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Steady flow, availability balance

Blasius steady-flow, laminar, flat-plate, boundary-layer solution is a numerical solution of his simplification of Prandtl s boundary-layer equations, which are a simplified, one-dimensional momentum balance and a mass balance. This type of solution is known in the boundary-layer literature as an exact solution. Exact solutions can be found for only a very limited number of cases. Therefore, approximate methods are available for making reasonable estimates of the behavior of laminar boundary layers (Prob. 11.8). [Pg.395]

Whether this completely general form of the linear momentum balance was available to the hydraulicians of the nineteenth century remains a question. However, it is certain that the fixed control volume, steady flow form of Eq. 2-5 was in use. As an example we note that Rouse and Ince (page 168, 1957) cite the work of Bresse who correctly anal3rzed the hydraulic Jump and the equation for gradually varied flow in an open channel. [Pg.69]

Steady-State Mass Balance Method In theory, the Ki a in an apparatus that is operating continuously under steady-state conditions could be evaluated from the flow rates and the concentrations of the gas and liquid streams entering and leaving, and the known rate of mass transfer (e.g., the oxygen consumption rate of microbes in the case of a fermentor). However, such a method is not practical, except when the apparatus is fairly large and highly accurate instruments such as flow meters and oxygen sensors (or gas analyzers) are available. [Pg.109]

It is encouraging that substantial progress has been made in analyzing the hydrodynamics of droplet interactions in dispersions from fundamental considerations. Effects of flow field, viscosity, holdup fraction, and interfacial surface tension are somewhat delineated. With appropriate models of coalescence and breakage functions coupled with the drop population balance equations, a priori prediction of dynamics and steady behavior of liquid-liquid dispersions should be possible. Presently, one universal model is not available. The droplet interaction processes (and... [Pg.248]

If Q represents the energy supplied at a temperature Tq to a steady-state or cyclic "heat engine" (Figure 2), it follows rrom an available energy balance that the net rate of available energy flowing from the cycle in the form of shaft work can at most be equal to the thermal available energy supplied to the cycle i.e.,... [Pg.20]

When symmetric membranes are used or when enzymes are fed to the spongy part of asymmetric membranes, enzyme immobilization results in either a uniform fixation of enzymes throughout the membrane wall, or in the formation of a carrier-enzyme insoluble network in the sponge of the membrane. Mass transfer through this solid phase must therefore be taken into account. A theoretical model neglecting radial convective transport and the dense layer in asymmetric membranes is available in the literature.81 The reacting solution is still assumed to be fed to the core of the hollow fibers. Steady state, laminar flow, and isothermal conditions are assumed. Moreover, the enzymes are assumed to be uniformly distributed and the membrane wall curvature is neglected. Differential dimensionless mass balance equations can be written as follows ... [Pg.458]

Adoption of this approach to microbial process development cannot occur until methods exist for determining the influence of reactor design and operating parameters on single-cell metabolic control actions and reaction rates. If this Information is available, population balance equations and associated medium conservation equations provide the required bases for reactor analysis (1, ). For example, for a well-mixed, continuous-flow Isothermal mTcroblal reactor at steady-state, the population balance equation may be written ... [Pg.135]

Once the effective rate forms at the particle/bubble level are established, and flow patterns as assumed in Figure 6.2 are available, one simply uses these effective rate expressions to write down the corresponding steady-state material balances for the reactor for the assumed flow patterns. Under steady-state conditions, this involves either first-order ordinary differential equations for the phases in which plug flow is assumed or simple difference equations in species concentration in phases in which completely mixed flow is assumed. The treatment in all these cases is very similar to what will be in a single-phase reactor (see, e.g.. Ref [48]), except that one has a separate differential equation balancing for each species concentration and they are coupled through the effective reaction rate term. [Pg.143]

The main advantage of this method is that it enables the size of individual flows to be determined and makes it possible to establish the general material balance, when data are available concerning the yields of the reaction products in one cycle of the passage of the raw material through the individual reactors (reaction units) when the process is in the steady state. [Pg.43]


See other pages where Steady flow, availability balance is mentioned: [Pg.239]    [Pg.189]    [Pg.481]    [Pg.229]    [Pg.144]    [Pg.11]    [Pg.427]    [Pg.648]    [Pg.380]    [Pg.1035]    [Pg.815]    [Pg.10]    [Pg.107]    [Pg.12]    [Pg.334]    [Pg.196]    [Pg.651]    [Pg.90]    [Pg.11]    [Pg.232]    [Pg.806]    [Pg.272]   
See also in sourсe #XX -- [ Pg.144 ]




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Steady balance

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