Misplaced Pages

#379620

54-402: The river is 733 kilometres (455 mi) long, and its watershed covers 96,400 square kilometres (37,200 sq mi). The average discharge at the mouth is 600 cubic metres per second (21,000 cu ft/s). The part of its basin near the source lies on the southern slopes of Putorana Plateau . It flows to the south direction through Syverma Plateau and joins Nizhnyaya Tunguska near

108-446: A "differential form" (in terms of the divergence operator) which applies at a point. Continuity equations underlie more specific transport equations such as the convection–diffusion equation , Boltzmann transport equation , and Navier–Stokes equations . Flows governed by continuity equations can be visualized using a Sankey diagram . A continuity equation is useful when a flux can be defined. To define flux, first there must be

162-472: A derivation of the equation above for electrons. A similar derivation can be found for the equation for holes. Consider the fact that the number of electrons is conserved across a volume of semiconductor material with cross-sectional area, A , and length, dx , along the x -axis. More precisely, one can say: Rate of change of electron density = ( Electron flux in − Electron flux out ) + Net generation inside

216-476: A quantity q which can flow or move, such as mass , energy , electric charge , momentum , number of molecules, etc. Let ρ be the volume density of this quantity, that is, the amount of q per unit volume. The way that this quantity q is flowing is described by its flux. The flux of q is a vector field , which we denote as j . Here are some examples and properties of flux: ( Rate that  q  is flowing through

270-580: A river in Siberia is a stub . You can help Misplaced Pages by expanding it . Discharge (hydrology) In hydrology , discharge is the volumetric flow rate (volume per time, in units of m /h or ft /h) of a stream . It equals the product of average flow velocity (with dimension of length per time, in m/h or ft/h) and the cross-sectional area (in m or ft ). It includes any suspended solids (e.g. sediment), dissolved chemicals like CaCO 3 (aq), or biologic material (e.g. diatoms ) in addition to

324-414: A simple example, V could be a building, and q could be the number of people in the building. The surface S would consist of the walls, doors, roof, and foundation of the building. Then the continuity equation states that the number of people in the building increases when people enter the building (an inward flux through the surface), decreases when people exit the building (an outward flux through

378-529: A slow recession . Because the peak flow also corresponds to the maximum water level reached during the event, it is of interest in flood studies. Analysis of the relationship between precipitation intensity and duration and the response of the stream discharge are aided by the concept of the unit hydrograph , which represents the response of stream discharge over time to the application of a hypothetical "unit" amount and duration of rainfall (e.g., half an inch over one hour). The amount of precipitation correlates to

432-452: A stochastic (random) process, like the location of a single dissolved molecule with Brownian motion , then there is a continuity equation for its probability distribution . The flux in this case is the probability per unit area per unit time that the particle passes through a surface. According to the continuity equation, the negative divergence of this flux equals the rate of change of the probability density . The continuity equation reflects

486-434: 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. The area is the cross sectional area across a river and the average velocity across that section needs to be measured for

540-408: A unit time, commonly a minute. Measurement of cross sectional area and average velocity, although simple in concept, are frequently non-trivial to determine. The units that are typically used to express discharge in streams or rivers include m /s (cubic meters per second), ft /s (cubic feet per second or cfs) and/or acre-feet per day. A commonly applied methodology for measuring, and estimating,

594-508: A variety of physical phenomena may be described using continuity equations. Continuity equations are a stronger, local form of conservation laws . For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed—i.e., the total amount of energy in the universe is fixed. This statement does not rule out the possibility that a quantity of energy could disappear from one point while simultaneously appearing at another point. A stronger statement

SECTION 10

#1732787160380

648-1269: A volume {\displaystyle {\text{Rate of change of electron density}}=({\text{Electron flux in}}-{\text{Electron flux out}})+{\text{Net generation inside a volume}}} Mathematically, this equality can be written: d n d t A d x = [ J ( x + d x ) − J ( x ) ] A e + ( G n − R n ) A d x = [ J ( x ) + d J d x d x − J ( x ) ] A e + ( G n − R n ) A d x d n d t = 1 e d J d x + ( G n − R n ) {\displaystyle {\begin{aligned}{\frac {dn}{dt}}A\,dx&=\left[J(x+dx)-J(x)\right]{\frac {A}{e}}+(G_{n}-R_{n})A\,dx\\&=\left[J(x)+{\frac {dJ}{dx}}dx-J(x)\right]{\frac {A}{e}}+(G_{n}-R_{n})A\,dx\\[1.2ex]{\frac {dn}{dt}}&={\frac {1}{e}}{\frac {dJ}{dx}}+(G_{n}-R_{n})\end{aligned}}} Here J denotes current density(whose direction

702-907: Is against electron flow by convention) due to electron flow within the considered volume of the semiconductor. It is also called electron current density. Total electron current density is the sum of drift current and diffusion current densities: J n = e n μ n E + e D n d n d x {\displaystyle J_{n}=en\mu _{n}E+eD_{n}{\frac {dn}{dx}}} Therefore, we have d n d t = 1 e d d x ( e n μ n E + e D n d n d x ) + ( G n − R n ) {\displaystyle {\frac {dn}{dt}}={\frac {1}{e}}{\frac {d}{dx}}\left(en\mu _{n}E+eD_{n}{\frac {dn}{dx}}\right)+(G_{n}-R_{n})} Applying

756-894: Is largely incompressible. In computer vision , optical flow is the pattern of apparent motion of objects in a visual scene. Under the assumption that brightness of the moving object did not change between two image frames, one can derive the optical flow equation as: ∂ I ∂ x V x + ∂ I ∂ y V y + ∂ I ∂ t = ∇ I ⋅ V + ∂ I ∂ t = 0 {\displaystyle {\frac {\partial I}{\partial x}}V_{x}+{\frac {\partial I}{\partial y}}V_{y}+{\frac {\partial I}{\partial t}}=\nabla I\cdot \mathbf {V} +{\frac {\partial I}{\partial t}}=0} where Conservation of energy says that energy cannot be created or destroyed. (See below for

810-424: Is positive) then the amount of charge within that volume is going to decrease, so the rate of change of charge density is negative. Therefore, the continuity equation amounts to a conservation of charge. If magnetic monopoles exist, there would be a continuity equation for monopole currents as well, see the monopole article for background and the duality between electric and magnetic currents. In fluid dynamics ,

864-656: Is that energy is locally conserved: energy can neither be created nor destroyed, nor can it " teleport " from one place to another—it can only move by a continuous flow. A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries. Continuity equations more generally can include "source" and "sink" terms, which allow them to describe quantities that are often but not always conserved, such as

918-844: Is the potential function . The partial derivative of ρ with respect to t is: ∂ ρ ∂ t = ∂ | Ψ | 2 ∂ t = ∂ ∂ t ( Ψ ∗ Ψ ) = Ψ ∗ ∂ Ψ ∂ t + Ψ ∂ Ψ ∗ ∂ t . {\displaystyle {\frac {\partial \rho }{\partial t}}={\frac {\partial |\Psi |^{2}}{\partial t}}={\frac {\partial }{\partial t}}\left(\Psi ^{*}\Psi \right)=\Psi ^{*}{\frac {\partial \Psi }{\partial t}}+\Psi {\frac {\partial \Psi ^{*}}{\partial t}}.} Multiplying

972-416: Is the sum of processes within the hydrologic cycle that increase the water levels of bodies of water. Most precipitation occurs directly over bodies of water such as the oceans, or on land as surface runoff . A portion of runoff enters streams and rivers, and another portion soaks into the ground as groundwater seepage . The rest soaks into the ground as infiltration, some of which infiltrates deep into

1026-404: Is typically expressed in units of cubic meters per second (m³/s) or cubic feet per second (cfs). The catchment of a river above a certain location is determined by the surface area of all land which drains toward the river from above that point. The river's discharge at that location depends on the rainfall on the catchment or drainage area and the inflow or outflow of groundwater to or from

1080-535: The Rhine river in Europe is 2,200 cubic metres per second (78,000 cu ft/s) or 190,000,000 cubic metres (150,000 acre⋅ft) per day. Because of the difficulties of measurement, a stream gauge is often used at a fixed location on the stream or river. A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel, or conduit carrying flow. The rate of flow

1134-1433: The Schrödinger equation by Ψ* then solving for Ψ* ⁠ ∂Ψ / ∂ t ⁠ , and similarly multiplying the complex conjugated Schrödinger equation by Ψ then solving for Ψ ⁠ ∂Ψ* / ∂ t ⁠ ; Ψ ∗ ∂ Ψ ∂ t = 1 i ℏ [ − ℏ 2 Ψ ∗ 2 m ∇ 2 Ψ + U Ψ ∗ Ψ ] , Ψ ∂ Ψ ∗ ∂ t = − 1 i ℏ [ − ℏ 2 Ψ 2 m ∇ 2 Ψ ∗ + U Ψ Ψ ∗ ] , {\displaystyle {\begin{aligned}\Psi ^{*}{\frac {\partial \Psi }{\partial t}}&={\frac {1}{i\hbar }}\left[-{\frac {\hbar ^{2}\Psi ^{*}}{2m}}\nabla ^{2}\Psi +U\Psi ^{*}\Psi \right],\\\Psi {\frac {\partial \Psi ^{*}}{\partial t}}&=-{\frac {1}{i\hbar }}\left[-{\frac {\hbar ^{2}\Psi }{2m}}\nabla ^{2}\Psi ^{*}+U\Psi \Psi ^{*}\right],\\\end{aligned}}} substituting into

SECTION 20

#1732787160380

1188-1248: The above quantities indicate this represents the flow of probability. The chance of finding the particle at some position r and time t flows like a fluid ; hence the term probability current , a vector field . The particle itself does not flow deterministically in this vector field . The time dependent Schrödinger equation and its complex conjugate ( i → − i throughout) are respectively: − ℏ 2 2 m ∇ 2 Ψ + U Ψ = i ℏ ∂ Ψ ∂ t , − ℏ 2 2 m ∇ 2 Ψ ∗ + U Ψ ∗ = − i ℏ ∂ Ψ ∗ ∂ t , {\displaystyle {\begin{aligned}-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\Psi +U\Psi &=i\hbar {\frac {\partial \Psi }{\partial t}},\\-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\Psi ^{*}+U\Psi ^{*}&=-i\hbar {\frac {\partial \Psi ^{*}}{\partial t}},\\\end{aligned}}} where U

1242-1523: The above result suggest that the right hand side is the divergence of j , and the reversed order of terms imply this is the negative of j , altogether: ∇ ⋅ j = ∇ ⋅ [ ℏ 2 m i ( Ψ ∗ ( ∇ Ψ ) − Ψ ( ∇ Ψ ∗ ) ) ] = ℏ 2 m i [ Ψ ∗ ( ∇ 2 Ψ ) − Ψ ( ∇ 2 Ψ ∗ ) ] = − ℏ 2 m i [ Ψ ( ∇ 2 Ψ ∗ ) − Ψ ∗ ( ∇ 2 Ψ ) ] {\displaystyle {\begin{aligned}\nabla \cdot \mathbf {j} &=\nabla \cdot \left[{\frac {\hbar }{2mi}}\left(\Psi ^{*}\left(\nabla \Psi \right)-\Psi \left(\nabla \Psi ^{*}\right)\right)\right]\\&={\frac {\hbar }{2mi}}\left[\Psi ^{*}\left(\nabla ^{2}\Psi \right)-\Psi \left(\nabla ^{2}\Psi ^{*}\right)\right]\\&=-{\frac {\hbar }{2mi}}\left[\Psi \left(\nabla ^{2}\Psi ^{*}\right)-\Psi ^{*}\left(\nabla ^{2}\Psi \right)\right]\\\end{aligned}}} so

1296-451: The accumulation (or loss) of mass in the system, while the divergence term represents the difference in flow in versus flow out. In this context, this equation is also one of the Euler equations (fluid dynamics) . The Navier–Stokes equations form a vector continuity equation describing the conservation of linear momentum . If the fluid is incompressible (volumetric strain rate is zero),

1350-399: The area, stream modifications such as dams and irrigation diversions, as well as evaporation and evapotranspiration from the area's land and plant surfaces. In storm hydrology, an important consideration is the stream's discharge hydrograph, a record of how the discharge varies over time after a precipitation event. The stream rises to a peak flow after each precipitation event, then falls in

1404-409: The continuity equation can be combined with Fourier's law (heat flux is proportional to temperature gradient) to arrive at the heat equation . The equation of heat flow may also have source terms: Although energy cannot be created or destroyed, heat can be created from other types of energy, for example via friction or joule heating . If there is a quantity that moves continuously according to

1458-980: The continuity equation is an empirical law expressing (local) charge conservation . Mathematically it is an automatic consequence of Maxwell's equations , although charge conservation is more fundamental than Maxwell's equations. It states that the divergence of the current density J (in amperes per square meter) is equal to the negative rate of change of the charge density ρ (in coulombs per cubic meter), ∇ ⋅ J = − ∂ ρ ∂ t {\displaystyle \nabla \cdot \mathbf {J} =-{\frac {\partial \rho }{\partial t}}} One of Maxwell's equations , Ampère's law (with Maxwell's correction) , states that ∇ × H = J + ∂ D ∂ t . {\displaystyle \nabla \times \mathbf {H} =\mathbf {J} +{\frac {\partial \mathbf {D} }{\partial t}}.} Taking

1512-567: The continuity equation is: ∂ ρ ∂ t = − ∇ ⋅ j ⇒ ∂ ρ ∂ t + ∇ ⋅ j = 0 {\displaystyle {\begin{aligned}&{\frac {\partial \rho }{\partial t}}=-\nabla \cdot \mathbf {j} \\[3pt]{}\Rightarrow {}&{\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {j} =0\\\end{aligned}}} The integral form follows as for

1566-546: The continuity equation reads: ∇ ⋅ j + ∂ ρ ∂ t = 0 ⇌ ∇ ⋅ j + ∂ | Ψ | 2 ∂ t = 0. {\displaystyle \nabla \cdot \mathbf {j} +{\frac {\partial \rho }{\partial t}}=0\mathrel {\rightleftharpoons } \nabla \cdot \mathbf {j} +{\frac {\partial |\Psi |^{2}}{\partial t}}=0.} Either form may be quoted. Intuitively,

1620-524: The continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system plus the accumulation of mass within the system. The differential form of the continuity equation is: ∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 {\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot (\rho \mathbf {u} )=0} where The time derivative can be understood as

1674-485: The corresponding discharge from the rating curve. If a continuous level-recording device is located at a rated cross-section, the stream's discharge may be continuously determined. Larger flows (higher discharges) can transport more sediment and larger particles downstream than smaller flows due to their greater force. Larger flows can also erode stream banks and damage public infrastructure. G. H. Dury and M. J. Bradshaw are two geographers who devised models showing

Kochechum - Misplaced Pages Continue

1728-422: The density of a molecular species which can be created or destroyed by chemical reactions. In an everyday example, there is a continuity equation for the number of people alive; it has a "source term" to account for people being born, and a "sink term" to account for people dying. Any continuity equation can be expressed in an "integral form" (in terms of a flux integral ), which applies to any finite region, or in

1782-418: The discharge of a river is based on a simplified form of the continuity equation . The equation implies that for any incompressible fluid, such as liquid water, the discharge (Q) is equal to the product of the stream's cross-sectional area (A) and its mean velocity ( u ¯ {\displaystyle {\bar {u}}} ), and is written as: where For example, the average discharge of

1836-527: The divergence of a curl is zero, so that ∇ ⋅ J + ∂ ( ∇ ⋅ D ) ∂ t = 0. {\displaystyle \nabla \cdot \mathbf {J} +{\frac {\partial (\nabla \cdot \mathbf {D} )}{\partial t}}=0.} But Gauss's law (another Maxwell equation), states that ∇ ⋅ D = ρ , {\displaystyle \nabla \cdot \mathbf {D} =\rho ,} which can be substituted in

1890-478: The divergence of both sides (the divergence and partial derivative in time commute) results in ∇ ⋅ ( ∇ × H ) = ∇ ⋅ J + ∂ ( ∇ ⋅ D ) ∂ t , {\displaystyle \nabla \cdot (\nabla \times \mathbf {H} )=\nabla \cdot \mathbf {J} +{\frac {\partial (\nabla \cdot \mathbf {D} )}{\partial t}},} but

1944-466: The fact that the molecule is always somewhere—the integral of its probability distribution is always equal to 1—and that it moves by a continuous motion (no teleporting ). Quantum mechanics is another domain where there is a continuity equation related to conservation of probability . The terms in the equation require the following definitions, and are slightly less obvious than the other examples above, so they are outlined here: With these definitions

1998-424: The flow of a real physical quantity. In the case that q is a conserved quantity that cannot be created or destroyed (such as energy ), σ = 0 and the equations become: ∂ ρ ∂ t + ∇ ⋅ j = 0 {\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {j} =0} In electromagnetic theory ,

2052-1542: The general equation. The total current flow in the semiconductor consists of drift current and diffusion current of both the electrons in the conduction band and holes in the valence band. General form for electrons in one-dimension: ∂ n ∂ t = n μ n ∂ E ∂ x + μ n E ∂ n ∂ x + D n ∂ 2 n ∂ x 2 + ( G n − R n ) {\displaystyle {\frac {\partial n}{\partial t}}=n\mu _{n}{\frac {\partial E}{\partial x}}+\mu _{n}E{\frac {\partial n}{\partial x}}+D_{n}{\frac {\partial ^{2}n}{\partial x^{2}}}+(G_{n}-R_{n})} where: Similarly, for holes: ∂ p ∂ t = − p μ p ∂ E ∂ x − μ p E ∂ p ∂ x + D p ∂ 2 p ∂ x 2 + ( G p − R p ) {\displaystyle {\frac {\partial p}{\partial t}}=-p\mu _{p}{\frac {\partial E}{\partial x}}-\mu _{p}E{\frac {\partial p}{\partial x}}+D_{p}{\frac {\partial ^{2}p}{\partial x^{2}}}+(G_{p}-R_{p})} where: This section presents

2106-469: The ground to replenish aquifers. Continuity equation A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity , but it can be generalized to apply to any extensive quantity . Since mass , energy , momentum , electric charge and other natural quantities are conserved under their respective appropriate conditions,

2160-439: The imaginary surface  S ) = ∬ S j ⋅ d S {\displaystyle ({\text{Rate that }}q{\text{ is flowing through the imaginary surface }}S)=\iint _{S}\mathbf {j} \cdot d\mathbf {S} } (Note that the concept that is here called "flux" is alternatively termed flux density in some literature, in which context "flux" denotes the surface integral of flux density. See

2214-424: The level of the stream is described by a rating curve . Average velocities and the cross-sectional area of the stream are measured for a given stream level. The velocity and the area give the discharge for that level. After measurements are made for several different levels, a rating table or rating curve may be developed. Once rated, the discharge in the stream may be determined by measuring the level, and determining

Kochechum - Misplaced Pages Continue

2268-472: The main article on Flux for details.) The integral form of the continuity equation states that: Mathematically, the integral form of the continuity equation expressing the rate of increase of q within a volume V is: d q d t + ∮ S j ⋅ d S = Σ {\displaystyle {\frac {dq}{dt}}+\oint _{S}\mathbf {j} \cdot d\mathbf {S} =\Sigma } where In

2322-455: The mass continuity equation simplifies to a volume continuity equation: ∇ ⋅ u = 0 , {\displaystyle \nabla \cdot \mathbf {u} =0,} which means that the divergence of the velocity field is zero everywhere. Physically, this is equivalent to saying that the local volume dilation rate is zero, hence a flow of water through a converging pipe will adjust solely by increasing its velocity as water

2376-402: The nuances associated with general relativity.) Therefore, there is a continuity equation for energy flow: ∂ u ∂ t + ∇ ⋅ q = 0 {\displaystyle {\frac {\partial u}{\partial t}}+\nabla \cdot \mathbf {q} =0} where An important practical example is the flow of heat . When heat flows inside a solid,

2430-426: The previous equation to yield the continuity equation ∇ ⋅ J + ∂ ρ ∂ t = 0. {\displaystyle \nabla \cdot \mathbf {J} +{\frac {\partial \rho }{\partial t}}=0.} Current is the movement of charge. The continuity equation says that if charge is moving out of a differential volume (i.e., divergence of current density

2484-476: The region of continuous permafrost with a frozen layer that varies in depth between 50 and 200 metres (160 and 660 ft). The permafrost effectively blocks any underground supply; all water flowing through the river comes from snow and rain. The river stays ice-bound from October to May or June every year. As watershed area does not contain any significant lakes. The flow of the Kochechum strongly depends on

2538-583: The relationship between discharge and other variables in a river. The Bradshaw model described how pebble size and other variables change from source to mouth; while Dury considered the relationships between discharge and variables such as stream slope and friction. These follow from the ideas presented by Leopold, Wolman and Miller in Fluvial Processes in Geomorphology . and on land use affecting river discharge and bedload supply. Inflow

2592-509: The season, approaching zero in early spring and reaching its maximum in June. The latter month corresponds to a seasonal inundation, which usually produces 75 percent of the overall annual yield of water. 64°17′00″N 100°13′00″E  /  64.28333°N 100.21667°E  / 64.28333; 100.21667 This Krasnoyarsk Krai location article is a stub . You can help Misplaced Pages by expanding it . This article related to

2646-600: The surface), increases when someone in the building gives birth (a source, Σ > 0 ), and decreases when someone in the building dies (a sink, Σ < 0 ). By the divergence theorem , a general continuity equation can also be written in a "differential form": ∂ ρ ∂ t + ∇ ⋅ j = σ {\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {j} =\sigma } where This general equation may be used to derive any continuity equation, ranging from as simple as

2700-2550: The time derivative of ρ : ∂ ρ ∂ t = 1 i ℏ [ − ℏ 2 Ψ ∗ 2 m ∇ 2 Ψ + U Ψ ∗ Ψ ] − 1 i ℏ [ − ℏ 2 Ψ 2 m ∇ 2 Ψ ∗ + U Ψ Ψ ∗ ] = 1 i ℏ [ − ℏ 2 Ψ ∗ 2 m ∇ 2 Ψ + U Ψ ∗ Ψ ] + 1 i ℏ [ + ℏ 2 Ψ 2 m ∇ 2 Ψ ∗ − U Ψ ∗ Ψ ] = − 1 i ℏ ℏ 2 Ψ ∗ 2 m ∇ 2 Ψ + 1 i ℏ ℏ 2 Ψ 2 m ∇ 2 Ψ ∗ = ℏ 2 i m [ Ψ ∇ 2 Ψ ∗ − Ψ ∗ ∇ 2 Ψ ] {\displaystyle {\begin{aligned}{\frac {\partial \rho }{\partial t}}&={\frac {1}{i\hbar }}\left[-{\frac {\hbar ^{2}\Psi ^{*}}{2m}}\nabla ^{2}\Psi +U\Psi ^{*}\Psi \right]-{\frac {1}{i\hbar }}\left[-{\frac {\hbar ^{2}\Psi }{2m}}\nabla ^{2}\Psi ^{*}+U\Psi \Psi ^{*}\right]\\&={\frac {1}{i\hbar }}\left[-{\frac {\hbar ^{2}\Psi ^{*}}{2m}}\nabla ^{2}\Psi +U\Psi ^{*}\Psi \right]+{\frac {1}{i\hbar }}\left[+{\frac {\hbar ^{2}\Psi }{2m}}\nabla ^{2}\Psi ^{*}-U\Psi ^{*}\Psi \right]\\[2pt]&=-{\frac {1}{i\hbar }}{\frac {\hbar ^{2}\Psi ^{*}}{2m}}\nabla ^{2}\Psi +{\frac {1}{i\hbar }}{\frac {\hbar ^{2}\Psi }{2m}}\nabla ^{2}\Psi ^{*}\\[2pt]&={\frac {\hbar }{2im}}\left[\Psi \nabla ^{2}\Psi ^{*}-\Psi ^{*}\nabla ^{2}\Psi \right]\\\end{aligned}}} The Laplacian operators ( ∇ ) in

2754-691: The town Tura . The primary tributaries of the Kochechum are Embenchime , Tembenchi and Turu . The confluence of Kochechum and Nizhnyaya Tunguska corresponds to the farthest point of fairway section upstream off the Yenisey . The basin of the river entirely belongs to the zone of continental subarctic climate. Winter period starts in October and ends in May, during calendar winter temperatures can plummet below −60 °C (−76 °F). Due to average temperatures below freezing in this area, its watershed belongs to

SECTION 50

#1732787160380

2808-473: The volume continuity equation to as complicated as the Navier–Stokes equations . This equation also generalizes the advection equation . Other equations in physics, such as Gauss's law of the electric field and Gauss's law for gravity , have a similar mathematical form to the continuity equation, but are not usually referred to by the term "continuity equation", because j in those cases does not represent

2862-420: The volume of water (depending on the area of the catchment) that subsequently flows out of the river. Using the unit hydrograph method, actual historical rainfalls can be modeled mathematically to confirm characteristics of historical floods, and hypothetical "design storms" can be created for comparison to observed stream responses. The relationship between the discharge in the stream at a given cross-section and

2916-410: 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 . 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

#379620