Volume steady state

The bioreactor involves sterile feed (C = 0) and constant volume steady state conditions imply that... 

Fig. 7.19 Dependence of the normalized fragment velocity of 16 explosives (Cu cylinder) on the expansion volume. Steady-state at velocity/final Velocity = 1.

The term chemostat refers to a tank fermentation which is operated continuously (Fig. 3.23). This bioreactor mode of operation normally involves sterile feed (Xq = 0) and constant volume, steady state conditions, meaning that dV/dt = 0, d(VSi)/dt = 0, d(VXi)/dt = 0. 

System = contents of turbine (open, constrant volume, steady-state)... 

A steady-state material balance can be carried out on a small section of length and volume (on the basis of unit cross-sectional area) ia the contactor ... 

At any point within the boundary layer, the convective flux of the macromolecule solute to the membrane surface is given by the volume flux,/ of the solution multipfled by the concentration of retained solute, c. At steady state, this convective flux within the laminar boundary layer is balanced by the diffusive flux of retained solute in the opposite direction. This balance can be expressed by equation 1 ... 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

SJng Je Rod-Fed Electron Beam Source. The disadvantages of multiple sources for alloy deposition can be avoided by using a single wire-fed or rod-fed source (Fig. 3) (3). A molten pool of limited depth is above the soHd rod. If the equiUbrium vapor pressures of the components of an alloy A B are in the ratio of 10 1 and the composition of the molten pool is A qB, under steady-state conditions, the composition of the vapor is the same as that of the soHd being fed into the molten pool. The procedure can be started with a pellet of appropriate composition A qB on top of a rod A B to form the molten pool initially, or with a rod of alloy A B to evaporate the molten pool until it reaches composition A qB. The temperature and volume of... 

Interaction between Gaseous and Condensed Phases. In a closed vessel of volume Ucontaining a nonionized, unexcited molecular gas having total number of molecules A/, the change in the pressure P in the gas can often be predicted if the steady-state absolute temperature Tis changed to another steady, constant level ... 

A useful simphfication of the total energy equation applies to a particular set of assumptions. These are a control volume with fixed solid boundaries, except for those producing shaft work, steady state conditions, and mass flow at a rate m through a single planar entrance and a single planar exit (Fig. 6-4), to whi(m the velocity vectors are perpendicular. As with Eq. (6-11), it is assumed that the stress vector tu is normal to the entrance and exit surfaces and may be approximated by the pressure p. The equivalent pressure, p + pgz, is assumed to be uniform across the entrance and exit. The average velocity at the entrance and exit surfaces is denoted by V. Subscripts 1 and 2 denote the entrance and exit, respectively. 

The primary function of a continuous thickener is to concentrate sus-penaed solids by gravity settling so that a steady-state material balance is achieved, solids being withdrawn continuously in the underflow at the rate they are supphed in the feed. Normally, an inventory of pulp is maintained in order to achieve the desired concentration. This volume will vary somewhat as operating conditions change on occasion, this inventoiy can be used for storage of sohds when reed and underflow rates are reduced or temporarily suspended. 

This is an old, familiar analysis that applies to any continuous culture with a single growth-limiting nutrient that meets the assumptions of perfect mixing and constant volume. The fundamental mass balance equations are used with the Monod equation, which has no time dependency and should be apphed with caution to transient states where there may be a time lag as [L responds to changing S. At steady state, the rates of change become zero, and [L = D. Substituting ... 

Constant Flow into Protected Equipment For the steady-state design scenario with a constant, steady flow of fluid from a pressure source that is above the maximum aUowed pressure in the protected equipment, volume is being generated within the equipment at a rate RV = F/ f. Substituting into Eq. (26-21) and noting that the specific volume of the vent stream is l/p, gives the required mass flow rate ... 

As another example of the first interac tion, a potential parameter in the analysis of the CSTR is estimating the actual reactor volume. CSTR shown in Fig. 30-7. The steady-state material balance for this CSTR having a sin e reaction can be represented as ... 

Models which assume uniform mixing throughout the volume of a three-dimensional box are useful for estimating concentrations, especially for first approximations. For steady-state emission and atmospheric conditions, with no upwind background concentrations, the concentration is given by... 

With the above as an introduction, we now consider the important operational case of filtration performed under constant pressure. In practice, all the parameters defined above are nearly constant under steady state conditions except V and r, which are varied by the operator. We may therefore integrate the working expression for filtration over the limits of volume from 0 to V, and for residence time over the limits of 0 to x ... 

Applying the steady state equations for the free radieals H, CH3, and C2H5, the rate of formation of ethylene C2H4 for a eonstant volume bateh reaetor is ... 

Applying the rate expressions to Equations 1-222, 1-223, 1-224, 1-225 and 1-226, and using the steady state approximation for CH3, C2H5, and H, for a eonstant volume bateh reaetor yields ... 

Industrial reactors operate in the steady state with the volume, concentration, and temperature of the reaction mixture being constant... 

Consider a first order, exothermic reaction (aA —> products) in a CFSTR having a constant supply of new reagents, and maintained at a steady state temperature T that is uniform throughout the system volume. Assuming perfect mixing and no density change, the material balance equation based on reactants is expressed as uC g = +... 

Briggs and Haldane [8] proposed a general mathematieal deseription of enzymatie kinetie reaetion. Their model is based on the assumption that after a short initial startup period, the eoneentration of the enzyme-substrate eomplex is in a pseudo-steady state (PSS). Eor a eonstant volume bateh reaetor operated at eonstant temperature T, and pH, the rate expressions and material balanees on S, E, ES, and P are... 

The growth of Mehylomonas L3 on methanol was observed in a CSTR. Working volume of the tank was V = 0.355 L. The eon-eentration of methanol in fresh medium was 1 g/L. The results of the experiment at a steady state are given in the following table [24]. 

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