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By H Jalalifar, N Aziz

In the ten years since the University of NSW proposed a pillar design methodology for bord and pillar operations, the Australian coal mining industry has changed substantially. What was primarily a bord and pillar design approach is now being applied to chain pillar design in longwall mines where the requirements are substantially different. The dimensions of chain pillars can impact on tailgate conditions (roof, rib and floor), seal performance, and surface subsidence. The status of chain pillar design practice in Australia is reviewed, with a focus on defining pillar strength, chain pillar loading, and assessing the performance of the roof/pillar/system. A new pillar strength equation is proposed for Australian coal that applies for all width/height ratios. An alternative analysis of probability of failure of chain pillars is presented.

Jan 1, 2005

By K G. Fleetwood

This paper proposes an approach to determine the influence of non-ideal detonation characteristics related to the charge diameter, explosive type and confinement conditions on the available shock energy of ANFO and a representative chemically-sensitised (gassed) emulsion. The proposed degrees of non-ideality of the two different blasting agents are indicated by the Gurney ratios, determined from existing cylinder expansion testing data. The influence of the non-ideal detonation properties on blast design and performance are also compared using a series of theoretical, equal powder factor open pit blasting patterns with hole diameters ranging from 102 mm to 270 mm. The non-ideal shock energy factor (NSEF), which is the available shock energy per tonne of blasted material (MJ/t), is used to compare the different blasting patterns as charged with either ANFO or the gassed emulsion of equal charge density (0.85 g/cm3). The intended purpose of this investigation is to provide explosive users with an approach to compare different explosive types or charge diameters in the absence of dedicated non-ideal detonation modelling, which is generally not available to explosives users.The results of the comparisons suggest that at low charge densities, the example gassed emulsion displays a higher velocity of detonation (VOD) than ANFO in smaller charge diameters but similar degrees of non-ideality (based on proposed Gurney ratios). The results also suggest that the confined, non-ideal gassed emulsion VOD at hole diameters greater than 270 mm can be less than ANFO due to the low density effects on the emulsion matrix. The differences in non-ideal detonation properties and Gurney ratios between the ANFO and gassed emulsion resulted in gassed emulsion NSEF values ranging from 15 per cent lower to 65 per cent higher than ANFO for equal powder-factor patterns in blasthole diameters from 102 mm to 270 mm.

Nov 8, 2011

A new lead refinery with a. capacity of 230,000 tons per year com-menced operation at*Port'Plsie in October, 1959. This plant' superseded the refinery which had operated from 1933 with the advent of thecontinuous lead refining process. The incorporation of new equipment following local metallurgical developments, together with the overseas demand for lead of extremely low antimony content, created difficulties in operating the original plant. The new refinery project was under-taken to cover this disability and to gain the full advantage of the new processes.Desilverising and softening are carried out in units identical in size to those used previously. Metallic'zinc is now recovered from the entire output of desilverised bullion by vacuum distillation. Final refining is then carried out by batch'treatinent with caustic soda yield-ing lead of purity previously unattainable at Port Pirie.These two processes have replaced continuous dezincing by oxidation, a high temperature process which caused large quantities of lead and antimony to be recirculated. As the final stage is a .batch process the product composition can be.checked before casting. Individual batches can be adjusted to produce special alloys to,consumer's specification.Improved casting equipment has allowed the quantity production of pigs of good physical characteristics either as 56 lb bars or 2000 lb pigs. This, together with the high purity of the lead, has assured the B.H.A.S. position in world markets.Automatic control systems have been extensively employed particularly on the vacuum dezincing unit.The anticipated financial benefits have been achieved mainly by a reduction in the tonnage of recirculated materials, a smaller labour force, and reduced maintenance requirements.

Jan 1, 1963

By E L. Kotova

Completeness of extraction of a mineral from ore depends on many reasons. First of all it is a function of quality of disintegration of ore. It is supposed that two basic factors: character of structure and texture of the ore aggregate and a disintegration technique influence the quality of the mineral aggregate destruction, æopeningÆ of its internal boundaries. In this paper, the problem of technological mineralogy from the point of view of genesis of the mineral aggregate, its typomorphical features and methods of their quantitative description are discussed. The purpose of this research is to provide information for technologists. It should enable the development of a rational flexible scheme of disintegration of ore with full extraction of a useful component, without its losses and without unnecessary expenses of energy. For achievement of this purpose the mineralogical information should have ½number and a measure+. By the authors, the technique of the quantitative analysis of fabric of the mineral aggregate based on several models û thermodynamic, crystallographic and geometrical is offered and discussed. The leading role in the quantitative analysis of a fabric of ore belongs to internal bounders. But internal bounders of the mineral aggregate by bounders or faces of the mineral individuals or mineral grains are formed. Their geometry, orientation concerning own (mineral grain) crystallographic lattices, orientation and distribution in space of the ore aggregate are proportional to the energy accumulated at origin and the further growth. These characteristics of mineral individuals are consequences of conditions of their formation. That is why the named triad of models is used. From crystallography it is known that faces of different stability and mobility form borders of crystals. They also contain different quantity of energy. Mineral grains also are faceted by different energy borders. They form intergrowths with each other according to a principle of balance or unbalance. That is why in addition to traditional parameters of the description of a fabric of the mineral aggregate (mode and grainmetrical composition) it is necessary to add new. For example, length and the square of intergrowthing bounders of mineral individuals differentiated (in couples), crystallographic symbols of borders, their roughness and so forth. Consequently, solving a problem of the geometrical characteristic of borders, we define also its power characteristic. In this paper experience of application of our technology in studying ores of one of deposits of Urals Mountains is presented. For realisation of these types of the analysis technologies of measurement, the program of calculation and the devices, which are carrying out the analysis in a semi-automatic mode, are possessed. Structure and texture of rock or ore aggregate reflect its formation and transformation conditions. It is important to understand that disintegration energy cannot be more than aggregation energy, the energy of intergrowths formation. The square and orientation of mineral individuals borders vary at pressures or stresses of mineral aggregate evolution. These phenomena often cause selective increase in the square of borders at constant average grain size, ie the granulation. Granulation presents the increase in quantity of mineral individuals while their modal share remains constant. At the same time their average mineral grains size. Some mineral individuals increase in size at increased pressure. When lithostatic or lateral pressure drops the majority of mineral grains increases in volume at the cost of intersticial or film solutions or fine grains. These are only special examples of the ontogenesis of the mineral aggregate. They illustrate our statement that all changes in fabric of the mineral aggregate are a reaction on varying external (ie geological) conditions. It is possible to consider that structurisation of totality of mineral individuals as a whole is a process of adaptation of the mineral aggregate, which forms and exists in varying force and energy fields. Differential and integrated geometry of total internal boundaries of the mineral aggregate serves as adaptation mechanism of the mineral grains system. Boundaries form intergrowths of the mineral aggregate. Thus, it is possible to consider that the most informative parameters of the stereometric analysis for restoration of the ontogenesis of the mineral aggregate are the following. First of all, it is a quantitative estimation of the volumetric shape of the ore mineral in crystallographic coordinates, a total area of borders of all mineral grains in the aggregate, the specific square of their boundaries, the specific square of intergrowth boundaries of the ore mineral separately with grains of each minerals of the matrix of the mineral aggregate as well as traditional grainsmetric and modal composition. For realisation of these types of the analysis technologies of measurement, the program of calculation and the devices that are carrying out the analysis in a semi-automatic mode are possessed.

Jan 1, 2008

By B F. J Kelly

Multiple-point simulation is a family of methods used to generate conditional facies simulations that present the same spatial dependence as a user-defined training image. The main advantage of using a training image is the easy integration of geological concepts in numerical subsurface models. The strength of multiple-point methods is that it allows making the best use of geological expertise when data are too sparse for inferring a model of spatial continuity. However, despite being appealing to geologists, the multiple-point methods are often not used in practice due to the difficulty of building complex 3D training images that contain realistic features.A new framework for multiple-point simulation is presented that involves small and simple training images. The main idea is to use random transformations to expand the range of structures available in the simple training image. The training image is not regarded any more as a global conceptual geological model, but rather a basic structural element of the subsurface. Complex geological structures are obtained, whose spatial structure can be parameterised by adjusting the statistics of the random transformations, based on field data or geological context. In most cases, such parameterisation is possible by adjusting two numbers only. One advantage is that the training images are so simple that they can be easily built even in 3D. The method allows building 3D models that reproduce shapes corresponding to a desired prior geological concept and are in phase with different types of field observations, such as orientation, facies or geophysical measurements. The flexibility of the approach allows for naturally integrating different types of data. This is demonstrated on an example involving seismic data assimilation. Examples where complex 3D folded structures are built from a simple training image and a few orientation data are shown.

Sep 26, 2011

The BLEG (Bulk Leach Extractable Gold) technique is a semiquantitative measure of cyanide extractable gold contained in a sample. A 5kg sample is leached in cyanide solution for 24 hours and gold is precipitated out of the pregnant solution using zinc and assayed by AAS. The detection limit is reported as ppb (parts per billion). Telfer is located 1300km north north-east from Perth in the Great Sandy Desert. The climate is one of hot summers with irregular rainfall and mild winters. A large portion of the area is covered by aeolian sand and seif dunes with poorly developed drainage, rare outcrop; topographic relief is a maximum of 96m. Poor outcrop and poorly developed drainage render conventional stream sediment sampling and soil geochemistry inadequate. Therefore a technique providing a minimum number of samples with maximum accuracy and sensitivity was needed. Consequently BLEG orientation surveys were conducted over the Telfer Mine area in 1983, 1984 and 1985.

Jan 1, 1988

By J Kinal, P Steinier

A considerable volume of work exists in the literature examining the electrochemical interactions between grinding media and sulfide minerals. Broadly, most sulfide minerals are more noble than forged steel grinding media used during comminution, therefore a galvanic couple between the media and the sulfide mineral(s) exists, which increases the corrosion rate of the grinding media. The corrosion products of the grinding media, iron oxy-hydroxide species, invariably precipitate on to the surfaces of the sulfide minerals thereby affecting their floatability. This paper explores the science behind these corrosion reactions, and provides an explanation of their impact on the pulp chemistry of sulfide mineral slurries and subsequent flotation behaviour. A number of laboratory and plant case studies are used to illustrate the benefits of changing to a more inert grinding media.

Jan 1, 2005

By S C. Barrie

St BarbaraÆs Marvel Loch operations have successfully used longhole open stoping as the primary mining method for a number of years. A transition to Core and Shell mining was implemented in 2009 to recover substantial ore grade resources remaining in sill and rib pillars. The transition to core and shell for the Exhibition lode required continuous waste filling of created voids and thus the removal of the crown pillar at the base of the Exhibition pit by blasting. Access to the top of pillar was denied as the pit was partially rock filled with waste rock from underground development.Beyond the technical challenges of the blasting project, a simple and transparent risk management process was developed to ensure appropriate controls and mitigating strategies were in place to minimise risk to personnel during the pillar removal process.Although failure of the crown pillar was anticipated but with the actual timing unknown, on 25 December 2011 the crown pillar yielded during normal mine operations. Engineered and isolation controls in place at the time were of a sufficiently high standard to ensure limited exposure of the underground workforce and minimal damage to mine infrastructure. Successful risk management through implementation of appropriate controls during the project lifecycle of two years and three months proved to be fundamental to the safe removal of the crown pillar.CITATION:Barrie, S C, 2012. Successful risk management through project life cycle for removal of the crown pillar at the Marvel Loch Underground Mine, in Proceedings International Mine Management 2012, pp 125-134 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 20, 2012

By X Liu

The crystal chemistry of carbonate in Ca apatites, including Na-free and Na-bearing hydroxylapatite (CHAP) and Na-bearing fluorapatite (CFAP) and chlorapatite (CCLAP), has been investigated by Fourier transform infrared (FTIR) spectroscopy and single-crystal X-ray structure, using crystals synthesised from carbonate-rich melts at 1 GPa, 1400 - 1000¦C. The carbonate ion substitutes for both the X (OH, F, Cl) anion species in the apatite channel (type A carbonate) and the phosphate group (type B carbonate). The type A carbonate ion is oriented in the channel with two oxygen atoms close to the c-axis, and the type B carbonate ion is located close to the sloping faces of the substituted phosphate tetrahedron, with details varying with composition series. Sodium promotes the uptake of type B carbonate and also has a profound effect on FTIR spectra. Crystal compositions correspond approximately to the substitution formula Ca10-(y+z)Nay z[(PO4)6-(y+2z)(CO3)y+2z][X2-2x(CO3)x], with x + y up to 1.0 and z + 0.0 for CHAP, x + y + 4z + 0.4 for CCLAP, and x + y + 2z + 0.1 for CFAP, for equivalent conditions of synthesis. The sodium cation and A and B carbonate ion defects are locally coupled in all three composition series to facilitate charge compensation and minimise the effects of spatial accommodation. Synthetic Na-bearing type A-B CHAP with x + y + 0.5 has a similar chemical composition and FTIR spectrum to biological apatite.

Jan 1, 2008

By A Woodley, N C. Kunz

A mine site water balance is important for communicating information to interested stakeholders, for reporting on water performance and for anticipating and mitigating water-related risks through water use/demand forecasting. Gaining accuracy over the water balance is therefore crucial for sites to achieve best practice water management and to maintain their social license to operate. For sites that are located in high rainfall environments the water received to storage dams through run-off can represent a large proportion of the overall inputs to site; inaccuracies in these flows can therefore lead to inaccuracies in the overall site water balance.Hydrological models that estimate run-off flows are often incorporated into simulation models used for water use/demand forecasting. The Australian Water Balance Model (AWBM) is one example that has been widely applied in the Australian context. However, the calibration of AWBM in a mining context can be challenging. Through a detailed case study, we outline an approach that was used to calibrate and validate AWBM at a mine site. Commencing with a data set of monitored dam levels, a mass balance approach was used to generate an observed run-off sequence. By incorporating a portion of this observed data set into the calibration routine, we achieved a closer fit between the observed versus simulated data set compared with the base case. We conclude by highlighting opportunities for future research to improve the calibration fit through improving the quality of the input data set. This will ultimately lead to better models for run-off prediction and thereby improve the accuracy of mine site water balances.CITATION:Kunz, N C and Woodley, A, 2013. Improving the accuracy of mine site water balances through improved estimation of run-off volumes, in Proceedings Water in Mining 2013 , pp 267-272 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 26, 2013

By Akerkar D. D, Dey M. L, Mathur S. B, Chowdhury S. K R

The extraction of gold and silver from chalcopyrite concentrates has been investigated. In view of the recent interest in non-cyanide leachants for gold and silver, one such alternative reagent, namely thiourea, has been employed in the present work. Precious metal leaching was attempted from received copper concentrates as well as pre-oxidised concentrates. Pre-oxidation of the concentrates was carried out by three different methods, namely roasting, pressure oxidation and biological oxidation. After pre-oxidation and leaching of the base metals, the leach residues were subjected to further leaching for precious metal extraction. The results obtained on the extraction of gold and silver from received concentrates as well as pre-oxidised concentrates are presented and the effectiveness of the three pre-oxidation routes employed is compared.

Jan 1, 1992

By M Ogle

"Booster fans are relatively rare in Australian coal mines. However, as mines become progressivelydeeper it is likely that such fans will be increasingly adopted as a method to sustain or improve the ventilation of underground workings. The reasons why booster fans may be an att ractive alternative include: increased cost of sinking additional ventilation shafts with greater seam depths; environmental objections to shaft sinking projects; and increasing urbanisation and surface constraints limiting availability of potential ventilation shaft sites. As Tahmoor Colliery movedinto its northern lease the ventilation constraints became the limiting factor on production. Thelimitations of the old workings meant that the existing ventilation system would be inadequateto sustain the required production. Extensive ventilation modelling was carried out to evaluatevarious potential solutions and the recommended option was the installation of a booster fanor fans, to gain underground access to an already approved shaft site in the northern lease.Proposals were sought from recognised fan manufacturers and various alternative arrangements were tendered. Ultimately the choice was between one large centrifugal fan and a set (three or four) of smaller æauxiliary-likeÆ fans in parallel. The successful tender was for a single centrifugal, an arrangement very similar to the booster fans that have been operating eff ectively at Westcliff Colliery for a number of years. This paper describes the current ventilation network, evaluation of the ventilation options, the fan selection process, and the project status to date."

Jun 1, 2012

Alcoa of Australia's Western Australian bauxite mining operations in the Darling Ranges, southeast of Perth, present major challenges in the control of air blast. The close proximity of rural communities and the face profile make the traditional methods of air blast control difficult.An extensive blast noise monitoring programme has been established. The development of a computerised blast noise prediction model and the establishment of a radiosonde weather balloon facility have reduced blast induced complaints by a factor of ten.The meteorological factors affecting blast noise transmission are discussed and examples are given of adverse weather conditions for the southwest region of Western Australia.

Jan 1, 1983

With the progress of modern mining engineering, one of the features of which is the mining from greater depths and the hoisting of greatly increased loads, it becomes a matter of increasing importance that the engineer should be able to determinewith some degree of precision the character of the strains on the hauling rope. But a wire rope is a complex structure; it is made up of spirally-twisted strands, which in turn are composed of spirally-twisted wires, and it is not particularly easy to say exactly what happens when this "doubly-twisted structure is wound round a drum or over a pulley.. The difficulty has been generally evaded in ordinary practice by the simple device of adopting a large factor of safety for the rope-usually from 8 to 10-a factor which experience has shown is sufficiently large to cover the bending strains set "up when the rope is passed over pulleys of the sizes commonly considered appropriate.When, however, we add the stress due to the bending of the rope to the stress produced by" the direct pull, we find that the actual factor of safety is usually more nearly 4 than 10, and frequently the bending stresses in the rope are so large compared with the simple tensile stresses that their neglect may easily lead to disastrous results when dealing with problems a little out of the common run. Common Empirical Rules.-It is always "recognized that the bending of a wire rope round too small a pulley is likely to do the rope serious injury, but as it is desirable in ordinary winding operations to reduce the inertia of the moving parts to a minimum...

Jan 1, 1907

Environmental management of minesites in general, and management of water discharges in particular, is receiving ever-increasing attention. One key component in the successful design and operation of water management systems is to address the presence of sediment in the water being conveyed. Sediment erosion in the mining environment is often greatly exacerbated by disturbing the ground surface of vast areas of catchment. If sediment avoidance, transport, deposition or release are not adequately addressed, the impact on water management facilities can include loss of storage and hydraulic capacity, more frequent equipment replacement, increased operational costs and potentially environmentally unacceptable sediment discharges to receiving waters. An overview of sediment management within water facilities is presented here, and design of one particular approach, the use of settling basins for sediment removal, is discussed in detail. Examples are used to illustrate lessons learnt where particular approaches to sediment management have been found to be lacking. The common themes in the lessons learnt include the need to characterise hydrodynamic conditions and sediment properties in the water source, to set performance targets for sediment management, and to develop operating procedures to meet these targets under a realistic range of scenarios. The examples show how analysis of expected performance of sediment management can help with planning of operation and maintenance strategies. For settling basins, use of a simulation model that includes the effects of turbulence on settling can provide considerable benefits in optimising basin design and evaluating performance. Even in the most basic approach to sediment settling, establishing performance targets based on design flow and sediment characteristics is critical.

Jan 1, 2003

By I M. Platten

Narrow reef gold deposits are generally less than 4 m in width and relatively complex geological phenomena. They often display variable geometry, attitude, continuity and internal architecture. Economic grades are mostly restricted to specific structural domain(s) and localised within discrete ore shoots that have a nuggety internal grade distribution. On account of the often extended history of geological events, the specific factors localising gold-rich domains are likely to be unique to a particular mine or even reef. These features lead to a high resource risk and require careful management during both evaluation and mining. The gross form, location and global continuity of gold reefs can generally be determined from surface diamond drilling leading to the definition of Inferred Mineral Resources. It is likely that for the definition of Indicated and Measured Mineral Resources underground development and/or close- spaced diamond drilling will be required. Understanding geometry and continuity permits the resource to be more effectively managed, lowering risk/uncertainty. This in turn will allow for well-informed financial and operational decisions. Most importantly, project expectations and milestones can be set at achievable levels.

Jan 1, 2008

The incidence of colliery disasters has highlighted the need for more centralised and directed coal mining safety research in Queensland, with particular impetus from explosions at Box Flat in 1972, Kianga in 1975 and Moura No 4 in 1986. Inquiries which identified the likely causes recommended measures and, research and two outcomes have been the present Mines Safety Research Advisory Committee and The Safety in Mines Testing and Research Station at Redbank, near Brisbane, dealing with all mining problems, coal and metalliferous. Already, important research into ignition and explosion and other health and safety matters has been accomplished; the Station has become an accredited testing laboratory; and international recognition has been achieved. Now the advisory, testing and research arms are soundly in place to pursue preventive investigations and be ready to provide assistance in any emergencies.

Jan 1, 1991

Up to 80 per cent of the copper in a bornite ore can be quickly leached with percolating acidified ferric sulphate solutions. The upper limit for rapid copper extraction is set by the conversion of bornite to slowly dissolving chalcopyrite. The dissolution occurs in two stages: a rapid linear initial stage, followed by a slow, non-linear stage. The initial step is largely controlled by the rate of oxidant supply (Fe2(S04)3); temperature is not an important variable during the initial reaction. The second leaching stage is controlled by chemical and physical factors and is temperature dependent. The initial copper leaching rates are insensitive to both the concentration of the ferrous sulphate reaction product, and the sulphuric acid concentration.

Jan 1, 1973

Ore textures in Australian BIF-derived ores are quite complex and have formed the basis for ore genesis models, which includes hypogene upgrading or supergene upgrading then regional metamorphism for the microplaty hematite ores and supergene upgrading for the martite-goethite ores. Despite a high level of ore texture knowledge, little is known about the spatial distribution of ore textures within deposits or their relationship to downstream processing. This paper describes a new iron ore texture classification system to better understand the vertical textural zonation characteristics of Australian BIF-derived deposits, the interpreted role of recent supergene upgrading processes on modifying primary ore textures and their implications for downstream mineral processing. The iron ore textural classification scheme presented uses textural groupings defined on the basis of similarities in mineralogy, ore texture, porosity, mineral associations and hardness. The scheme is non-genetic and has been successfully applied to deposits in the Pilbara, Yilgarn and Gawler cratons. The main ore texture groups include dense martite/hematite, microplaty hematite, microplaty hematite-goethite, martite-goethite, goethite-martite and goethite-rich. Each group can be further subdivided into physically hard to softer subcategories. The ore textural groups can be divided into those interpreted to be associated with primary replacement of BIF and secondary textures resulting from more recent modification by near-surface hydration or dehydration processes. A schematic vertical section through BIF-derived deposits consists (from surface) of detritals underlain by a carapace, both of which may have been eroded, followed by a hydrated zone with replacement of primary ore martite and microplaty hematite by vitreous goethite. The hydrated zone is underlain by 0.2 - 6 m thick zones of intense dehydration and textural infilling of porosity with hematite and hydrohematite. Immediately below the dehydration zone is a strong zone of leaching, where more porous and friable ore textures occur, followed underneath by a gradational contact with primary ore. Secondary supergene processes can impact on beneficiation with hydration and leaching resulting in more difficult density separations at the concentrator stage due to reductions in density differences between ore and gangue and loss of heavy media into pores. Supergene modification of primary BIF-derived ore textures can substantially change lump metallurgical properties, with hydration and dehydration favourably increasing lump yield but reducing resistance to thermal shock whilst leaching will give the opposing outcome. The lump properties of ore textural groups appear to be relatively consistent within and between the iron ore deposits examined.

Jan 1, 2002

By Propster M, Choudhry M

THIS note gives comments on the paper by Kitaev et al on p. 68 of this book and compares results with those obtained by ourselves. We wish to say that the authors are to be congratulated on their sophisticated approach to an important problem and that it complements our efforts on flow maldistribution.1-5 It is our view that Eqs. (1)-(5) on p. 69 are impressive, but unfortunately with present day computers and computational facilities, it would be quite impractical to contemplate the numerical solution of these. Eq. (8) in the authors' paper, on p. 70, does provide the logical starting point for tackling flow maldistribution problems and strictly speaking this equation is more accurate than Eq. (1) in our paper in this book. We note in passing that there is direct experimental evidence to support the contention that our Eq. (1) is at least a reasonable approximation and one may question in a practical sense whether the refinement afforded by Eq. (8) in the paper by Kitaev et a/ is justified. While one must readily accept the appropriateness of Eq. (8) of Kitaev et al as a starting point, the subsequent mathematical manipulation by the authors is open to serious criticism. In order to solve this complex, non-linear equation Kitaev et al postulated irrotational flow, which afforded considerable simplification. One can argue simply on physical grounds that the assumption of irrotational flow is inappropriate, a fact which should be readily apparent on inspection of the flow fields shown in Figs. 2 and 3 of Kitaev's paper. It follows that while the starting point through the use of Eq. (8) is correct the results derived from this starting point may be suspect because of the erroneous nature of the irrotational flow assumption.

Jan 1, 1975