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62-449: Similitude's main application is in hydraulic and aerospace engineering to test fluid flow conditions with scaled models. It is also the primary theory behind many textbook formulas in fluid mechanics . The concept of similitude is strongly tied to dimensional analysis . Engineering models are used to study complex fluid dynamics problems where calculations and computer simulations aren't reliable. Models are usually smaller than

124-491: 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 discovery of the principle of the valve tower, or valve pit, (Bisokotuwa in Sinhalese) for regulating

186-511: A desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around Kuwait , using multiple supercomputers in the DoD High Performance Computer Modernization Program. Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms,

248-400: A different answer for each execution. Although this might seem obvious, this is a special point of attention in stochastic simulations , where random numbers should actually be semi-random numbers. An exception to reproducibility are human-in-the-loop simulations such as flight simulations and computer games . Here a human is part of the simulation and thus influences the outcome in a way that

310-430: A finite rate of pressure rise requires that any net flow into the collected fluid volume create a volumetric change. Computer simulation Computer simulation is the running of a mathematical model on a computer , the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to

372-400: A full sized vessel nearly so well as can be done for an aircraft or submarine—each of which operates entirely within one medium. Similitude is a term used widely in fracture mechanics relating to the strain life approach. Under given loading conditions the fatigue damage in an un-notched specimen is comparable to that of a notched specimen. Similitude suggests that the component fatigue life of

434-402: 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. At least seven long aqueducts worked it, and

496-470: A map that uses numeric coordinates and numeric timestamps of events. Similarly, CGI computer simulations of CAT scans can simulate how a tumor might shrink or change during an extended period of medical treatment, presenting the passage of time as a spinning view of the visible human head, as the tumor changes. Other applications of CGI computer simulations are being developed to graphically display large amounts of data, in motion, as changes occur during

558-508: A reciprocating device with hinged valves. The earliest programmable machines were water-powered devices developed in the Muslim world. A music sequencer , a programmable musical instrument , was the earliest type of programmable machine. The first music sequencer was an automated water-powered flute player invented by the Banu Musa brothers, described in their Book of Ingenious Devices , in

620-493: A simulation run. Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description: Specific examples of computer simulations include: Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows ' World3 used in the Limits to Growth , James Lovelock's Daisyworld and Thomas Ray's Tierra . In social sciences, computer simulation

682-646: A simulation". Computer simulation developed hand-in-hand with the rapid growth of the computer, following its first large-scale deployment during the Manhattan Project in World War II to model the process of nuclear detonation . It was a simulation of 12 hard spheres using a Monte Carlo algorithm . Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple closed form analytic solutions are not possible. There are many types of computer simulations; their common feature

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744-420: A state in which the system is in equilibrium. Such models are often used in simulating physical systems, as a simpler modeling case before dynamic simulation is attempted. Formerly, the output data from a computer simulation was sometimes presented in a table or a matrix showing how data were affected by numerous changes in the simulation parameters . The use of the matrix format was related to traditional use of

806-579: A watering channel for Samos , the Tunnel of Eupalinos . An early example of the usage of hydraulic wheel, probably the earliest in Europe, is the Perachora wheel (3rd century BC). In Greco-Roman Egypt , the construction of the first hydraulic machine automata by Ctesibius (flourished c. 270 BC) and Hero of Alexandria (c. 10 – 80 AD) is notable. Hero describes several working machines using hydraulic power, such as

868-419: A wide variety of practical contexts, such as: The reliability and the trust people put in computer simulations depends on the validity of the simulation model , therefore verification and validation are of crucial importance in the development of computer simulations. Another important aspect of computer simulations is that of reproducibility of the results, meaning that a simulation model should not provide

930-434: Is a technology and applied science using engineering , chemistry , and other sciences involving the mechanical properties and use of liquids . At a very basic level, hydraulics is the liquid counterpart of pneumatics , which concerns gases . Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on applied engineering using the properties of fluids. In its fluid power applications, hydraulics

992-501: Is achieved when testing conditions are created such that the test results are applicable to the real design. The following criteria are required to achieve similitude; To satisfy the above conditions the application is analyzed; It is often impossible to achieve strict similitude during a model test. The greater the departure from the application's operating conditions, the more difficult achieving similitude is. In these cases some aspects of similitude may be neglected, focusing on only

1054-439: Is an integral component of the five angles of analysis fostered by the data percolation methodology, which also includes qualitative and quantitative methods, reviews of the literature (including scholarly), and interviews with experts, and which forms an extension of data triangulation. Of course, similar to any other scientific method, replication is an important part of computational modeling Computer simulations are used in

1116-414: Is hard, if not impossible, to reproduce exactly. Vehicle manufacturers make use of computer simulation to test safety features in new designs. By building a copy of the car in a physics simulation environment, they can save the hundreds of thousands of dollars that would otherwise be required to build and test a unique prototype. Engineers can step through the simulation milliseconds at a time to determine

1178-400: Is in validation of computer simulations with the ultimate goal of eliminating the need for physical models altogether. Another application of similitude is to replace the operating fluid with a different test fluid. Wind tunnels, for example, have trouble with air liquefying in certain conditions so helium is sometimes used. Other applications may operate in dangerous or expensive fluids so

1240-450: Is much harder is knowing what the accuracy (compared to measurement resolution and precision ) of the values are. Often they are expressed as "error bars", a minimum and maximum deviation from the value range within which the true value (is expected to) lie. Because digital computer mathematics is not perfect, rounding and truncation errors multiply this error, so it is useful to perform an "error analysis" to confirm that values output by

1302-503: Is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states of the model would be prohibitive or impossible. The external data requirements of simulations and models vary widely. For some, the input might be just a few numbers (for example, simulation of a waveform of AC electricity on a wire), while others might require terabytes of information (such as weather and climate models). Input sources also vary widely: Lastly,

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1364-458: Is the branch of hydraulics dealing with free surface flow, such as occurring in rivers , canals , lakes , estuaries , and seas . Its sub-field open-channel flow studies the flow in open channels . Early uses of water power date back to Mesopotamia and ancient Egypt , where irrigation has been used since the 6th millennium BC and water clocks had been used since the early 2nd millennium BC. Other early examples of water power include

1426-399: Is transmitted undiminished throughout the fluids. A French physician, Poiseuille (1797–1869) 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

1488-436: Is used for the generation, control, and transmission of power by the use of pressurized liquids. Hydraulic topics range through some parts of science and most of engineering modules, and they cover concepts such as pipe flow , dam design, fluidics , and fluid control circuitry. The principles of hydraulics are in use naturally in the human body within the vascular system and erectile tissue . Free surface hydraulics

1550-480: Is very important to perform a sensitivity analysis to ensure that the accuracy of the results is properly understood. For example, the probabilistic risk analysis of factors determining the success of an oilfield exploration program involves combining samples from a variety of statistical distributions using the Monte Carlo method . If, for instance, one of the key parameters (e.g., the net ratio of oil-bearing strata)

1612-891: The Qanat system in ancient Persia and the Turpan water system in ancient Central Asia. In the Persian Empire or previous entities in Persia, the Persians constructed an intricate system of water mills, canals and dams known as the Shushtar Historical Hydraulic System . The project, commenced by Achaemenid king Darius the Great and finished by a group of Roman engineers captured by Sassanian king Shapur I , has been referred to by UNESCO as "a masterpiece of creative genius". They were also

1674-477: The ancient Near East in the 4th century BC, specifically in the Persian Empire before 350 BCE, in the regions of Iraq , Iran , and Egypt . In ancient China there was Sunshu Ao (6th century BC), Ximen Bao (5th century BC), Du Shi (circa 31 AD), Zhang Heng (78 – 139 AD), and Ma Jun (200 – 265 AD), while medieval China had Su Song (1020 – 1101 AD) and Shen Kuo (1031–1095). Du Shi employed

1736-454: The force pump , which is known from many Roman sites as having been used for raising water and in fire engines. In the Roman Empire , 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

1798-541: The ribosome , in 2005; a complete simulation of the life cycle of Mycoplasma genitalium in 2012; and the Blue Brain project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level. Because of the computational cost of simulation, computer experiments are used to perform inference such as uncertainty quantification . A model consists of

1860-401: The 9th century. In 1206, Al-Jazari invented water-powered programmable automata/ robots . He described four automaton musicians, including drummers operated by a programmable drum machine , where they could be made to play different rhythms and different drum patterns. In 1619 Benedetto Castelli , a student of Galileo Galilei , published the book Della Misura dell'Acque Correnti or "On

1922-580: The Islamic world, including fulling mills, gristmills , paper mills , hullers , sawmills , ship mills , stamp mills , steel mills , sugar mills , and tide mills . By the 11th century, every province throughout the Islamic world had these industrial mills in operation, from Al-Andalus and North Africa to the Middle East and Central Asia . Muslim engineers also used water turbines , employed gears in watermills and water-raising machines, and pioneered

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1984-657: 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.e., management of rivers in the Papal States, beginning in 1626. The science and engineering of water in Italy from 1500-1800 in books and manuscripts is presented in an illustrated catalog published in 2022. Blaise Pascal (1623–1662) studied fluid hydrodynamics and hydrostatics, centered on

2046-416: 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: Assuming an incompressible fluid or a "very large" ratio of compressibility to contained fluid volume,

2108-678: The buildup of queues in the simulation of humans evacuating a building. Furthermore, simulation results are often aggregated into static images using various ways of scientific visualization . In debugging, simulating a program execution under test (rather than executing natively) can detect far more errors than the hardware itself can detect and, at the same time, log useful debugging information such as instruction trace, memory alterations and instruction counts. This technique can also detect buffer overflow and similar "hard to detect" errors as well as produce performance information and tuning data. Although sometimes ignored in computer simulations, it

2170-406: 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 end in the container, i.e., any change in pressure applied at any point of the liquid

2232-415: The equations used to capture the behavior of a system. By contrast, computer simulation is the actual running of the program that perform algorithms which solve those equations, often in an approximate manner. Simulation, therefore, is the process of running a model. Thus one would not "build a simulation"; instead, one would "build a model (or a simulator)", and then either "run the model" or equivalently "run

2294-478: The escape of water is credited to ingenuity more than 2,000 years ago. By the first century AD, several large-scale irrigation works had been completed. Macro- and micro-hydraulics to provide for domestic horticultural and agricultural needs, surface drainage and erosion control, ornamental and recreational water courses and retaining structures and also cooling systems were in place in Sigiriya , Sri Lanka. The coral on

2356-428: The exact stresses being put upon each section of the prototype. Computer graphics can be used to display the results of a computer simulation. Animations can be used to experience a simulation in real-time, e.g., in training simulations . In some cases animations may also be useful in faster than real-time or even slower than real-time modes. For example, faster than real-time animations can be useful in visualizing

2418-451: The final design, but not always. Scale models allow testing of a design prior to building, and in many cases are a critical step in the development process. Construction of a scale model, however, must be accompanied by an analysis to determine what conditions it is tested under. While the geometry may be simply scaled, other parameters, such as pressure , temperature or the velocity and type of fluid may need to be altered. Similitude

2480-591: The inventors of the Qanat , an underground aqueduct, around the 9th century BC. Several of Iran's large, ancient gardens were irrigated thanks to Qanats. The Qanat spread to neighboring areas, including the Armenian highlands . There, starting in the early 8th century BC, the Kingdom of Urartu undertook significant hydraulic works, such as the Menua canal . The earliest evidence of water wheels and watermills date back to

2542-415: The laborious task of dimensional analysis and formula derivation. Simplification of the formulas (by neglecting some aspects of similitude) is common, and needs to be reviewed by the engineer for each application. Similitude can be used to predict the performance of a new design based on data from an existing, similar design. In this case, the model is the existing design. Another use of similitude and models

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2604-614: The like. Joseph Bramah (1748–1814) was an early innovator and William Armstrong (1810–1900) perfected the apparatus for power delivery on an industrial scale. In London, the London Hydraulic Power Company 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

2666-452: The massive rock at the site includes cisterns for collecting water. Large ancient reservoirs of Sri Lanka are Kalawewa (King Dhatusena), Parakrama Samudra (King Parakrama Bahu), Tisa Wewa (King Dutugamunu), Minneriya (King Mahasen) In Ancient Greece , the Greeks constructed sophisticated water and hydraulic power systems. An example is a construction by Eupalinos , under a public contract, of

2728-452: The matrix concept in mathematical models . However, psychologists and others noted that humans could quickly perceive trends by looking at graphs or even moving-images or motion-pictures generated from the data, as displayed by computer-generated-imagery (CGI) animation. Although observers could not necessarily read out numbers or quote math formulas, from observing a moving weather chart they might be able to predict events (and "see that rain

2790-504: The most important parameters. The design of marine vessels remains more of an art than a science in large part because dynamic similitude is especially difficult to attain for a vessel that is partially submerged: a ship is affected by wind forces in the air above it, by hydrodynamic forces within the water under it, and especially by wave motions at the interface between the water and the air. The scaling requirements for each of these phenomena differ, so models cannot replicate what happens to

2852-433: The practical limitation, especially for laminated structures. Relaxing some of the scaling laws may eliminate the limitation of the design under complete similarity condition and yields the scaled models that are partially similar to their prototype. However, the design of the scaled structures under the partial similarity condition must follow a deliberate methodology to ensure the accuracy of the scaled structure in predicting

2914-532: The pressure coefficient. This gives a required test velocity of: A model test is then conducted at that velocity and the force that is measured in the model ( F m o d e l {\displaystyle F_{model}} ) is then scaled to find the force that can be expected for the real application ( F a p p l i c a t i o n {\displaystyle F_{application}} ): The power P {\displaystyle P} in watts required by

2976-417: The principles of hydraulic fluids. His discovery on the theory behind hydraulics led to his invention of the hydraulic press , 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 exact change of pressure) at both locations. Pascal's law or principle states that for an incompressible fluid at rest,

3038-409: The real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics ( computational physics ), astrophysics , climatology , chemistry , biology and manufacturing , as well as human systems in economics , psychology , social science , health care and engineering . Simulation of a system is represented as

3100-604: The running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions . Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997,

3162-423: The scaled-down composite structures can be successfully carried out using the complete and partial similarities. In the design of the scaled structures under complete similarity condition, all the derived scaling laws must be satisfied between the model and prototype which yields the perfect similarity between the two scales. However, the design of a scaled-down structure which is perfectly similar to its prototype has

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3224-436: The simulation will still be usefully accurate. Models used for computer simulations can be classified according to several independent pairs of attributes, including: Another way of categorizing models is to look at the underlying data structures. For time-stepped simulations, there are two main classes: For steady-state simulations, equations define the relationships between elements of the modeled system and attempt to find

3286-529: The structural response of the prototype. Scaled models can be designed to replicate the dynamic characteristic (e.g. frequencies, mode shapes and damping ratios) of their full-scale counterparts. However, appropriate response scaling laws need to be derived to predict the dynamic response of the full-scale prototype from the experimental data of the scaled model. Hydraulic Hydraulics (from Ancient Greek ὕδωρ ( húdōr )  ' water ' and αὐλός ( aulós )  ' pipe ')

3348-435: The submarine is then: Note that even though the model is scaled smaller, the water velocity needs to be increased for testing. This remarkable result shows how similitude in nature is often counterintuitive. Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities. These formulas and quantities are easy to use without having to repeat

3410-678: The system are: This example has five independent variables and three fundamental units . The fundamental units are: meter , kilogram , second . Invoking the Buckingham π theorem shows that the system can be described with two dimensionless numbers and one independent variable. Dimensional analysis is used to rearrange the units to form the Reynolds number ( R e {\displaystyle R_{e}} ) and pressure coefficient ( C p {\displaystyle C_{p}} ). These dimensionless numbers account for all

3472-410: The testing is carried out in a more convenient substitute. Some common applications of similitude and associated dimensionless numbers; Similitude analysis is a powerful engineering tool to design the scaled-down structures. Although both dimensional analysis and direct use of the governing equations may be used to derive the scaling laws, the latter results in more specific scaling laws. The design of

3534-446: The time at which data is available varies: Because of this variety, and because diverse simulation systems have many common elements, there are a large number of specialized simulation languages . The best-known may be Simula . There are now many others. Systems that accept data from external sources must be very careful in knowing what they are receiving. While it is easy for computers to read in values from text or binary files, what

3596-473: The two objects will also be similar. Consider a submarine modeled at 1/40th scale. The application operates in sea water at 0.5 °C, moving at 5 m/s. The model will be tested in fresh water at 20 °C. Find the power required for the submarine to operate at the stated speed. A free body diagram is constructed and the relevant relationships of force and velocity are formulated using techniques from continuum mechanics . The variables which describe

3658-435: The use of dams as a source of water power, used to provide additional power to watermills and water-raising machines. Al-Jazari (1136–1206) described designs for 50 devices, many of them water-powered, in his book, The Book of Knowledge of Ingenious Mechanical Devices , including water clocks, a device to serve wine, and five devices to lift water from rivers or pools. These include an endless belt with jugs attached and

3720-596: The variables listed above except F , which will be the test measurement. Since the dimensionless parameters will stay constant for both the test and the real application, they will be used to formulate scaling laws for the test. Scaling laws: The pressure ( p {\displaystyle p} ) is not one of the five variables, but the force ( F {\displaystyle F} ) is. The pressure difference (Δ p {\displaystyle p} ) has thus been replaced with ( F / L 2 {\displaystyle F/L^{2}} ) in

3782-516: The water streams were used to erode the soft deposits, and then wash the tailings for the valuable gold content. In the Muslim world during the Islamic Golden Age and Arab Agricultural Revolution (8th–13th centuries), engineers made wide use of hydropower as well as early uses of tidal power , and large hydraulic factory complexes. A variety of water-powered industrial mills were used in

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3844-402: Was headed their way") much faster than by scanning tables of rain-cloud coordinates . Such intense graphical displays, which transcended the world of numbers and formulae, sometimes also led to output that lacked a coordinate grid or omitted timestamps, as if straying too far from numeric data displays. Today, weather forecasting models tend to balance the view of moving rain/snow clouds against

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