929 research outputs found
Air Pollution and Mortality for 60 US Cities in 1960
No full textData includes measurements on mortality rate and explanatory variables(air-pollution, socio-economic and meteorological) for 60 US cities in 1960. This data was originally published in McDonald, G.C. and Schwing,R.C. (1973) 'Instabilities of regression estimates relating air pollution to mortality', Technometrics, vol.15, 463-482. It was redistributed through Carnegie Mellon University's StatLib (lib.stat.cmu.edu
Unsteady draining of a fluid from a circular tank
No full textThree-dimensional draining flow of a two-fluid system from a circular tank is considered. The two fluids are inviscid and incompressible, and are separated by a sharp interface. There is a circular hole positioned centrally in the bottom of the tank, so that the flow is axially symmetric. The mean position of the interface moves downwards as time progresses, and eventually a portion of the interface is withdrawn into the drain. For narrow drain holes of small radius, the interface above the centre of the drain is pulled down towards the hole. However, for drains of larger radius the portion of the interface above the drain edge is drawn down first, rather than the central section. Non-linear results are obtained with a novel spectral technique, and are also compared against the predictions of linearized theory. Unstable Rayleigh-Taylor type flows, in which the upper fluid is heavier than the lower one, are also discussed
Draining under gravity in steel galvanization.
No full textThe problem of the coating of steel has been considered in several Mathematics in Industry study groups. In this process, after passing through a bath of molten alloy, steel sheeting is drawn upward to allow draining under gravity and stripping using an air knife, leaving a coating of desirable thickness. Here we discuss some aspects of the problem and in particular the gravity draining component. The problem is a very nice introduction to industrial modelling for students, but is also relevant for manufacturing.
References
Elsaadawy, E. A., Hanumanth, G. S., Balthazaar, A. K. S., McDermid, J. R., Hrymak, A. N. and Forbes, J.F. ``Coating weight model for the continuous hot-dip galvanizing process'', Metal. Mat. Trans. B, 38:413–424, 2007. doi:10.1007/s11663-007-9037-2
Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Roberts M. ``Coating Deformation in the jet stripping process'' in Proceedings of the 2009 Mathematics and Statistics in Industry Study Group, Eds. T. Marchant, M. Edwards, G. Mercer. Wollongong, Austealia, 2010. https://documents.uow.edu.au/content/groups/public/@web/@inf/@math/documents/doc/uow073330.pdf
Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Breward, C. ``Deformations arising during air-knife stripping in the galvanization of steel'', in Progress in Industrial Mathematics at ECMI 2010, Eds. M. Gunther, A. Bartel, M. Brunk, S. Schops, M. Striebel. Mathematics in Industry 17, pp. 311-317. Springer, Berlin Heidelberg, 2011. doi:10.1007/978-3-642-25100-9_36
Hocking, G. C., Lavalle, G., Novakovic, R., O'Kiely, D., Thomson, S., Mitchell, S. J., Herterich, R. ``Bananas–-defects in the jet stripping process''. Proceedings of the European Study Group with Industry in Mathematics and Statistics Research Collection. Rome Italy, 2016. https://researchrepository.ucd.ie/handle/10197/10215
Howison, S. D. and King, J. R. ``Explicit solutions to six free-boundary problems to fluid flow and diffusion''. IMA J. Appl. Math. 42:155–175, 1989. doi:10.1093/imamat/42.2.155
Hocking, G. C., Sweatman, W., Fitt, A. D. and Breward, C. ``Deformations during jet-stripping in the galvanizing process''. J. Eng. Math. Tuck Special Issue, 70:297–306, 2011. doi:10.1007/s10665-010-9394-8
Thornton, J. A. and Graff, H. F. ``An analytical description of the jet-finishing process for hot-dip metallic coatings on strip''. Metal. Mat. Trans. B, 7:607–618, 1976. doi:10.1007/BF02698594
Tuck, E. O. ``Continuous coating with gravity and jet stripping''. Phys. Fluids, 26(9):2352–2358, 1983. doi:10.1063/1.864438
Tuck, E. O., Bentwich, M., and van der Hoek, J. ``The free boundary problem for gravity-driven unidirectional viscous flows''. IMA J. Appl. Math. 30:191–208, 1983. doi:10.1093/imamat/30.2.19
Super-critical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth
No full textThe steady response of a fluid consisting of two regions of different density, the lower of which is of finite depth, is considered during withdrawal. Super-critical flows are considered in which water from both layers is being withdrawn, meaning that the interface is drawn down directly into the sink. The results indicate that if the flow rate is above some minimum, the angle of entry of the interface depends more strongly on the relative depth of the sink than on the flow rate. This has quite dramatic consequences for the understanding of selective withdrawal from layered fluids
Withdrawal of layered fluid through a line sink in a porous medium
No full textThe flow induced when fluid is withdrawn through a line sink from a layered fluid in a homogeneous, vertically confined porous medium is studied. A nonlinear integral equation is derived and solved numerically. For a given sink location, the shape of the interface can be determined for various values of the flow rate. The results are compared with exact solutions obtained using hodograph methods in a special case. It is found that the cusped and coning shapes of the interface can be accurately obtained for the sink situated at different depths in the fluid and the volume of flow into the sink per unit of time
A numerical model for withdrawal from a two-layer fluid
No full textThis paper reports the results of several direct numerical simulations of the withdrawal of a two-layer fluid with a finite-thickness interface through a slot in the base of a finite rectangular cavity. Particular attention is paid to the role of long (basin scale) interfacial waves on the processes leading to drawdown of the interface into the slot. It is shown that these waves play an important role and can either delay or accelerate drawdown. This means that drawdown can occur over a range of Froude numbers. The results are compared with previous work for ideal flow and experimental results
A note on the flow of a homogeneous intrusion into a two-layer fluid
No full textThe intrusion of a constant density fluid at the interface of a two-layer fluid is considered. Numerical solutions are computed for a model of a steady intrusion resulting from flow down a bank and across a broad lake or reservoir. The incoming fluid is homogeneous and spreads across the lake at its level of neutral buoyancy. Solutions are obtained for a range of different inflow angles, flow rate and density differences. Except in extreme cases, the nature of the solution is predicted quite well by linear theory, with the wavelength at any Froude number given by a dispersion relation and wave steepness determined largely by entry angle. However, some extreme solutions with rounded meandering flows and non-unique solutions in the parameter space are also obtained
Withdrawal from a two-layer inviscid fluid in a duct
No full textThe steady simultaneous withdrawal of two inviscid fluids of different densities in a duct of finite height is considered. The flow is two-dimensional, and the fluids are removed by means of a line sink at some arbitrary position within the duct. It is assumed that the interface between the two fluids is drawn into the sink, and that the flow is uniform far upstream. A numerical method based on an integral equation formulation yields accurate solutions to the problem, and it is shown that under normal operating conditions, there is a solution for each value of the upstream interface height. Numerical solutions suggest that limiting configurations exist, in which the interface is drawn vertically into the sink. The appropriate hydraulic Froude number is derived for this situation, and it is shown that a continuum of solutions exists that are supercritical with respect to this Froude number. An isolated branch of subcritical solutions is also presented
Withdrawal from the lens of freshwater in a tropical island: The two interface case
No full textFresh water held in the soil beneath a tropical island is one source of drinking water for the island population. If recharge through rainfall is insufficient, this resource may drain away. This work considers the circumstances under which artificial recharge will maintain the lens of freshwater. A Green function approach is used to derive an integral equation that is solved numerically for the case in which there exist two interfaces - one between salt and freshwater and one between freshwater and air. There appear to be bounds on the flow rates that produce steady interface shapes, but the height of the seepage faces is affected much more by the density ratios than the flow rates. Several different scenarios of withdrawal and influx are considered with a goal of determining some optimal management strategies
Coning during withdrawal from two fluids of different density in a porous medium
No full textThe steady response of the interface between two fluids with different density in a porous medium is considered during extraction through a line sink. Supercritical withdrawal, or coning as it is often called, in which both fluids are being withdrawn, is investigated using a coupled integral equation formulation. It is shown that for each entry angle of the interface into the sink there is a range of supercritical solutions that depend on the flow rate, and that as the flow rate decreases the cone narrows. As the magnitude of the entry angle increases this range of flow-rate values decreases to a narrow range as the entry becomes vertical. Only one branch of solutions (that with horizontal entry) has the property that the interface levels off at a finite height, and this is investigated as a separate branch of solution
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