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34-653: The Cheshire Plain is a relatively flat expanse of lowland within the county of Cheshire in North West England but extending south into Shropshire. It extends from the Mersey Valley in the north to the Shropshire Hills in the south, bounded by the hills of North Wales to the west and the foothills of the Pennines to the north-east. The Wirral Peninsula lies to the north-west whilst

68-448: A l − ω u p s t r e a m {\displaystyle \Delta \omega =\omega _{local}-\omega _{upstream}} ) to identify patterns such as sudden jumps or drops in stream power, these features can help identify locations where the local terrain controls the flow or widens out as well as areas prone to erosion. Stream power can be used as an indicator of potential damages to bridges as

102-1040: A riffle and pool structure and cooler water temperatures. Rivers with a course that drops in elevation very slowly will have slower water flow and lower force. This in turn produces the other characteristics of a lowland river—a meandering course lacking rapids , a river bed dominated by fine sediments and higher water temperatures. Lowland rivers tend to carry more suspended sediment and organic matter as well, but some lowland rivers have periods of high water clarity in seasonal low-flow periods. The generally clear, cool, fast-flowing waters and bedrock and coarse sediment beds of upland rivers encourage fish species with limited temperature tolerances, high oxygen needs, strong swimming ability and specialised reproductive strategies to prevent eggs or larvae being swept away. These characteristics also encourage invertebrate species with limited temperature tolerances, high oxygen needs and ecologies revolving around coarse sediments and interstices or "gaps" between those coarse sediments. The term "upland"

136-412: A better estimation of the sediment carrying capacity of the river as wide rivers with high stream power are exerting less force per surface area than a narrow river with the same stream power, as they are losing the same amount of energy but in the narrow river it is concentrated into a smaller area. Critical unit stream power is the amount of stream power needed to displace a grain of a specific size, it

170-442: A criterion to determine whether a river is in a state of reshaping itself or whether it is stable. A value of unit stream power between 30 and 35 W m in which this transition occurs has been found by multiple studies. Another technique gaining popularity is using a gradient of stream power by comparing the unit stream power upstream to the local unit stream power ( Δ ω = ω l o c

204-401: A rectangle with the characteristic width and depth. This absorbs velocity, width, and depth. We define stream power per unit channel length, so that term goes to 1, and the derivation is complete. Ω = ρ g Q L 1 S {\displaystyle \Omega =\rho gQ{\cancelto {1}{L}}S} Stream power is the rate of energy dissipation against

238-672: Is a stub . You can help Misplaced Pages by expanding it . Lowland Upland and lowland are portions of a plain that are conditionally categorized by their elevation above the sea level . Lowlands are usually no higher than 200 m (660 ft), while uplands are somewhere around 200 m (660 ft) to 500 m (1,600 ft). On unusual occasions, certain lowlands such as the Caspian Depression lie below sea level. Uplands areas tend to spike into valleys and mountains , forming mountain ranges while lowland areas tend to be uniformly flat, although both can vary such as

272-727: Is also used in wetland ecology , where "upland" plants indicate an area that is not a wetland. The generally more turbid , warm, slow-flowing waters and fine sediment beds of lowland rivers encourage fish species with broad temperature tolerances and greater tolerances to low oxygen levels, and life history and breeding strategies adapted to these and other traits of lowland rivers. These characteristics also encourage invertebrate species with broad temperature tolerances and greater tolerances to low oxygen levels and ecologies revolving around fine sediments or alternative habitats such as submerged woody debris ("snags") or submergent macrophytes ("water weed"). Lowland alluvial plains form when there

306-688: Is deposition of sediment over a long period of time by one or more rivers coming from highland regions, and then are deposited in lowland regions for long periods of time. Examples include American Bottom , a flood plain of the Mississippi River in Southern Illinois, Bois Brule Bottom , and Bottomland hardwood forest a deciduous hardwood forest found in broad lowland floodplains of the United States. Stream power Stream power , originally derived by R. A. Bagnold in

340-524: Is energy per time and using the equivalence between work against the bed and loss in potential energy, we can write: Ω = Δ P E Δ t {\displaystyle \Omega ={\frac {\Delta PE}{\Delta t}}} Finally, we know that mass is equal to density times volume. From this, we can rewrite the mass on the right hand side m = ρ L b h {\displaystyle m=\rho Lbh} where L {\displaystyle L}

374-413: Is generally considered to be land that is at a higher elevation than the alluvial plain or stream terrace , which are considered to be "lowlands". The term "bottomland" refers to low-lying alluvial land near a river. Much freshwater fish and invertebrate communities around the world show a pattern of specialization into upland or lowland river habitats. Classifying rivers and streams as upland or lowland

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408-427: Is given by the equation: ω 0 = τ 0 ν 0 {\displaystyle \omega _{0}=\tau _{0}\nu _{0}} where τ 0 is the critical shear stress of the grain size that will be moved which can be found in the literature or experimentally determined while v 0 is the critical mobilization speed . Critical stream power can be used to determine

442-404: Is important in freshwater ecology , as the two types of river habitat are very different, and usually support very different populations of fish and invertebrate species. In freshwater ecology, upland rivers and streams are the fast-flowing rivers and streams that drain elevated or mountainous country, often onto broad alluvial plains (where they become lowland rivers). However, elevation is not

476-458: Is often used for this, because simple models use and evolve a 1-dimensional downstream profile of the river channel. It is also used with relation to river channel migration , and in some cases is applied to sediment transport . By plotting stream power along the length of a river course as a second-order exponential curve, you are able to identify areas where flood plains may form and why they will form there. Stream power has also been used as

510-419: Is the channel length, b {\displaystyle b} is the channel width ( b readth), and h {\displaystyle h} is the channel depth ( h eight). We use the definition of discharge Q = u b h {\displaystyle Q=ubh} where A {\displaystyle A} is the cross-sectional area, which can often be reasonably approximated as

544-477: Is the downstream flow velocity. It is noted that for small angles, sin ⁡ ( α ) ≈ tan ⁡ ( α ) = S {\displaystyle \sin(\alpha )\approx \tan(\alpha )=S} . Rewriting the first equation, we now have: Δ P E Δ t = m g u S {\displaystyle {\frac {\Delta PE}{\Delta t}}=mguS} Remembering that power

578-468: Is the length of the stream. Unit stream power is stream power per unit channel width, and is given by the equation: ω = ρ g Q S b {\displaystyle \omega ={\frac {\rho gQS}{b}}} where ω is the unit stream power, and b is the width of the channel. Normalizing the stream power by the width of the river allows for a better comparison between rivers of various widths. This also provides

612-490: Is the shear stress, S is the slope of the water, ρ is the density of water (1000 kg/m ), g is acceleration due to gravity (9.8 m/s ). Shear stress can be used to compute the unit stream power using the formula ω = τ   V {\displaystyle \omega =\tau \ V} Where V is the velocity of the water in the stream. Stream power is used extensively in models of landscape evolution and river incision. Unit stream power

646-469: The Mongolian Plateau . Upland habitats are cold, clear and rocky whose rivers are fast-flowing in mountainous areas; lowland habitats are warm with slow-flowing rivers found in relatively flat lowland areas, with water that is frequently colored by sediment and organic matter. These classifications overlap with the geological definitions of "upland" and "lowland". In geology an "upland"

680-438: The stream competency of a river, which is a measure to determine the largest grain size that will be moved by a river. In rivers with large sediment sizes the relationship between critical unit stream power and sediment diameter displaced can be reduced to: ω 0 = 0.030 D i 1.69 {\displaystyle \omega _{0}=0.030D_{i}^{1.69}} While in intermediate-sized rivers

714-437: The 1960s, is the amount of energy the water in a river or stream is exerting on the sides and bottom of the river. Stream power is the result of multiplying the density of the water, the acceleration of the water due to gravity, the volume of water flowing through the river, and the slope of that water. There are many forms of the stream power formula with varying utilities, such as comparing rivers of various widths or quantifying

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748-733: The Cheshire Plain, providing as they do a passage between the Clwydian Hills , in Wales on the one hand and the Peak District and South Pennines on the other. Weather systems are often guided down this "gap", penetrating much further inland than elsewhere along the coast of the Irish Sea . 53°12′N 2°28′W  /  53.200°N 2.467°W  / 53.200; -2.467 This Cheshire location article

782-479: The bed and banks of a river or stream per unit downstream length. It is given by the equation: Ω = ρ g Q S {\displaystyle \Omega =\rho gQS} where Ω is the stream power, ρ is the density of water (1000 kg/m ), g is acceleration due to gravity (9.8 m/s ), Q is discharge (m /s), and S is the channel slope . Total stream power often refers simply to stream power, but some authors use it as

816-433: The bed and banks, which is the stream power. We know that change in potential energy over change in time is given by the equation: Δ P E Δ t = m g Δ z Δ t {\displaystyle {\frac {\Delta PE}{\Delta t}}=mg{\frac {\Delta z}{\Delta t}}} where water mass and gravitational acceleration are constant. We can use

850-736: The channel slope and the stream velocity as a stand-in for Δ z / Δ t {\displaystyle {\Delta z}/{\Delta t}} : the water will lose elevation at a rate given by the downward component of velocity u z {\displaystyle u_{z}} . For a channel slope (as measured from the horizontal) of α {\displaystyle \alpha } : Δ z Δ t = u z = u sin ⁡ ( α ) ≈ u S {\displaystyle {\frac {\Delta z}{\Delta t}}=u_{z}=u\sin(\alpha )\approx uS} where u {\displaystyle u}

884-424: The energy required to move sediment of a certain size. Stream power is closely related to other criteria such as stream competency and shear stress . Stream power is a valuable measurement for hydrologists and geomorphologists tackling sediment transport issues as well as for civil engineers , who use it in the planning and construction of roads, bridges, dams, and culverts. Although many authors had suggested

918-399: The fact that if the water is not accelerating and the river cross-section stays constant (generally good assumptions for an averaged reach of a stream over a modest distance), all of the potential energy lost as the water flows downstream must be used up in friction or work against the bed: none can be added to kinetic energy . Therefore, the potential energy drop is equal to the work done to

952-409: The ice-sheets of the last glacial period melted away between 20,000 and 15,000 years ago leaving behind a thick cover of glacial till and extensive tracts of glacio-fluvial sand and gravel. The primary agricultural use of the Cheshire Plain is dairy farming , creating the general appearance of enclosed hedgerow fields. Meteorologists use the term Cheshire Gap when referring to the lowlands of

986-442: The name "stream power" while not always measuring the entity in the same way; this led to partially failed efforts to establish naming conventions for the various forms of the formula by Rhoads two decades later in 1986. Today stream power is still used and new ways of applying it are still being discovered and researched, with a large integration into modern numerical models utilizing computer simulations . It can be derived by

1020-654: The plain merges with the South Lancashire Plain in the embayment occupied by Manchester to the north. In detail, the plain comprises two areas with distinct characters, the one to the west of the Mid Cheshire Ridge and the other, larger part, to its east. The plain is the surface expression of the Cheshire Basin , a deep sedimentary basin that extends north into Lancashire and south into Shropshire . It assumed its current form as

1054-404: The rate of energy dissipation against the bed and banks of a river or stream per entire stream length. It is given by the equation: T o t a l   s t r e a m   p o w e r = Ω   L {\displaystyle Total\ stream\ power=\Omega \ L} where Ω is the stream power, per unit downstream length and L

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1088-493: The relationship was found to follow: ω 0 = 0.130 D i 1.438 {\displaystyle \omega _{0}=0.130D_{i}^{1.438}} Shear stress is another variable used in erosion and sediment transport models representing the force applied on a surface by a perpendicular force, and can be calculated using the following formula τ = h S ρ g {\displaystyle \tau =hS\rho g} Where τ

1122-426: The sole determinant of whether a river is upland or lowland. Arguably the most important determinants are those of stream power and stream gradient . Rivers with a course that drops rapidly in elevation will have faster water flow and higher stream power or "force of water". This in turn produces the other characteristics of an upland river—an incised course , a river bed dominated by bedrock and coarse sediments,

1156-546: The use of power formulas in sediment transport in the decades preceding Bagnold's work, and in fact Bagnold himself suggested it a decade before putting it into practice in one of his other works, it wasn't until 1966 that R. A. Bagnold tested this theory experimentally to validate whether it would indeed work or not. This was successful and since then, many variations and applications of stream power have surfaced. The lack of fixed guidelines on how to define stream power in this early stage lead to many authors publishing work under

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