Simple formulas

Fig. 5 systematic error of the simple formula (3) compared to the correct model according equation (2) depending on the ratio of film focus distance to pipe diameter. The wall thickness calculated according to (3) is smaller then (2) by the given error. 

Let us consider the calculation of sensitivity threshold in the case when the cracks are revealing by PT method. Constant distance H between crack s walls along the whole defect s depth is assumed for the simplicity. The calculation procedure depends on the dispersity of dry developer s powder [1]. Simple formula has to be used in the case when developer s effective radius of pores IC, which depends mainly on average particle s size, is smaller than crack s width H. One can use formula (1) when Re is small enough being less than the value corresponding maximum sensitivity (0,25 - 1 pm). For example. Re = 0,25 pm in the case when fine-dispersed magnesia oxide powder is used as the developer. In this case minimum crack s width H that can be detected at prescribed depth lo is calculated as... 

According to the simple formula, the maximum bubble pressure is given by f max = 27/r where r is the radius of the circular cross-section tube, and P has been corrected for the hydrostatic head due to the depth of immersion of the tube. Using the appropriate table, show what maximum radius tube may be used if 7 computed by the simple formula is not to be more than 5% in error. Assume a liquid of 7 = 25 dyn/cm and density 0.98 g/cm. ... 

Body washes are another more recent introduction into the marketplace. These products have become a mainstay in the European market and, in only a few years, have grown to be a significant fraction of the U.S. market. Body washes can be simple formulas similar to those used for Hquid handsoaps or complex 2-in-l oil-in-water emulsion, moisturizing formulations. These products contain a wide range of synthetic surfactants not typically found in bar... 

The capacity of vibrating conveyors is extremely broad, ranging from thousands of tons down to grams or ounces. Since so many variables affect their abihty to convey, there is no simple formula for figuring capacity and power. Available data are generally the results of... 

The identity of eqs. (2.6) (at T = 0) and (3.47) for the cubic parabola is also demonstrated in appendix A. Although at first glance the infinite determinants in (3.46) might look less attractive than the simple formulas (2.6) and (2.7), or the direct WKB solution by Schmid, it is the instanton approach that permits direct generalization to dissipative tunneling and to the multidimensional problem. 

The importance of present worth, also known as present value, lies in the fact that time is money. The preference between a dollar now and a dollar one year from now is driven by the fact that a dollar in-hand can earn interest. Present value can be expressed by a simple formula ... 

There are several different definitions relating to second moments in the literature, and it is necessary to take care when applying seemingly simple formulae that involve such quantities. Not only that, authors often use the same name for the different definitions. 

Cocking 1 has constructed a simple formula by which the amount of free alcohol may be accurately determined in the presence of any ester or mixture of esters, providing that these are unaffected by acetylation. 

For the case of a binary system with linear adsorption isotherms, very simple formulas can be derived to evaluate the better TMB flow rates [19, 20]. For the linear case, the net fluxes constraints are reduced to only four inequalities, which are assumed to be satisfied by the same margin /3 (/3 > 1) and so ... 

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

For a particular material of pipeline construction, the friction factor can be assumed. This allows a simple formula to be derived ... 

The study of liquids is divided into two main parts liquids at rest, hydrostatics and liquids in motion, hydraulics. The effect of liquids at rest can often be expressed by simple formulas. The effects of liquids in motion are more difficult to express due to frictional and other factors whose actions cannot be expressed by simple mathematics. 

The interpretive difficulty has been discussed in detail by Pawel and by Mortonin papers which appeared almost simultaneously. Both authors use arguments to show that the simple formula of bending-beam theory utilised by Stoney... 

This simple formula does not apply to pH values over 9 0, and high salinities affect its accuracy. The term (pKj - pKJ is a function of temperature and ionic strength (dissolved solids). In an analysis of a given water at a constant temperature much useful information can be obtained from the equation. 

The generalization of this simple formula to the case when p 1/2 is straightforward. In this case, each of the eight possible 3-tuple neighborhoods a = 010203 ... 

Allicin is responsible for the distinctive taste and odor of garlic Its simple formula is C6H10O2S. How many grams of sulfur can be obtained from 25.0 g of allicin ... 

In previous chapters we have referred from time to time to compounds of the transition metals. Many of these have relatively simple formulas such as CuSO CrCI3, and FetNO These compounds are ionic The transition metal is present as a simple cation (Cu2+, Cr3+, Fe3+). In that sense, they resemble the ionic compounds formed by the main-group metals, such as CaS04 and AKNOJ ... 

The results of [91] supply ample evidence in support of this qualitative picture. The authors determined the baric viscosity factor b = [0 In j/(0P)-1] T (where t] is viscosity, P is pressure) for impact-resistant polystyrene filled with antimony trioxide. The viscosity piezocoefficient is known to be related to the free volume. A very simple formula for this relationship has been proposed in [92] in this form ... 

In this early work, both initiation and termination were seen to lead to formation of structural units different from those that make up the bulk of the chain. However, the quantity of these groups, when expressed as a weight fraction of the total material, appeared insignificant. In a polymer of molecular weight 100,000 they represent only ca 0.2% of units Thus, polymers formed by radical polymerization came to be represented by, and their physical properties and chemistry interpreted in terms of, the simple formula 1. 

The set of central second moments is related to the autocorrelation function by means of the following simple formula,... 

Variation of the relaxation times subject to x = 1 /T is shown in Fig. 6.3. It is really monotonic, and after the Q-branch collapse it can be describe by a very simple formula... 

Figure 13-5 is the box model of the remote marine sulfur cycle that results from these assumptions. Many different data sets are displayed (and compared) as follows. Each box shows a measured concentration and an estimated residence time for a particular species. Fluxes adjoining a box are calculated from these two pieces of information using the simple formula, S-M/x. The flux of DMS out of the ocean surface and of nss-SOl back to the ocean surface are also quantities estimated from measurements. These are converted from surface to volume fluxes (i.e., from /ig S/(m h) to ng S/(m h)) by assuming the effective scale height of the atmosphere is 2.5 km (which corresponds to a reasonable thickness of the marine planetary boundary layer, within which most precipitation and sulfur cycling should take place). Finally, other data are used to estimate the factors for partitioning oxidized DMS between the MSA and SO2 boxes, for SO2 between dry deposition and oxidation to sulfate, and for nss-SO4 between wet and dry deposition. 

The solution for Ya is simple, even elegant, but what is the value of F It is equal to the mass holdup divided by the mass throughput. Equation (1.41), but there is no simple formula for the holdup when the density is variable. The same gas-phase reactor will give different conversions for A when the reactions are A 2B and A —> B, even though it is operated at the same temperature and pressure and the first-order rate constants are identical. 

The simple formula Review the principles until you understand how each of them fits into the plot then focus all of your remaining time on solving problems. Don t worry. The course is not that bad if you approach it with the right attitude. This book will act as a road map for your studying efforts. 

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