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This condition must be evaluated in order to predict the actual behavior of a particular fluid during field application. Design and operation of the apparatus used to determine fluid-flow behavior permit obtaining data under such non-equilibrium conditions. This paper shows methods used to obtain rheology measurements, develop hydraulic relationships and evaluate chemical reactions producing unsteady-state conditions.
How these charts and chemical reaction rate information are then combined to predict actual turbulent hydraulic behavior during unsteady-state field conditions is also discussed. Many fluids used in hydraulic fracturing contain chemical additives which impart non-Newtonian fluid properties that may drastically alter their hydraulic behavior. Equally drastic alteration in wellhead pressure, injection rate and hydraulic horsepower requirement may result from these fluid properties.
Prior research conducted to relate non-Newtonian fluid properties with hydraulic behavior has not as yet produced a universal relationship, particularly for the turbulent flow region. Which of the many possible non-Newtonian fluid properties is responsible has not been conclusively established.
A systematic description, suggested by Metzner, of the many possible non-Newtonian fluid properties exhibited by real - fluid behavior, and a current discussion of theoretical and applied aspects of non-Newtonian fluid technology can be found in Handbook of Fluid Dynamics. Little or no research has previously been attempted with fluids exhibiting time - dependent properties. Addition of chemicals during a fracturing treatment is often accomplished by continuously mixing and displacing the fluid.
This produces a time-dependent effect or unsteady-state condition while the fluid is progressing through surface and wellbore conductors. This condition is due to solution or chemical reaction of the additive. Considerable departure from conventional methods of obtaining and interpreting data was found necessary to consider these conditions.
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Therefore methods were developed to obtain hydraulic behavior information under these complex, unsteady-state conditions. Relationships presented in this paper to predict hydraulic behavior of non-Newtonian fluids in circular pipes were obtained by constructing and operating a small pipeline apparatus in the manner of a pilot-plant study. These relationships are suggested as scale-up equations and are not proposed as fundamental rheological parameters.
While perhaps deficient from a fundamental research viewpoint, a pilot-plant study does permit the determination and convenient evaluation of variables pertinent to a process.
A pilot-plant study can result in a valid engineering application procedure even when fundamental relationships are still undefined. An excellent series of articles by Bowen has appeared in the chemical engineering literature. These give a thorough review of proposed hydraulic relationships and their limitations for non-Newtonian fluid behavior in circular pipes.
A graphical method is presented to scale up data for a fluid exhibiting an anomalous hydraulic behavior in the turbulent flow region. Du Shi employed a waterwheel to power the bellows of a blast furnace producing cast iron. Zhang Heng was the first to employ hydraulics to provide motive power in rotating an armillary sphere for astronomical observation.
In ancient Sri Lanka , hydraulics were widely used in the ancient kingdoms of Anuradhapura and Polonnaruwa. The coral on the massive rock at the site includes cisterns for collecting water. In Ancient Rome , many different hydraulic applications were developed, including public water supplies, innumerable aqueducts , power using watermills and hydraulic mining. They were among the first to make use of the siphon to carry water across valleys, and used hushing on a large scale to prospect for and then extract metal ores.
They used lead widely in plumbing systems for domestic and public supply, such as feeding thermae. Hydraulic mining was used in the gold-fields of northern Spain, which was conquered by Augustus in 25 BC. The alluvial gold-mine of Las Medulas was one of the largest of their mines. It was worked by at least 7 long aqueducts, and the water streams were used to erode the soft deposits, and then wash the tailings for the valuable gold content.
In Benedetto Castelli — — , a student of Galileo Galilei , published the book Della Misura dell'Acque Correnti or "On the Measurement of Running Waters", one of the foundations of modern hydrodynamics.
He served as a chief consultant to the Pope on hydraulic projects, i. Blaise Pascal — studied fluid hydrodynamics and hydrostatics, centered on the principles of hydraulic fluids.
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His discovery on the theory behind hydraulics led to the invention of the hydraulic press by Joseph Bramah, which multiplied a smaller force acting on a smaller area into the application of a larger force totaled over a larger area, transmitted through the same pressure or same change of pressure at both locations.
Pascal's law or principle states that for an incompressible fluid at rest, the difference in pressure is proportional to the difference in height and this difference remains the same whether or not the overall pressure of the fluid is changed by applying an external force. This implies that by increasing the pressure at any point in a confined fluid, there is an equal increase at every other point in the container, i.
A French physician, Poiseuille — researched the flow of blood through the body and discovered an important law governing the rate of flow with the diameter of the tube in which flow occurred. Several cities developed citywide hydraulic power networks in the 19th century, to operate machinery such as lifts, cranes, capstans and the like. Joseph Bramah [18] — was an early innovator and William Armstrong [19] — perfected the apparatus for power delivery on an industrial scale.
In London, the London Hydraulic Power Company [20] was a major supplier its pipes serving large parts of the West End of London , City and the Docks , but there were schemes restricted to single enterprises such as docks and railway goods yards.
After students understand the basic principles of hydraulics, some teachers use a hydraulic analogy to help students learn other things. For example:. The conservation of mass requirement combined with fluid compressibility yields a fundamental relationship between pressure, fluid flow, and volumetric expansion, as shown below [21] :. Assuming an incompressible fluid or a "very large" ratio of compressibility to contained fluid volume, a finite rate of pressure rise requires that any net flow into the contained fluid volume create a volumetric change.
From Wikipedia, the free encyclopedia. For other uses, see Hydraulic disambiguation. For the mechanical technology, see hydraulic machinery. Retrieved 19 March The Journal of Sexual Medicine. The Annual of the British School at Athens. Retrieved 1 September The qanats of Iran. Archived from the original on 14 April Origins of Chinese science and technology. Archived from the original PDF on 5 September