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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] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...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] |
Flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. Terminology The word ''flux'' comes from Latin: ''fluxus'' means "flow", and ''fluere'' is "to flow". As ''fluxion'', this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. His seminal treatise ''Théorie analytique de la chaleur'' (''The Analytical Theory of Heat''), defines ''fluxion'' as a central quantity and proceeds to derive the now well-known express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discharge (hydrology)
In hydrology, discharge is the volumetric flow rate of water that is transported through a given cross-sectional area. It includes any suspended solids (e.g. sediment), dissolved chemicals (e.g. CaCO3(aq)), or biologic material (e.g. diatoms) in addition to the water itself. Terms may vary between disciplines. For example, a fluvial hydrologist studying natural river systems may define discharge as streamflow, whereas an engineer operating a reservoir system may equate it with outflow, contrasted with inflow. Theory and calculation A discharge is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass. Thus the water discharge of a tap (faucet) can be measured with a measuring jug and a stopwatch. Here the discharge might be 1 litre per 15 seconds, equivalent to 67 ml/second or 4 litres/minute. This is an average measure. For measuring the discharge of a river we need a different method and the most common is the 'area-velocity' method. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supercritical Flow
A supercritical flow is a flow whose velocity is larger than the wave velocity. The analogous condition in gas dynamics is supersonic speed. According to the website Civil Engineering Terms, supercritical flow is defined as follows: The flow at which depth of the channel is less than critical depth, velocity of flow is greater than critical velocity and slope of the channel is also greater than the critical slope is known as supercritical flow. Information travels at the wave velocity. This is the velocity at which waves travel outwards from a pebble thrown into a lake. The flow velocity is the velocity at which a leaf in the flow travels. If a pebble is thrown into a supercritical flow then the ripples will all move down stream whereas in a subcritical flow some would travel up stream and some would travel down stream. It is only in supercritical flows that hydraulic jumps ( bores) can occur. In fluid dynamics, the change from one behaviour to the other is often describ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conservation Of Energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite. Classically, conservation of energy was distinct from conservation of mass. However, special relativity shows that mass is related to energy and vice versa by ''E = mc2'', and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Denominator
In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions. Description The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple. The product of the denominators is always a common denominator, as in: : \frac+\frac\;=\;\frac+\frac\;=\;\frac but it is not always the lowest common denominator, as in: : \frac+\frac\;=\;\frac+\frac\;=\;\frac Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers: : \frac+\frac=\frac+\frac=\frac. With variables rather than numbers, the same principles apply: : \frac+\frac\;=\;\frac+\frac\;=\;\frac Some methods of calculating the LCD are at . Role in arithmetic and algebra The same fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Hand Side
In mathematics, LHS is informal shorthand for the left-hand side of an equation. Similarly, RHS is the right-hand side. The two sides have the same value, expressed differently, since equality is symmetric. definition and example of abbreviation More generally, these terms may apply to an or ; the right-hand side is ever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the Expression (mathematics), expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex number, c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
