Thesis (M.Sc. (Applied Mathematics)) -- University of Limpopo, 2008 / Understanding the effects of blood viscosity variation plays a very crucial role in hemodynamics, thrombosis and inflammation and could provide useful information for diagnostics and therapy of (cardio) vascular diseases. Blood viscosity, which arises from frictional interactions between all major blood constituents, i.e. plasma, plasma proteins and red blood cells, constitutes blood inherent resistance to flow in the blood vessel. Generally, blood viscosity in large arteries is lower near the vessel wall due to the presence of plasma layer in this peripheral region than the viscosity in the central core region which depends on the hematocrit. In this dissertation, the flow of blood in a large artery is investigated theoretically using the fluid dynamics equations of continuity and momentum. Treating artery as a rigid channel with uniform width and blood as a variable viscosity incompressible Newtonian fluid, the basic flow structure and its stability to small disturbances are examined. A fourth-order eigenvalue problem which reduces to the well known Orr–Sommerfeld equation in some limiting cases is obtained and solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials implemented in MATLAB. Graphical results for the basic flow axial velocity, disturbance growth rate and marginal stability curve are presented and discussed. It is worth pointing out that, a decrease in plasma viscosity near the arterial wall has a stabilizing effect on the flow.

The development of a cost-effective multiphase flow meter to determine the individual phase flow rates of oil, water and gas was investigated through the exploitation of a single clamp-on gamma densitometer and signal processing techniques. A fast-sampling (250 Hz) gamma densitometer was installed at the top of the 10.5 m high, 108.2 mm internal diameter, stainless steel catenary riser in the Cranfield University multiphase flow test facility. Gamma radiation attenuation data was collected for two photon energy ranges of the caesium-137 radioisotope based densitometer for a range of air, water and oil flow mixtures, spanning the facility’s delivery range. Signal analysis of the gamma densitometer data revealed the presence of quasi-periodic waveforms in the time-varying multiphase flow densities and discriminatory correlations between statistical features of the gamma count data and key multiphase flow parameters. The development of a mechanistic approach to infer the multiphase flow rates from the gamma attenuation information was investigated. A model for the determination of the individual phase flow rates was proposed based on the gamma attenuation levels; while quasi-periodic waveforms identified in the multiphase fluid density were observed to exhibit a strong correlation with the gas and liquid superficial phase velocity parameters at fixed water cuts. Analysis of the use of pattern recognition techniques to correlate the gamma densitometer data with the individual phase superficial velocities and the water cut was undertaken. Two neural network models were developed for comparison: a single multilayer-perceptron and a multilayer hierarchical flow regime dependent model. The pattern recognition systems were trained to map the temporal fluctuations in the multiphase mixture density with the individual phase flow rates using statistical features extracted from the gamma count signals as their inputs. Initial results yielded individual phase flow rate predictions to within ±10% based on flow regime specific correlations.

The development of a cost-effective multiphase flow meter to determine the individual phase flow rates of oil, water and gas was investigated through the exploitation of a single clamp-on gamma densitometer and signal processing techniques. A fast-sampling (250 Hz) gamma densitometer was installed at the top of the 10.5 m high, 108.2 mm internal diameter, stainless steel catenary riser in the Cranfield University multiphase flow test facility. Gamma radiation attenuation data was collected for two photon energy ranges of the caesium-137 radioisotope based densitometer for a range of air, water and oil flow mixtures, spanning the facility’s delivery range. Signal analysis of the gamma densitometer data revealed the presence of quasi-periodic waveforms in the time-varying multiphase flow densities and discriminatory correlations between statistical features of the gamma count data and key multiphase flow parameters. The development of a mechanistic approach to infer the multiphase flow rates from the gamma attenuation information was investigated. A model for the determination of the individual phase flow rates was proposed based on the gamma attenuation levels; while quasi-periodic waveforms identified in the multiphase fluid density were observed to exhibit a strong correlation with the gas and liquid superficial phase velocity parameters at fixed water cuts. Analysis of the use of pattern recognition techniques to correlate the gamma densitometer data with the individual phase superficial velocities and the water cut was undertaken. Two neural network models were developed for comparison: a single multilayer-perceptron and a multilayer hierarchical flow regime dependent model. The pattern recognition systems were trained to map the temporal fluctuations in the multiphase mixture density with the individual phase flow rates using statistical features extracted from the gamma count signals as their inputs. Initial results yielded individual phase flow rate predictions to within ±10% based on flow regime specific correlations.

No description available.

This thesis describes a simplified method for estimating distances directly from terrestrial photographs. It was felt that any method devised must overcome present limitations and meet three basic criteria to be practical. These criteria are: 1) that the method require no subject-visible markings, 2) that it require no special equipment or training to use, and 3) that it provides sufficient accuracy to be useful. A number of possible methods were considered, and were evaluated against these criteria. the Accuacy ( reliablity) of the methods was tested using a variety of statistical tests. The recommended method consists of first selecting a reference distance whose length is known. This reference should be in a plane parallel to and approximately the same distance from the camera as the desired distance. It was found that a vehicle dimension such as the tire track gives consistently the best results. Both the reference and the desired distances are then scaled on the photograph and a ratio is applied to drectly estimate the desired distance. Greatest reliability is achieved when the subject is directly in fromt of, or behind the camera and at a distance between 50 and 250 feet. By following thers guidelines the stated objectives can be met by using this method.

The fluvial geomorphology of the Colorado River cutting across the Colorado Plateau in the western United States is bedrock controlled and largely governed by rapids. Rapids on the Colorado River control the water-surface profile and influence the bathymetry, the storage of sand, and the aquatic ecology. Despite their importance, little data on the hydraulics, sediment transport, and long-term stability of rapids have been collected. By comparing water-surface profiles, the average rate of aggradation at the head of 91 rapids in Grand Canyon between 1923 and 2000 was calculated to be 0.26 ± 0.15 m. In addition, while in 1923, 50% of the cumulative drop through the river corridor occurred in just 9% of the distance, by 2000, the cumulative drop over the same distance increased to 66%. A new hydraulic model, incorporating one-dimensional step-backwater theory, was constructed for the Colorado River in Grand Canyon. The model includes 2,690 cross sections and simulates discharge up to 5,600 m³/s, offering the opportunity to simulate large floods, rare under the current regulated flow regime. Flow velocities were measured directly in rapids using three separate flow measurement instruments. An acoustic Doppler velocimeter (ADV) was used to measure velocity in five Grand Canyon rapids. While the instrument was able to measure velocity in three dimensions up to 3.0 m/s, limitations rendered data unusable for flow above 3.0 m/s. An acoustic Doppler current profiler (ADCP) was used to measure the flow field in rapids throughout the water column in Cataract Canyon. The peak average velocity measured by the ADCP was roughly 4.0 m/s. Similarly, average flow velocity of 5.2 m/s was measured in a Cataract Canyon rapid using a pitot-static tube. The pitot-static tube measured instantaneous flow velocities up to 6.5 m/s, one of the fastest velocity measurements made in a river. Using the combination of the ADCP and pitot-static tube, the flow structure and nature of turbulence within rapids were analyzed. Finally, techniques were developed to enable the measurement and construction of detailed water surface, shoreline, and bathymetric maps directly in rapids on the Colorado River.

No description available.

The calibration and use of seven hole pressure probes for hot flow measurement was studied extensively, and guidelines were developed for the calibration and use of these probes. The influence of tip shape, Reynolds number, calibration grid density, and curve fit were studied and reported. Calibration was done using the well established polynomial curve fit method of Gallington. An improvement to this method was proposed that improved the uniformity and magnitude of measurement error. A hemispherical tip was found to be less sensitive to manufacturing defects, and less sensitive to changes in tip Reynolds number than a conical tip. The response of the probes was found to be Reynolds number independent over a tip Reynolds number of 6000 for the entire calibrated range. For flows with an angle of attack less than approximately 20°, the response of the probe was found to be independent above Re = 3000. A minimum calibration grid density of 5° was recommended. Error in the measurement of high angle flows was found to increase significantly when the calibration grid was sparser than this. The response of the probe was found to contain features that were not properly represented by third order polynomial terms, and it was found that it was necessary to include fourth order terms in the polynomial curve fit. The uniformity of calibration error was found to improve significantly when the high angle sectors were calibrated using a small number of additional points from adjacent sectors. The calibration data sorting algorithm was modified to include a calibration point in a given sector if that sector’s port read the highest pressure, or if that port read within a specified tolerance (“overlap pressure”) of the highest pressure. An overlap pressure of 15-20% of the calibration flow dynamic pressure was found to decrease the maximum calibration errors by 10-15%. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2011-04-19 18:40:08.677

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No description available.