|
Hydraulic Jumps In Rectangular Channels
Hydraulic jump in a rectangular channel, also known as classical jump, is a natural phenomenon that occurs whenever flow changes from supercritical to subcritical flow. In this transition, the water surface rises abruptly, surface rollers are formed, intense mixing occurs, air is entrained, and often a large amount of energy is dissipated. Numeric models created using the standard step method or HEC-RAS are used to track supercritical and subcritical flows to determine where in a specific reach a hydraulic jump will form. There are common hydraulic jumps that occur in everyday situations such as during the use of a household sink. There are also man-made hydraulic jumps created by devices like weirs or sluice gates. In general, a hydraulic jump may be used to dissipate energy, to mix chemicals, or to act as an aeration device. To produce equations describing the jump, since there is an unknown energy loss, there is a need to apply conservation of momentum. To develop this equation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydraulic Jump
A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface. The rapidly flowing liquid is abruptly slowed and increases in height, converting some of the flow's initial kinetic energy into an increase in potential energy, with some energy irreversibly lost through turbulence to heat. In an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shockwave forms. It was first observed and documented by Leonardo da Vinci in the 1500s. The mathematics were first described by Giorgio Bidone of Turin University when he published a paper in 1820 called ''Experiences sur le remou et sur la propagation des ondes''. The phenomenon is dependent upon the initial fluid speed. If the initial speed of the fluid is below the critical s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riverfront Park WA 0271
A riverfront is a region along a river. Often in larger cities that are traversed or bordered by one or more rivers, the riverfront is lined with marinas, docks, cafes, museums, parks, or minor attractions. Today many riverfronts are a staple of modernism and city beautification. List of riverfronts in Asia India Japan China List of riverfronts in Europe Finland Poland Germany List of riverfronts in North America United States of America List of riverfronts in South America List of riverfronts in Oceania Australia List of riverfronts in Africa Images See also * Boardwalk * Esplanade * Riverwalk (other) Riverwalk may refer to: Paths and trails Australia * Brisbane Riverwalk * Surfers Riverwalk, Gold Coast Canada * Jack and Jean Leslie RiverWalk, in Downtown Calgary, Alberta Mexico * Santa Lucía riverwalk in Monterrey, Nuevo León Unit ... * Corniche Urban design Pedestrian infrastructure Riverfront {{geo-ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Y-axis
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjugate Depth
In fluid dynamics, the conjugate depths refer to the depth (''y''1) upstream and the depth (''y''2) downstream of the hydraulic jump whose momentum fluxes are equal for a given discharge (volume flux) ''q''. The depth upstream of a hydraulic jump is always supercritical. It is important to note that the conjugate depth is different from the alternate depths for flow which are used in energy conservation calculations. Mathematical derivation Beginning with an equal momentum flux ''M'' and discharge ''q'' upstream and downstream of the hydraulic jump: :M=\frac+\frac=\frac+\frac. Rearranging terms gives: :\frac\left(\frac-\frac\right)=\frac\left(y_z^2-y_1^2\right). Multiply to get a common denominator on the left-hand side and factor the right-hand side: :\frac\left(\frac\right)=\frac(y_2-y_1)(y_2+y_1). The (''y''2−''y''1) term cancels out: :\frac\left(\frac\right)=\frac(y_2+y_1)\qquad\textq_1^2=y_1^2 v_1^2=y_2^2 v_2^2. Divide by ''y''12 :\frac\left(\frac\right)=\f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists. The concepts of Fitch-style proof, sequent calculus and natural deduction are generalizations of the concept of proof. The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Laws Of Motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. # When a body is acted upon by a force, the time rate of change of its momentum equals the force. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his '' Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems, which laid the foundation for classical mechanics. In the time since Newton, the conceptual content of classical physics has been reformulated in alternative ways, involving diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservation Of Momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is : \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christiaan Huygens
Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of all time and a major figure in the Scientific Revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, a breakthrough in timekeeping and the most accurate timekeeper for almost 300 years. An exceptionally talented mathematician and physicist, Huygens was the first to idealize a physical problem by a set of mathematical parameters, and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon.Dijksterhuis, F.J. (2008) Stevin, Huygens and the Dutch republ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
René Descartes
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was central to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, later becoming a central intellectual of the Dutch Golden Age. Although he served a Protestant state and was later counted as a deist by critics, Descartes considered himself a devout Catholic. Many elements of Descartes' philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differed from the schools on two major points: first, he rejected the splitting of corporeal substance into mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Vector
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Griggs Dam Columbus, OH
Griggs may refer to: Places *Griggs County, North Dakota, U.S. *Mount Griggs (also known as Knife Peak Volcano), Katmai range, Alaska, U.S. Other uses *Griggs (surname) *''Griggs v. Duke Power Co.'' (1971), an employment discrimination lawsuit in the United States {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
