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By J Cortinez, P Vallejos, J Yianatos, M Rodriguez

Nowadays, one of the main problems in current flotation plants and new projects is the significant decrease in feed grades and changes in the mineral composition, which has an important effect on the mineral liberation and associations. Additionally, flotation plants usually operate with feed throughput higher than the original design, which has a significant impact on the feed particle size. All these conditions affect metallurgical performance, and must be evaluated and addressed, by improving control strategies for banks optimisation. For this purpose, the flotation of valuable minerals along the circuits requires better understanding, considering the compromise between performance and selectivity in flotation circuits. This paper presents a characterisation of the different minerals recovered along industrial flotation circuits. Plant sampling campaigns, performed in a copper industrial concentrator in Chile, provided the data for the study. Two rougher flotation banks consisting of cells of 130 m3 and 300 m3 were analysed. All the samples from the industrial surveys were analysed by screening and mineralogy, and the mineral recovery along the circuits was evaluated per particle size class, liberation class, type of associations, and others. Additionally, operating data on froth depth profiles complemented the evaluation of the mineral composition of concentrate streams, along the circuit. The results allowed for identifying and quantifying the main factors that affect the copper recovery and concentrate grade along the flotation banks. It was found that minerals with liberation lower than 50 per cent have a significant impact on the recovery. On the other hand, the decrease in the Cu grade in concentrates along the flotation circuits is mainly due to the relative increase of middling minerals (less liberated), non-valuable floatable minerals, such as free pyrite, and gangue entrainment. The characterisation of the gangue entrainment flow rate along the flotation banks showed a strong relationship with froth depth, which becomes more critical towards the last cells of the banks.

Aug 24, 2022

By A E. Waltho, W J. Shaw

Predicting the physical characteristics of various ore types has for long been a difficult problem during mining. Grade control practices tend to concentrate on the chemical grade of the ore. Estimation of physical characteristics such as beneficiation behaviour is commonly limited to the simplistic application of historical averages. Large amounts of geochemical data are often gathered during the exploration and mining stages of a project, especially in ferrous and base metal deposits. In addition to the elements of principal economic interest, samples are often analysed for suites of gangue constituents to determine whether the mineralisation lies within target specifications. This multi-element data is often put to no other use than this simple chemical classification, yet it may present the geologist or metallurgist with valuable insights into the mineral content and physical characteristics of the deposit. Normative mineral estimates have been used as a method for characterising igneous rocks for almost 100 years. The method establishes and applies a set of sequential rules, by which the chemical components of a sample are assigned to mineral components. Provided that it is possible to make some realistic assumptions about the mineral species likely to be present in a rock unit or deposit and their paragenesis, this approach can be extended to a variety of mineral deposits. The geochemical data that are routinely collected when, for example, drilling iron ore and base metal deposits, can be used to derive estimates of normative mineral content. These estimates can be used to characterise physical or metallurgical aspects of the ore, such as density, beneficiation behaviour and metal recovery. This paper examines the application of normative mineral estimates to a variety of practical resource characterisation problems. The potential for predicting the lump and fines proportions of iron and manganese ores is also discussed.

Jan 1, 1999

By D Johns, L Murray

This paper discusses pore pressures in the embankments of tailings dams by comparing real world data with common design assumptions. Assessment of pore pressures has implications on material behaviour interpretation from CPT investigations and, therefore, on the design. For example, the assumption of hydrostatic pressure is conservative for limit equilibrium stability analyses but may be un-conservative in assessing the potential for contractive behaviour and strength loss during shearing. This paper presents some real world data, the investigation methods to determine the pore pressures, and subsequent interpretation of CPT data and material parameters such as the state parameter. It also examines the design implications of assuming a hydrostatic pressure distribution, by comparing results from that assumption with those obtained using the real pore pressures.CITATION:Johns, D and Murray, L, 2018. Characterisation of pore pressure in tailings dams and the implications for design, in Proceedings Mine Waste and Tailings Stewardship Conference 2018, pp 239–249 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 23, 2018

By Y. Belloa, C. Dorfling

The presence of impurities such as Se and Te in copper sulfate leach solutions can have a detrimental effect on electrowinning efficiency. These elements can be removed from the solution by precipitation; sulfurous acid is commonly used as a precipitation reagent, while studies have also reported improved precipitation with the addition of metallic copper. This paper aimed to determine the effect of conditions used during the solution purification step on the characteristics of the precipitates that formed. Precipitation tests were performed in a batch reactor with copper sulfate leach solutions obtained from the base metal refinery of a platinum group metal producer. The effects of agitation rate (250 and 500 rpm), SO2 flow rate (4.4 and 5.8 mL/min.L), temperature (65 and 95°C) and metallic copper powder addition (0, 1 and 2 g/L) on the characteristics of the precipitates formed during the tests were determined using scanning electron microscopy. The major phases detected in the precipitates formed when using SO2 as the only precipitation reagent were elemental Se and Cu2Se. The introduction of copper powder led to the production of different sulfide phases for the experiments conducted at 65°C irrespective of the values of the other reaction parameters. At 95°C, Cu crystals, Cu2O and tiny inclusions of Cu2(Se,Te) were the prominent phases noticed in the precipitates produced from all the tests conducted with copper powder as precipitation enhancing reagent. Keywords: copper, precipitation, selenium, tellurium

Jan 1, 2020

By S Slouka

Airborne rock dust poses serious long-term health complications to workers in the underground mining and civil environment where rock excavation is utilised. During drilling, airborne rock particles are immediately released into the breathable environment where additionally, the settled dust can be reintroduced into the air further down in production. The purpose of this study is to build a characterisation suite of dust particles such that underground operations can implement more appropriate dust suppression and mitigation techniques in accordance to pick wear. Therefore, concrete is cut to create a preliminary dust characterisation baseline, where future cutting tests will be performed on limestone and sandstone rocks.In this study, three conical pick wears (new, moderately worn, and fully worn picks) are used to generate dust from a concrete block and characteristics are statistically compared between the dusts. Airborne respirable particles are collected during cutting and deposited fine material, orparticles left on the surface of the block, are collected after cutting. The dusts are then analysed through standardised methods, field emission scanning electron microscope image capture with image analyses, and laser diffraction methods. Findings reveal that the worn pick generated thehighest concentration of respirable dust, all picks generated dust containing quartz, the three picks generally generated respirable dusts with similar particle shapes (in terms of roundness, roughness, and aspect ratio), and the worn pick generated the largest deposited fine material particles.

Oct 12, 2022

By M I. Pownceby, S Hapugoda, H Han, E Donskoi, L Lu

Iron ore sinter mineralogy and its associated macro-/micro – structure has a strong impact on sinter quality. At a macroscopic scale, sinter ideally consists of a strong, porous matrix which bonds relict ore nuclei together. Microscopically, the sinter matrix (solidified from the melt part of the initial sinter mix) generally consists of complex calcium ferrites known as SFCA, secondary magnetite and hematite grains (precipitated from the primary sinter melt), glass and silicates. Depending on the conditions under which the sinter structure is formed, two major forms of SFCA with different morphologies are generally recognised, ie fine micro-platy SFCA (usually termed SFCA-I) and coarse columnar/prismatic SFCA. Detailed optical microscope observations of several pot grate and compact sinter samples revealed the presence of a variety of fine, coarse and dense forms of both types of SFCA. The controlled cooling tests revealed that cooling rate has an impact on the form and size of SFCA crystals. In this work, EPMA analysis of SFCA compositions from a variety of pot grate and compact sinter samples are presented. Results show that the SFCA types exhibit a broad range of complex compositions within the system Fe2O3/CaO/SiO2/Al2O3/MgO/TiO2/MnO2. Although SFCA-I and SFCA are known to be crystallographically distinct and with different, well-defined ranges in composition, there was considerable overlap in compositions of the experimental sinter samples. The development of SFCA textures depend on several parameters including the local chemistry and conditions including the maximum temperature attained and the cooling rate, within the sinter bed, thereby suggesting that SFCA identification based on morphology alone may be erroneous.

Nov 8, 2021

By N Guresin, M Rohde

A lead-zinc flotation tailings sample containing silver from BHP Billiton’s Cannington Mine has been characterised to understand occurrences of silver in the tailings by conventional elemental, X-ray diffraction (XRD) and size analyses followed by mineralogical analysis with a scanning electron microscope (SEM) equipped with mineral liberation analysis (MLA) software and the use of an adapted diagnostic leach process originally developed for gold containing materials.The tailings sample contained 67 g/t Ag, 1.8 per cent Pb and 0.52 per cent Zn. The XRD analysis showed that the sample consisted of 74 per cent silicates, nine per cent sulfides, 11 per cent magnetite and small amounts of other minerals such as fluorite, fluorapatite and rutile. The p80 and p50 of the sample were determined to be 106 µm and 38 µm, respectively. The silver distribution was high in the small size fraction with 52.1 per cent of the silver being in the -8 µm fraction. The silver minerals freibergite, acanthite, jamesonite, pyrargyrite and native silver were observed in the mineralogical analysis of the sample by SEM/MLA. The associations of the minerals were intricate and the occurrences of silver were complex. There were finely disseminated silver minerals and also coarser grains of silver minerals in composites with the host minerals. It was estimated that almost 50 per cent of the silver was contained in pyrargyrite, around 14 per cent as native silver and contained in acanthite, 12.5 per cent in galena and around ten per cent in freibergite and jamesonite.These composite particles and the type of the silver minerals present were expected to limit leaching efficiencies of the silver in hydrometallurgical processing. The diagnostic leach tests showed that around 50 per cent of the silver could be recovered by direct cyanidation and higher extractions could be achieved by more aggressive acidic systems.Cyanidation tests were conducted to confirm the findings of the diagnostic leach studies. The investigated cyanidation parameters were time (up to 48 hours), solid to liquid ratio (1:1 and 1:2), cyanide concentration (0.025 M, 0.5 M and 0.1 M) and particle size (p80 of 106 µm, 63 µm and 7.5 µm). The effects of oxygen and lead nitrate were also studied. The tests were conducted at atmospheric temperatures. The maximum silver recovery obtained was about 50 per cent for all the parameter ranges trialled except particle size. The decrease in particle size from 106 µm to 7.5 µm by fine grinding resulted in an increase in silver recoveries from 50 per cent up to approximately 82 per cent indicating that the liberation of the silver grains/minerals is one of the factors affecting the cyanidation recovery of silver in addition to the presence of refractory silver minerals not amenable to cyanidation.Low head grades of silver in the tailings and relatively low cyanidation recoveries of silver (without fine grinding) necessitate a thorough cost analysis for the cyanidation of the Cannington lead and zinc tailings to assess if cyanidation would be a suitable process option for the extraction of silver. It is clear that one of the most important factors in determining the cost feasibility will be the price of silver in the world metal market.CITATION:Rohde, M, Guresin, N and Johnson, N W, 2014. Characterisation of silver minerals in lead-zinc flotation tailings and their response to cyanidation, in Proceedings 12th AusIMM Mill Operators’ Conference 2014 , pp 163–172 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 1, 2014

By B Godel, E R. Ramanaidou, M Verrall

Fortescue Metals Group Ltd Iron Bridge (IB) operation is a magnetite deposit located in the Pilbara region of Western Australia situated around 145 km south of Port Hedland. This Mesoarchean deposit belongs to the 3230 Ma Pincunah banded-iron formations (BIF), a member of the Kangaroo Caves Formation, Sulfur Springs Group (van Kranendonk, 2000).

Sep 18, 2023

By G. Heymann, T. Grobler

Many tailings storage facilities in the Rustenburg region of South Africa’s North-West Province are founded on reworked residual norite derived from the weathering of the Bushveld Igneous Complex. With the implementation of the Global Industry Standard on Tailings Management, increased emphasis is placed on robust material characterisation, but laboratory testing is challenging. The results of Oedometer and undrained triaxial shear testing support a nonlinear failure envelope for effective stresses below the yield stress, transitioning to linear behaviour at higher stresses.

Apr 8, 2026

By J. Temuujin

Mongolia has some of the world?s largest coal reserves with an estimated total coal reserve of over 150 billion tonnes. At present, over 90% of Mongolian electricity is produced by combined heat and thermal power stations. The main coal deposits used for Central power system's power stations are Baganuur, Shivee-ovoo lignite type coal and Shariin gol bituminous coal. In Mongolia almost 600,000 tonnes of coal combustion by-products are disposed of in waste ponds. In this research, we have thoroughly characterized Mongolian coal combustion by-products including fly ashes sourced directly from thermal power stations and ash retrieved from ponds. It was determined that fly ashes generated from Baganuur and Shivee-ovoo coal deposits are class C, while ash from Shariin gol coal is class F (according the ASTM C618). All ash products were characterized by chemical, mineralogical, granulometrical, porosity, FE-SEM and radiation methods. Fly ashes sourced directly from power stations were found to be more suitable for manufacture of geopolymers for building materials application and zeolite synthesis than ashes retrieved from ash ponds. The adsorption and porous properties of zeolitic compounds were measured and found to be suitable for adsorption of Cr6+ from simulated tannery waste water. Keywords: coal, coal combustion by products, synthesis, geopolymers, zeolitic compound

Sep 1, 2012

By T. Schmidt, H. Assadi, F. Gartner, H. Kreye

Among all spraying processes, cold spraying has attracted a special attention in recent years, both as a coating - and more recently - as a rapid manufacturing technique. The interest in this process is mainly because of the fact that the deposition of spray material takes place at moderately low temperatures, and thus, oxidation and unfavourable microstructural changes can be alleviated. In this process, a highly compressed gas, flowing through a de Laval nozzle, accelerates the particles of the spray powder to high velocities of up to 1200 m/s. Although there is no melting of particles prior to impact on the substrate, cold-sprayed deposits can be denser and more tightly bonded as compared to the equivalent deposits produced by conventional thermal spraying methods. The present contribution focuses on this unique aspect of cold spraying. Modelling of particle impact, combined with various experimental observations, is employed to illustrate that bonding of particles and hence material deposition occurs through shear instability - associated with severe plastic deformation and localized heat generation - at the interacting surfaces of particles and substrate. The results of modelling also provide an insight to the influence of material and process parameters on the critical velocity and on the microstructural properties of cold-sprayed deposits.

Jan 1, 2006

By T Kon, K Ohno

Slag foaming is an important control item in the process of refining molten steel. This study aims to investigate the factors controlling slag foaming by observing the bubble formation behaviour resulting from the chemical reaction between iron oxide and Fe-C alloy in the slag. In this study, 0.06 g of Fe- C alloy was introduced at the bottom of a BN crucible, and 6.0 g of slag (SiO2:CaO:Fe2O3 = 40:40:30) was placed on top of it. The crucible was positioned inside an infrared image heating furnace, where the temperature was rapidly raised to 1370°C at a rate of 1000°C/min in a nitrogen stream, and then held at that temperature for a predetermined time before rapid cooling. Following rapid cooling, the internal structure of the sample was examined using a high-resolution X-ray CT device. The spherical equivalent volume was calculated based on the number of observed bubbles and their equivalent circle diameter. Additionally, the relationship between the volume ratio of small bubbles in the slag volume and the distance from the bottom of the crucible was determined, along with the calculation of bubble density and volume ratio. Under various experimental conditions, numerous bubbles with equivalent circular diameters ranging from 200 to 300 μm were consistently observed. The density and volume fraction of bubbles with circular equivalent diameters between 200 and 500 μm showed a tendency to increase as the distance from the bottom of the crucible increased. Bubbles with equivalent circular diameters of 500 μm or more consistently exhibited lower bubble densities, regardless of their height within the crucible. The formation of larger bubbles is attributed to a decrease in iron oxide concentration within the slag as the reaction progresses. However, this is believed to be due to their higher buoyancy, resulting in shorter residence times within the slag and a reduction in the number of encapsulated bubbles.

Aug 21, 2024

By M Khanal, J Qin, B Shen, Y Duan, X Luo

Gaining confidence in interpreting rock and strata properties of the coalmine roof is necessary for design, maintenance, modelling and optimisation of roadways supports. One of the key causes of roadway instabilities experienced in underground coalmines is an extreme variable nature (thickness, competence, discontinuities etc) of the coalmine roof. Normally, the thickness and strength of the roof are characterised with the geotechnical and geological data gathered from exploration boreholes, which are drilled often at considerable distances apart. This limited data cannot capture localised geological variations in the coalmine roof. With this background, this paper explores feasibility of using measurement while drilling concept to perform geotechnical characterisation of the coalmine roof. The parameters, for example, penetration rate, rotary speed, torque, sound, vibration, obtained during the drilling process can provide valuable insights into geotechnical properties. The paper describes the progress of the experimental work conducted at the laboratory on synthesized concrete samples representing various rock strata using a field-scale drilling machine. The samples with and without interfaces have been tested to replicate various underground roof strata. The signals returned from the drill machine, as the drill bit passes through the layers, have been analysed and interpreted to characterise whether the drill response data can differentiate various strengths associated with the rock layers. The initial laboratory results are promising as they show distinct responses of the various sample blocks in a controlled environment. The drilling data can differentiate the synthesized rock samples and detect ‘signatures’ of the roof strength variability and delineation of lithological interfaces (transitions). The weight and torque on the bit vary and show dependency on the strength of the blocks.

Nov 29, 2022

By G R. Ballantyne, V Souto, K Bartram

Particle sorting allows partially liberated minerals to be separated prior to energy intensive fine grinding. Sensors select particles for separation and air, water or mechanical ejectors are used to physically deflect those selected. To achieve effective separation there has to be sufficient liberation, accurate detection and presentation of a separated monolayer of particles. These three physical constraints determine the particle size limits, the sorting technology utilised, the separation efficiency, and the throughput that can be achieved. The combination of all these factors controls the effective limits on the degree to which sorting can reduce the specific comminution requirements and increasing energy efficiency. This paper will explore two case studies: the application of sorting in base metal mining and precious metal mining.CITATION:Ballantyne, G R, Hilden, M, Bartram, K and Souto, V, 2018. Characterising energy efficiency of particle sorting, in Proceedings 14th AusIMM Mill Operators' Conference 2018, pp 531–540 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Aug 29, 2018

By A Scott, I Onederra

A great deal of technical and research effort has been applied to the development of models to predict fragmentation from rock blasting. A number of quite useful empirical or engineering models are currently available to blasting engineers and consultants, while more sophisticated approaches using mechanistic and numerical descriptions of rock breakage continue to be developed and applied by researchers and explosives companies.The fragmentation resulting from any blast will be heavily dependent on the properties of the rock mass being blasted; however, most empirical models rely on ‘rock factors’ generated from simple rock mass properties to describe the influence of the rock on the blasting outcome. In contrast, mechanistic models need explicit rock mass properties that require sophisticated laboratory measurements and detailed structural data if realistic outcomes are to be generated. The fragmentation modeller is caught between excessively simple rock mass descriptions for the empirical models and excessively complex data requirements for the mechanistic models.This paper briefly reviews the basis of a range of fragmentation models and the rock mass properties on which they rely. Shortcomings in the way that the mining industry tends to characterise the blasting properties of rock are discussed and some practical approaches are described to quantify these properties in both operating and greenfield mining environments. Case studies are presented where specific additional breakage properties and modelling features have been needed to generate a useful description of the fragmentation achieved.CITATION:Scott, A and Onederra, I, 2015. Characterising rock mass properties for fragmentation modelling, in Proceedings 11th International Symposium on Rock Fragmentation by Blasting, pp 149–160 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Aug 24, 2015

By A Scott, I Onederra

Most iron ores occur in mine benches as complex mixtures of lithologies and ore types. This significantly complicates their characterisation for both blast design and fragmentation modelling. A great deal of technical and research effort has been applied to the development of models to predict fragmentation from rock blasting. A number of quite useful engineering models are currently available to blasting engineers and consultants, and more sophisticated approaches using mechanistic descriptions of rock breakage continue to be developed and applied by researchers and explosives companies.The engineering or empirical models that are in more general use within the industry, such as the Kuz-Ram model, require appropriate data if they are to generate useful fragmentation predictions. Some of these models have reached significant sophistication and have made very useful contributions to both routine blasting operations and the exploration of new blasting paradigms. However, these models struggle to adequately deal with rock that is as complex as iron ore. This paper reviews the characteristics of the most successful blast fragmentation models available to the industry and discusses approaches to the derivation of suitable rock mass properties to adequately describe blast fragmentation in a range of iron ores.CITATION:Scott, A and Onederra, I, 2015. Characterising the blasting properties of iron ore, in Proceedings Iron Ore 2015, pp 481–490 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 13, 2015

By F D. I Hodgson

Twenty-seven observation test pits were excavated at four different spoils dumps at three collieries in the Witbank Coalfield. The holes were dug into the upper three metres of the spoils to ascertain if any weathering profiles, variation with age or influence of topsoil covering could be gauged. Samples from these holes were also subjected to laboratory testing (ABA, humidity cells and mineralogy on several selected samples). The test pits showed that there was a good correlation between in situ paste pH-values and ABA results for samples taken from the pits. At all the collieries, no correlation between age of spoils and in situ acidity could conclusively be drawn. The depth of soil cover also appears to be a minor consideration in determining the eventual acidity of the spoil. In the pits where acidity was found, the weathering was evident when contrasted to areas still buffered. It is unclear if the weathering leads to the acidity or vice versa, as the soil covering appeared to be similar. The spoils proved to be extremely variable with regard to particle size and material on a micro and macro scale. Evidence from most of the holes suggested that there was enough water contained in the fine material in the spoils to support the initiation of acid generation. Conclusions from this investigation are that the mineralogy of the spoils is the most important factor in determining the eventual occurrence of acidic hotspots, and that prior characterisation and selective handling will provide the best management practice for these spoils.

Jan 1, 2003

By J Theiler, B Beamish

The presence of reactive metal sulfide minerals in waste rock contributes to the hazard of spontaneous combustion in dumps, as these minerals react with air and water entering the dump at ambient temperatures to form various mineral products and significant heat. This reaction series can also be an initiator of self-heating of carbonaceous material present in the waste rocks if sufficiently high temperatures are reached. Characterisation of these reactive minerals has primarily been to assess the risk of acid mine drainage, which is not necessarily an indicator of spontaneous combustion risk. No systematic testing procedure has been adopted by industry to assess the spontaneous combustion propensity of the waste rock. As a consequence, the principal management strategy for spontaneous combustion has been a reactive approach of dealing with events as they arise.Recent advances in adiabatic oven-testing have enabled more definitive assessment of the spontaneous combustion propensity of coals, including the quantification of the accelerating influence of reactive pyrite (Beamish and Beamish, 2011, 2012; Beamish, Lin and Beamish, 2012). This same test procedure has been used to assess the self-heating performance of metal concentrates and is therefore amenable to assessing the metal sulfide oxidation process from low ambient temperatures. The data obtained from such testing can be used to quantify the more prone waste rock sequences of a mineral deposit in advance of mining. This enables appropriate management planning for emplacement and long-term storage of waste rock in dumps.CITATION:Beamish, B and Theiler, J, 2016. Characterising the spontaneous combustion propensity of waste rock, in Proceedings Life-of-Mine 2016 Conference , pp 93–96 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jun 28, 2016

By Guangwei Wang, Changle Zheng, Yifan Chai, Jian Guo, Weiwei Geng, Jianliang Zhang

In this paper, characteristic and kinetics of CO2 reaction with four different kinds of coke such as top-loading coke, dry quenching tamping coke, wet quenching tamping coke and semi-coke were investigated based on isothermal method. Electric resistance reduction furnace was used to heat the sample. Volume Model (VM) and Shrinking Core Model (SCM) were used to calculate the kinetic parameters and to contrast with the experimental results. The results showed that the Volumetric Model (VM) was much suitable for the reaction of top-loading coke, dry quenching tamping coke and wet quenching tamping coke, while Shrinking Core Model (SCM) was much suitable for semi-coke.

Jan 1, 2015

By L. M. English

When plotted as head vs. volume, fan curves start high and decrease in head with increasing volume while mine head curves start low and rise with increasing volume. Their intersection is the system operating point But wait a minute: Isn't head loss a negative number, a debit? And isn't fan head an energy addition, a credit? This, as every ventilation instructor knows, is often a stumbling block to student or audience comprehension. It is possible to use the intuitively correct curves -pressure losses as negative values and energy additions as positive values -and still obtain the correct operating point: adding the two curves produces a third curve that intersects the x-axis at the operating point, the point at \\tIich the fan energy input exactly matches air circulation energy loss. Using this technique also makes it easier to account for outside influences on the system, such as natural ventilating pressure; with the standard approach it is quite easy to add or subtract such influences to the wrong curve. This approach can be extended to the graphical solution of any series/parallel circuit or ventilation net\wrk. The results are the same, and the approach is logically consistent and less confusing.

Jan 1, 1997