Water turbineA water turbine is a rotary machine that converts kinetic energy and potential energy of water into mechanical work. Water turbines were developed in the 19th century and were widely used for industrial power prior to electrical grids. Now, they are mostly used for electric power generation. Water turbines are mostly found in dams to generate electric power from water potential energy. Water wheels have been used for hundreds of years for industrial power. Their main shortcoming is size, which limits the flow rate and head that can be harnessed.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Kaplan turbineThe Kaplan turbine is a propeller-type water turbine which has adjustable blades. It was developed in 1913 by Austrian professor Viktor Kaplan, who combined automatically adjusted propeller blades with automatically adjusted wicket gates to achieve efficiency over a wide range of flow and water level. The Kaplan turbine was an evolution of the Francis turbine. Its invention allowed efficient power production in low-head applications which was not possible with Francis turbines.
Francis turbineThe Francis turbine is a type of water turbine. It is an inward-flow reaction turbine that combines radial and axial flow concepts. Francis turbines are the most common water turbine in use today, and can achieve over 95% efficiency. The process of arriving at the modern Francis runner design took from 1848 to approximately 1920. It became known as the Francis turbine around 1920, being named after British-American engineer James B. Francis who in 1848 created a new turbine design.
Axial compressorAn axial compressor is a gas compressor that can continuously pressurize gases. It is a rotating, airfoil-based compressor in which the gas or working fluid principally flows parallel to the axis of rotation, or axially. This differs from other rotating compressors such as centrifugal compressor, axi-centrifugal compressors and mixed-flow compressors where the fluid flow will include a "radial component" through the compressor. The energy level of the fluid increases as it flows through the compressor due to the action of the rotor blades which exert a torque on the fluid.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Laminar flowIn fluid dynamics, laminar flow (ˈlæmənər) is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface.
Blade Runner 2049Blade Runner 2049 is a 2017 American epic neo-noir science fiction film directed by Denis Villeneuve and written by Hampton Fancher and Michael Green. A sequel to the 1982 film Blade Runner, the film stars Ryan Gosling and Harrison Ford, with Ana de Armas, Sylvia Hoeks, Robin Wright, Mackenzie Davis, Dave Bautista, and Jared Leto in supporting roles. Ford and Edward James Olmos reprise their roles from the original film. Gosling plays K, a Nexus-9 replicant "blade runner" who uncovers a secret that threatens to destabilize society and the course of civilization.
Centrifugal compressorCentrifugal compressors, sometimes called impeller compressors or radial compressors, are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. They achieve pressure rise by adding energy to the continuous flow of fluid through the rotor/impeller. The equation in the next section shows this specific energy input. A substantial portion of this energy is kinetic which is converted to increased potential energy/static pressure by slowing the flow through a diffuser.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
Pelton wheelThe Pelton wheel or Pelton Turbine is an impulse-type water turbine invented by American inventor Lester Allan Pelton in the 1870s. The Pelton wheel extracts energy from the impulse of moving water, as opposed to water's dead weight like the traditional overshot water wheel. Many earlier variations of impulse turbines existed, but they were less efficient than Pelton's design. Water leaving those wheels typically still had high speed, carrying away much of the dynamic energy brought to the wheels.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Computational fluid dynamicsComputational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.
Blade RunnerBlade Runner is a 1982 science fiction film directed by Ridley Scott, and written by Hampton Fancher and David Peoples. Starring Harrison Ford, Rutger Hauer, Sean Young, and Edward James Olmos, it is an adaptation of Philip K. Dick's 1968 novel Do Androids Dream of Electric Sheep? The film is set in a dystopian future Los Angeles of 2019, in which synthetic humans known as replicants are bio-engineered by the powerful Tyrell Corporation to work on space colonies.
Lift (force)A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it is defined to act perpendicular to the flow and therefore can act in any direction. If the surrounding fluid is air, the force is called an aerodynamic force.
Stokes flowStokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.
