this layer does not alter the value of the convective velocity. Several studies have modeled the convective-flow profiles in a hollow-fiber and/or flat-sheet membranes [11, 35, 44, 53-56]. Bruining [44] gives a general description of flows and pressures for enzyme membrane reactor. Three main modes... 

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