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| | I'm a 50 years old, married and working at the university (Continuing Education and Summer Sessions).<br>In my free time I try to learn Portuguese. I've been twicethere and look forward to returning anytime soon. I like to read, preferably on my beloved Kindle. I really love to watch How I Met Your Mother and Sons of Anarchy as well as documentaries about anything astronomical. I enjoy Rock stacking.<br><br>Feel free to surf to my blog post ... [http://cmpproj.cms.livjm.ac.uk/cmpdkidd/index.php/122819/ sexy Nebraska women] |
| The '''Manning formula''' is also known as the '''Gauckler–Manning formula''', or '''Gauckler–Manning–Strickler formula''' in Europe. In the United States, in practice, it is very frequently called simply '''Manning's Equation'''. The '''Manning formula''' is an [[Empirical relationship|empirical formula]] estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., [[open channel flow]]. All flow in so-called open channels is driven by [[gravity]]. It was first presented by the French engineer Philippe Gauckler in 1867,<ref>Gauckler, P. (1867), Etudes Théoriques et Pratiques sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Académie des Sciences, Paris, France, Tome 64, pp. 818–822</ref> and later re-developed by the [[Irish people|Irish]] [[engineer]] [[Robert Manning (engineer)|Robert Manning]] in 1890.<ref>Manning R. (1891). On the flow of water in open channels and pipes. Transactions of the
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| Institution of Civil Engineers of Ireland, 20, 161-207</ref>
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| The Gauckler–Manning formula states:
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| :<math>V = \frac{k}{n} {R_h}^{2/3} \, S^{1/2}</math>
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| where:
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| * ''V'' is the cross-sectional average velocity ([[Length|L]]/[[Time|T]]; ft/s, m/s);
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| * ''k'' is a conversion factor of (L<sup>1/3</sup>/T), 1 m<sup>1/3</sup>/s for [[SI]], or 1.4859 ft<sup>1/3</sup>/s [[U.S. customary units]], if required. (Note: (1 m)<sup>1/3</sup>/s = (3.2808399 ft) <sup>1/3</sup>/s = 1.4859 ft<sup>1/3</sup>/s);
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| * ''n'' is the '''Gauckler–Manning coefficient''', it is unitless;
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| * ''R''<sub>''h''</sub> is the hydraulic radius (L; ft, m);
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| * ''S'' is the slope of the hydraulic grade line or the linear [[hydraulic head]] loss (L/L), which is the same as the channel bed slope when the water depth is constant. (''S'' = ''h''<sub>''f''</sub>/''L'').
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| NOTE: ''Ks'' strickler = 1/''n'' manning. The coefficient ''Ks'' strickler varies from 20 (rough stone and rough surface) to 80 m<sup>1/3</sup>/s (smooth concrete and cast iron).
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| The [[Discharge (hydrology)|discharge]] formula, ''Q'' = ''A'' ''V'', can be used to ''manipulate'' Gauckler–Manning's equation by substitution for ''V''. Solving for ''Q'' then allows an estimate of the [[volumetric flow rate]] (discharge) without knowing the limiting or actual flow velocity.
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| The Gauckler–Manning formula is used to estimate the average velocity of water flowing in an open channel in locations where it is not practical to construct a weir or flume to measure flow with greater accuracy. The friction coefficients across weirs and orifices are less subjective than ''n'' along a natural (earthen, stone or vegetated) channel reach. Cross sectional area, as well as ''n''', will likely vary along a natural channel. Accordingly, more error is expected in estimating the average velocity by assuming a Manning's ''n'', than by direct sampling (i.e., with a current flowmeter), or measuring it across [[weir]]s, [[flume]]s or [[:wikt:orifice|orifice]]s. Manning's equation is also commonly used as part of a numerical '''step method''', such as the [[Standard Step Method]], for delineating the free surface profile of water flowing in an open channel.<ref>[[Ven Te Chow|Chow]] (1959) pp. 262-267</ref>
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| The formula can be obtained by use of [[dimensional analysis]]. Recently this formula was derived theoretically using the phenomenological theory of [[turbulence]].<ref>[http://cee.engr.ucdavis.edu/faculty/bombardelli/PRL14501.pdf]. Also see [http://web.mechse.illinois.edu/research/gioia/Art/gioia_Chakraborty_pipes_PRL.pdf]</ref>
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| ==Hydraulic radius==<!-- [[Hydraulic radius]] redirects here -->
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| The '''hydraulic radius''' is a measure of a channel flow efficiency. Flow speed along the channel depends on its cross-sectional shape (among other factors), and the hydraulic radius is a characterisation of the channel that intends to capture such efficiency. Based on the 'constant [[Shear_stress#Shear_stress_in_fluids|shear stress]] at the boundary' assumption,<ref>An Introduction to Hydrodynamics & Water Waves, Bernard Le Méhauté, Springer - Verlag, 1976, p. 84</ref> hydraulic radius is defined as the ratio of the channel's cross-sectional area of the flow to its [[wetted perimeter]] (the portion of the cross-section's perimeter that is "wet"):
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| :<math>R_h = \frac{A}{P}</math>
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| where:
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| * ''R''<sub>''h''</sub> is the hydraulic radius ([[Length|L]]);
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| * ''A'' is the cross sectional area of flow (L<sup>2</sup>);
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| * ''P'' is the [[wetted perimeter]] (L).
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| The greater the hydraulic radius, the greater the efficiency of the channel and the more volume it can carry. For channels of a given width, the hydraulic radius is greater for the deeper channels.
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| The hydraulic radius is ''not'' half the [[hydraulic diameter]] as the name may suggest. It is a function of the shape of the pipe, channel, or river in which the water is flowing. In wide rectangular channels, the hydraulic radius is approximated by the flow depth. The measure of a channel's efficiency (its ability to move water and [[sediment]]) is used by water engineers to assess the channel's capacity.
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| ==Gauckler–Manning coefficient==
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| The Gauckler–Manning coefficient, often denoted as ''n'', is an empirically derived coefficient, which is dependent on many factors, including surface roughness and [[sinuosity]]. When field inspection is not possible, the best method to determine ''n'' is to use photographs of river channels where ''n'' has been determined using Gauckler–Manning's formula.
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| In natural streams, ''n'' values vary greatly along its reach, and will even vary in a given reach of channel with different stages of flow. Most research shows that ''n'' will decrease with stage, at least up to bank-full. Overbank ''n'' values for a given reach will vary greatly depending on the time of year and the velocity of flow. Summer vegetation will typically have a significantly higher ''n'' value due to leaves and seasonal vegetation. Research has shown, however, that ''n'' values are lower for individual shrubs with leaves than for the shrubs without leaves.<ref>Freeman, Rahmeyer and Copeland, http://libweb.erdc.usace.army.mil/Archimages/9477.PDF</ref> This is due to the ability of the plant's leaves to streamline and flex as the flow passes them thus lowering the resistance to flow. High velocity flows will cause some vegetation (such as grasses and forbs) to lay flat, where a lower velocity of flow through the same vegetation will not.<ref>Hardy, Panja and Mathias, http://www.fs.fed.us/rm/pubs/rmrs_gtr147.pdf</ref>
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| In open channels, the [[Darcy–Weisbach equation]] is valid using the hydraulic diameter as equivalent pipe diameter. It is
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| the only sound method to estimate the energy loss in man-made open channels. For various reasons (mainly historical reasons), empirical resistance coefficients (e.g. Chézy, Gauckler–Manning–Strickler) were and are still used. The [[Chézy coefficient]] was introduced in 1768 while the Gauckler–Manning coefficient was first developed in 1865, well before the classical pipe flow resistance experiments in the 1920–1930s. Historically both the Chézy and the Gauckler–Manning coefficients were expected to be constant and functions of the roughness only. But it is now well recognised that these coefficients are only constant for a range of flow rates. Most friction coefficients (except perhaps the Darcy–Weisbach friction factor) are estimated ''100% empirically'' and they apply only to fully rough turbulent water flows under steady flow conditions.
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| One of the most important applications of the Manning equation is its use in sewer design. Sewers are often constructed as circular pipes. It has long been accepted that the value of ''n'' varies with the flow depth in partially filled circular pipes.<ref>Camp, T. R. (1946). Design of Sewers to Facilitate Flow. Sewage Works Journal, 18: 3-16.</ref> A complete set of explicit equations that can be used to calculate the depth of flow and other unknown variables when applying the Manning equation to circular pipes is available.<ref>Akgiray, Ö. (2005). Explicit solutions of the Manning Equation for Partially Filled Circular Pipes, Canadian J. of Civil Eng., 32:490-499.</ref> These equations account for the variation of ''n'' with the depth of flow in accordance with the curves presented by Camp.
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| ==Authors of flow formulas==
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| Albert Brahms (1692–1758)<br>
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| Antoine de Chézy (1718–1798)<br>
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| Henry Darcy (1803–1858)<br>
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| Robert Manning (1816–1897) (en)<br>
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| Wilhelm Rudolf Kutter (1818–1888)<br>
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| Henri Bazin (1843–1917)<br>
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| Ludwig Prandtl (1875–1953)<br>
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| Albert Strickler (1887–1963)<br>
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| Cyril Frank Colebrook (1910–1997)
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| ==See also==
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| * [[Chézy formula]]
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| * [[Darcy–Weisbach equation]]
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| * [[Hydraulics]]
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| == References ==
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| ===Notes===
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| <references/>
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| ===General===
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| * [[Hubert Chanson|Chanson]], H. (2004), The Hydraulics of Open Channel Flow, Butterworth-Heinemann, Oxford, UK, 2nd edition, 630 pages (ISBN 978 0 7506 5978 9)
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| * [[Ven Te Chow|Chow]] (1959). Open-Channel Hydraulics. McGraw-Hill. New York. xviii + 680 pp. Illus. ISBN 1-9328461-8-2
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| * Walkowiak, D. (Ed.) ''Open Channel Flow Measurement Handbook'' (2006) Teledyne ISCO, 6th ed., ISBN 0-9622757-3-5.
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| ==External links==
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| *[http://www.ajdesigner.com/phphydraulicradius/hydraulic_radius_equation.php Hydraulic Radius Design Equations Formulas Calculator]
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| *[http://manning.sdsu.edu/ History of the Manning Formula]
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| *<!--the circular pipe calculations need to be tweaked - 07-01-2013)-->[http://www.wq.illinois.edu/dg/Equations/Mannings.exe Manning formula calculator for several channel shapes ]
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| *[http://wwwrcamnl.wr.usgs.gov/sws/fieldmethods/Indirects/nvalues/index.htm Manning ''n'' values associated with photos]
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| *[http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Mannings_n_Tables.htm Table of values of Manning's n]
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| *[http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Manning_Equation_Flow_Generator.htm Interactive demo of Manning's equation]
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| [[Category:Fluid dynamics]]
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| [[Category:Hydrology]]
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| [[Category:Piping]]
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| [[Category:Hydraulic engineering]]
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| [[Category:Sedimentology]]
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| [[Category:Geomorphology]]
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I'm a 50 years old, married and working at the university (Continuing Education and Summer Sessions).
In my free time I try to learn Portuguese. I've been twicethere and look forward to returning anytime soon. I like to read, preferably on my beloved Kindle. I really love to watch How I Met Your Mother and Sons of Anarchy as well as documentaries about anything astronomical. I enjoy Rock stacking.
Feel free to surf to my blog post ... sexy Nebraska women