Common Calculations

Overheads in the chemical-process industries are commonly calculated as a percentage of (I) direct materials cost, (2) direct labor cost, or (3) prime or direct costs. Other methods of allocating overheads are on the basis of (I) plant area, (2) number of employees, (3) capital value, and (4) elec tric power. 

More extensive data can be found in standard references such as Perry s Chemical Engineering Handbook or the CRC Handbook of Chemistry and Physics. The following table, however will provide some basic information for many common calculations that the process engineer can easily run on his or her PC. 

The raw output of a molecular structure calculation is a list of the coefficients of the atomic orbitals in each LCAO (linear combination of atomic orbitals) molecular orbital and the energies of the orbitals. The software commonly calculates dipole moments too. Various graphical representations are used to simplify the interpretation of the coefficients. Thus, a typical graphical representation of a molecular orbital uses stylized shapes (spheres for s-orbitals, for instance) to represent the basis set and then scales their size to indicate the value of the coefficient in the LCAO. Different signs of the wavefunctions are typically represented by different colors. The total electron density at any point (the sum of the squares of the occupied wavefunctions evaluated at that point) is commonly represented by an isodensity surface, a surface of constant total electron density. 

In the case of noncarcinogenic substances, there exists a threshold this is an exposure with a dose below which there would not be adverse effect on the population that is exposed. This is the reference dose (RfD), and it is defined as the daily exposure of a human population without appreciable effects during a lifetime. The RfD value is calculated by dividing the no observed effect level (NOEL) by uncertainty factors. When NOEL is unknown, the lowest observed effect level (LOEL) is used. NOEL and LOEL are usually obtained in animal studies. The main uncertainty factor, usually tenfold, used to calculate the RfD are the following the variations in interspecies (from animal test to human), presence of sensitive individuals (child and old people), extrapolation from subchronic to chronic, and the use of LOEL instead of NOEL. Noncancer risk is assessed through the comparison of the dose exposed calculated in the exposure assessment and the RfD. The quotient between both, called in some studies as hazard quotient, is commonly calculated (Eq. 2). According to this equation, population with quotient >1 will be at risk to develop some specific effect related to the contaminant of concern. 

The density of a substance is commonly calculated in chemistry. The density (D) of an object is calculated by dividing the mass of the object by its volume. (Some authors will use a lowercase d to represent the density term be prepared for either.) Since density is independent of the quantity of matter (a big piece of gold and a little piece have the same density), it can be used for identification purposes. The most common units for density in chemistry are g/cm3 or g/mL. 

The other computation is that of relative bioavailability. This calculation is determined when two products are compared to each other, not to an intravenous standard. This is commonly calculated in the generic drug industry to determine that the generic formulation (e.g., a tablet) is bioequivalent to the original formulation (e.g., another tablet). Thus, bioavailability is not routinely calculated in an individual patient but reserved for product development by a drug manufacturer. However, it is important to have an idea of how formulations or routes of administration differ with respect to bioavailability so as to allow proper dosage adjustment when changing formulations or routes of administration. 

Indeed, these values appear to be more constant for various polymers than those commonly calculated. Fractions y>fi and corresponding state at glass temperature. From Eqs. (59) it follows that at Tt the ratio of hole volume to expansion volume must be constant, the latter being determined by translational movements of molecules. In particular, these values are present in the equation describing T as a function of degree of polymerization. 

Volume of distribution is commonly calculated for a particular patient using body weight (70 kg body weight is assumed for the values in Table 3-1). If a patient is obese, drugs that do not readily penetrate fat (eg, gentamicin and digoxin) should have their volumes calculated from ideal body... 

The ab initio reaction energy that is most commonly calculated is simply the difference in ZPE-corrected energies, AE 1, which is the reaction enthalpy change at 0 K (Eq. 5.181). This provides an easily-obtained indication of whether a reaction is likely to be exothermic or endothermic, or of the relative stabilities of isomers. Table 5.9 illustrates this procedure. The results are only semiquantitatively correct, and the HF/6-31G method is not necessarily better here than the HF/3-21G for such direct (simple subtraction) energies. In fact, it has been documented by... 

The example provided in Table 2 is for a four component mixture of hydrocarbons (methane, ethane, propane, and n-octane). The weighting method is a common calculation procedure that process engineers will encounter many times. Computations for simple systems can be easily set up on an Excel spreadsheet. 

As stated in section 2.10, the velocity by which groundwater flows is commonly calculated from the water table gradient and the coefficient of permeability (k, or the related parameter of transmissivity). The k value is determined by a pumping test. During such a test a studied well is intensively pumped and the water table is monitored in it as well as in available adjacent observation wells. The change in water table level as a function of the pumping rate serves to compute the aquifer permeability. 

Total product costs are commonly calculated on one of three bases namely, daily basis, unit-of-product basis, or annual basis, The annual cost basis is probably the best choice for estimation of total cost because (1) the effect of seasonal variations is smoothed out, (2) plant on-stream time or equipment-operating factor is considered, (3) it permits more-rapid calculation of operating costs at less than full capacity, and (4) it provides a convenient way of considering infrequently occurring but large expenses such as annual turnaround costs in a refinery. 

The proportions of raw materials are commonly calculated on the basis of the above parameters, most obviously by setting up and solving simultaneous equations to fix n parameters, /i -1- I raw materials of appropriate composition are required. It is also necessary to consider the desired or allowable contents of minor components. 

Currently the bulk of aU N uptake rates ever measured have used some form of glass fiber filter. As a result, the rates represent uptake by autotrophs as well as a variable fraction of the bacterial community. This has broad implications when one considers the use of such commonly calculated parameters as the f-ratio, the ratio of new to... 

Calculations involving mineral saturation state (D in Equations (19) and (20)) are dependent on accurate characterization of the thermodynamic states of the reactants and products and are commonly calculated using speciation codes (see Chapter 5.02 for additional information). Although the equilibrium constants for most simple primary silicates have been determined, thermodynamic data do not exist for many complex silicates or for solid solutions. 

The reference substance for liquids and solids is normally water. Thus the specific gravity is the ratio of the density of the substance in question to the density of water. The specific gravity of gases frequently is referred to air, but may be referred to other gases, as discussed in more detail in Chap. 3. Liquid density can be considered to be nearly independent of pressure for most common calculations, but, as indicated in Fig. 1.1 it varies somewhat with temperature therefore, to be very precise when referring to specific gravity, state the temperature at which each density is chosen. Thus... 

Because measurements depending on wb rely on the accurate positioning of tangents to the chromatographic peak, another common calculation of N uses the more easily measured peak width at half-height, where w0.s = 2.354o. 

The ab initio reaction energy that is most commonly calculated is simply the difference in ZPE-corrected energies, which is the reaction enthalpy change at... 

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