Computing rates convenient factorization

Many factors affect dry deposition, but for computational convenience air quaUty models resort to using a single quantity called the deposition velocity, designated or to prescribe the deposition rate. The deposition velocity is defined such that the flux T of species i to the ground is... 

In treating the simultaneous burning of both fast and slow coke, it is convenient for computation purposes to reformulate the slow-coke kinetics in terms of a new effectiveness factor t)t. The total rate of slow coke burning dyjdt)j of Eq. (12) is set equal to r)j(dyjdt)i ... 

Increasing attention is being given to developing methods to predict failure rate data for process equipment and systems. Such methods are beginning to appear in published literature. These methods include correlations, factored estimation procedures, and analogies to predict equipment failure rates. They are desirable because they offer efficient means of providing equipment failure rate data for risk assessments, and they can be conveniently incorporated into computer software. 

The concentration history appears to be a function of three dimensionless parameters, a modified Thiele modulus, y, the mass Biot number, gj, and the dimensionless feed concentration, /3. The set of non-linear equations is uncoupled by introducing an effectiveness factor, r, and numerically solved. In order to reduce computer time, the effectiveness factor has been conveniently expressed as a weighted sum of its value for the zero and first order reaction rate. Different regime conditions are depicted in terms of a dimensionless parameter,... 

It is convenient to define the size factor, Sj, for task j, as the capacity required per unit of product. Commonly, it is defined as the volume required to produce a unit mass of product. For example, for the third cultivator in the tPA process of Sections 3.4 and 4.5, 4,000 L of medium yields 2.24 kg of tPA, which eventually yields 1.6 kg of final tPA product. Consequently, its size factor is 4,000 L/ 1.6 kg = 2,500 L/kg tPA product. Size factors can be computed for each task in a recipe. Normally, equipment vessel sizes are selected that exceed batch volume by 10 to 20%. Clearly, the batch factor in volume/mass produced is determined by the rate of processing the batch (e.g., kg/hr) multiplied by the batch time (hr) and divided by the density of the batch (kg/L) and the mass of product produced (kg). 

Contemporary Fracture Mechanics recognises the crack-tip stress singularity represented by the stress intensity factor as a fiction — emphasising, in its place, the role of die crack-tip cohesive zone which aimuls it. This movement in Fracture Mechanics conveniently reconciles physically-based models of damage and cohesion with computational models which represent cohesion as a holding-back force in order to calculate the energy release rate. 

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