Use Of Nomographs Research Articles

Biodegradation of Some Organic Materials in Soils and Soil Constructions: Experiments, Modeling and Prevention.

The decomposition of natural and synthetic polymeric materials (peat, humates, biochar, strongly swelling hydrogels and other soil conditioners) in a biologically and chemically active soil environment inevitably leads to a reduced ability to improve the structure, water-retention, absorptive capacity and fertility of artificial soil constructions in urbanized ecosystems and agro landscapes (constructozems). Quantitative assessment of the biodegradation process using field and laboratory incubation experiments, as well as mathematical modeling, showed the possibility of significant (up to 30–50% per year) losses of organic matter of constructozems and a corresponding deterioration of soil quality. Incubation experiments that track the carbon dioxide emission rates of polymeric materials under given thermodynamic conditions allow for the estimation of decomposition rates in addition to an exploration on the dependence of such rates on additions of microbial inhibitors. The use of nomographs provide an opportunity to optimize long-term amendment performance in soil constructions by identifying the most favorable depths to apply amendments to ensure stable functioning during desired in-service timelines in the built environment. The results of the study are useful for geo-engineers and landscaping practitioners.

Direct determination of the width or the height for a box culvert applying dimensionless equations

To determine dimensions of a rectangular culvert section, current design approaches need several trial calculations. It is a standard approach in the culvert section design to use nomographs provided by the Federal Highway Association. The height and the width of a box culvert are two basic unknowns. The approach proposed here assumes that the height or the width is known and the approach directly determines the other unknown variable without further trial calculations. The use of nomographs may be a major obstacle for computer modeling. It may also result in subjective errors when reading the graph. In order to find an explicit way of solving this problem, approximate relations of the hydraulic radius to shape factor was devised for a rectangular culvert. Then, the computational equations for the width or height of a box culvert were derived using dimensionless variables. Reasonable initial values were also proposed to solve the nonlinear computational equations. A verification test was performed by way of a worked example. Using the governing equations and the initial values, one can find a computer solution of box culvert dimensions.

A Practical Approach for Cost/Benefit Analysis of Early Design Decisions: Application to Architectural Daylighting

Although several methods exist for performing cost/benefit analysis in architecture, mechanical and civil engineering, etc., the use of these methods in early design phases remains limited. Realizing the importance of the decisions made early in the design process and their effect on cost performance, several research efforts have developed tools and aids to help design professionals perform early cost/benefit analyses. Examples include rules of thumb, simplified formulae, algorithms, spreadsheets and nomographs. Nomographs have been developed to help in cost/benefit analyses for various applications such as generic time-value of money analysis, mechanical equipment sizing, engineering, architectural design, etc. This paper compares and discusses the use of nomographs in relation to specialized spreadsheets as tools for practical cost/benefit analysis. The paper suggests that spreadsheets in general offer a more effective and robust analysis tool when it comes to cost/benefit analysis in the built environment fields, especially for decisions in the early stages of design. The superiority of spreadsheets to nomographs is demonstrated through a practical cost/benefit analysis application to architectural daylighting design decisions. The spreadsheet method has several advantages over the nomograph method, which are explored through an actual case study of daylight cost/benefit analysis for the Kuwait Autism Center. The comparisons can be generalized for several disciplines and domains in other parts of the world.

Prediction of Size Distribution of Particles Penetrating Dry Cyclone Separators

The efficiency of cyclones varies widely with the size of particles and complex mathematic formulations are used for predicting the collection efficiency of a single particle size. Numerical integration of the latter, in conjunction with the appropriate in each case input particle size distribution, or direct use of nomographs if lognormal input particle size distribution can be assumed, yields the overall efficiency. In either case, no information is available regarding the size distribution of the penetrating particles. As shown in this paper, lognormal input particle size distributions yield lognormal output particle size distributions. Based on this and on the analysis of functional relations, a set of nomographs is developed directly yielding the mean diameter and standard deviation of penetrating particles as a function of the input particle size distribution parameters and key cyclone design and operating conditions. The above set the stage for the rigorous computation of the size-specific emissions from cyclones and the overall and size-specific efficiencies of secondary control systems that may follow. This analysis is in line with current trends, which, on the basis of health considerations, place emphasis on the size-specific rather than on the overall particle emissions.

Designing an effective exponential cusum chart without the use of nomographs

The development of control charts for monitoring processes associated with very low rates of nonconformities is increasingly becoming more important as manufacturing processes become more capable. Since the rate of nonconformities can typically be modeled by a simple homogeneous Poisson process, the perspective of monitoring the interarrival times using the exponential distribution becomes an alternative. Gan (1994) developed a CUSUM-based approach for monitoring the exponential mean. In this paper, we propose an alternative CUSUM-based approach based on its ease of implementation. We also provide a study of the relative performance of the two approaches.

Design of Sewers Based on Minimum Velocity

For the computation of uniform flow velocity and discharge in partially filled circular sewers Manning's equation is used. Determination of the hydraulic and geometric elements of flow requires either iterative solutions of the Manning's equation or use of nomographs prepared for this purpose. Both methods are time consuming. A procedure is described for the direct determination of the slope of a partially filled sewer when the minimum velocity of flow is specified. Alternately, the depth of flow can be calculated when the slope is given. The diameter of the sewer and the minimum flow rate expected must be known. The equations developed are valid for circular sewers for which the depth of flow is less than 40% of the sewer diameter representing a reasonable range of initial design conditions. The maximum error between the actual water depths and those computed by the approximate equations is ±2.4%. This is much less than the probable error in selecting an appropriate value for the roughness coefficient.

Simple Method for Determination of Substation Spacing for AC and DC Electrification Systems

A simple method for the determination of traction power substation spacings is developed for ac railroad electrification systems. Single-end-feed, center-feed, and double-end-feed systems with or without booster transformers can be represented, being the most common supply configurations. The method is extended to include autotransformer systems and can also be used for calculation of substation spacings for dc light rail and heavy rail systems. The entire power system is represented, including the electric utility system, the traction substations, the catenary system or third rail, the return current system, and the trains. Multitrack systems can be approximated, and effects of currents at harmonic frequencies produced by the electrical locomotives are evaluated. The mathematical description results in a number of equations suitable for microcomputer solution. The use of the method is demonstrated a sample case, and a convenient way of presenting the substation spacings for a given set of conditions is illustrated by the use of nomographs.

Nomograph for Thicknesses Calculation in a Filament-Wound Pressure Vessel

The use of nomographs in engineering has been in decline for some years; however, there are still engineering applications where charting the equations is a useful aid in understanding the problem at hand. The nomograph, a representation of a large number of equations, possesses a number of advantages; it consists of very few lines and is easy to construct, requires little skill to use, and permits immediate visualization of the changes in one parameter due to changes in other parameters. The fundamental principle in constructing the chart is simply representing the equations by means of scales along certain straight lines.

Gravity Nomographs for Fault Solutions

The gravity field over high angle faults is characterized by linear zones of high gravity gradient. The total anomaly caused by a fault, the difference in gravitational attraction between the high and low sides of the gradient zone, is a function of throw of the fault. An equation that expresses this relationship provides a graphical solution of fault displacements when put into the form of a nomograph. The horizontal gradient of the field in a direction perpendicular to the strike of the fault is related to the depth of the plate produced by faulting. The gradient is obtained by differentiation and provides a graphical solution to the mean depth of a faulted plate when put into the form of a nomograph. Two measurements made on the gravity map, the total anomaly and maximum gradient, and the use of nomographs are all that is necessary to solve fault problems when the geometry of the structures is near ideal and the assignment of densities is realistic.

Use of nomographs in computing procedures for drilling boreholes

Use of nomographs in computing procedures for drilling boreholes

Use of Nomographs for Routine Calculations in Infrared Spectrophotometry

Various devices are used to reduce the labor of calculating the concentrations of components with mutually interfering bands in quantitative infrared analysis. Computers (7) or IBM equipment (8,10) may be used for complex systems, or successive approximation methods (3,5,11) may be satisfactory. For systems of two or three components, exact solutions can be obtained by solving simultaneous equations (4,6), but such a procedure becomes tedious when large numbers of samples are involved. It is the purpose of this note to point out that nomographs can be easily constructed which give exact solutions to these simultaneous equations with a minimum of effort. Several forms of nomographs have been suggested for this purpose (2,9,12), but the type described here seems to offer some advantages in ease of construction and use.

A nomograph for conversion of Fourier coefficients occurring in geomagnetic computations

Whenever a numerical operation of standard type is to be repeated a great number of times, as often occurs with geomagnetic material of statistical character, the use of nomographs may prove convenient, since it represents a considerable saving of time, provided that the amount of work is large enough to compensate the time of preparing and drawing the nomograph. In the present note, attention is drawn to the practical advantages of this method, widely used in other branches of geophysics and in engineering.A very simple example is given by the following case, referring to an analysis of S and L at Batavia. In the course of that investigation, a great number of pairs of harmonic coefficients representing diurnal and semidiurnal variations on individual days had to be transformed in amplitude and phase due to a change, in 1920, of the tabulating scheme adopted by that observatory. Starting with January 1, 1920, hourly mean values according to standard time (105° meridian) were published instead of instantaneous values for local mean time. Therefore, the harmonic coefficients for days after January 1, 1920, must be reduced in the following way:

The Calculation of Alkalinities and Free Carbon Dioxide in Water by the Use of Nomographs

The Calculation of Alkalinities and Free Carbon Dioxide in Water by the Use of Nomographs

Insulation resistance of armature windings

Insulation resistance of the windings of an electric machine may be used as a barometer for indicating the condition of the windings. On the basis of tests on many machines of different types it is recommended that all insulation resistance readings be taken after the application of 500 volts (d-c) for one minute. The slope of the resistance-time curve at that point gives a combined indication of the moisture content and the quality of the insulation. In this paper are given formulas for the insulation resistance of different types of windings derived from the winding insulation dimensions and expressed in terms of the rated voltage, capacity, and speed of the machine. By the use of nomographs, insulation resistances can be determined in about 15 second's time; 5 of these prepared for different types of machines are included in the paper.

Insulation Resistance of Armature Windings

Insulation resistance of the windings of an electric machine may be used as a barometer for indicating the condition of the windings. On the basis of tests on many machines of different types it is recommended that all insulation resistance readings be taken after the application of 500 volts (d-c) for one minute. The slope of the resistance-time curve at that point gives a combined indication of the moisture content and the quality of the insulation. In this paper are given Formulas for the insulation resistance of different types of windings derived from the winding insulation dimensions and expressed in terms of the rated voltage, capacity, and speed of the machine. By the use of nomographs, insulation resistances can be determined in about 15 second's time; 5 of these prepared for diferent types of machines are included in the paper.