Papyrus 39: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Yobot
m WP:CHECKWIKI error fixes using AWB (9075)
en>Dexbot
m Removing Link GA template (handled by wikidata)
 
Line 1: Line 1:
The '''depth–slope product''' is used to calculate the [[shear stress]] at the bed of an [[open channel flow|open channel]] containing [[fluid]] that is undergoing [[steady flow|steady]], [[uniform flow|uniform]] flow. It is widely used in [[river engineering]], [[stream restoration]], [[sedimentology]], and [[Geomorphology#Fluvial|fluvial geomorphology]]. It is the [[product (mathematics)|product]] of the water [[wikt:depth|depth]] and the mean bed [[slope]], along with the [[gravitational acceleration|acceleration due to gravity]] and [[density]] of the fluid.
Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. You can either install Word - Press yourself or use free services offered on the web today. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster. <br><br>Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. There are number of web services that offer Word press development across the world. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself. <br><br>It is very easy to install Word - Press blog or website. Word - Press has ensured the users of this open source blogging platform do not have to troubleshoot on their own, or seek outside help. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine.  Here is more on [http://2am.eu/backupplugin627125 wordpress backup] check out our website. To turn the Word - Press Plugin on, click Activate on the far right side of the list. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. <br><br>Word - Press installation is very easy and hassle free. But the Joomla was created as the CMS over years of hard work. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. If your site does well you can get paid professional designer to create a unique Word - Press theme. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. I don't want that for my visitors and I'm quite sure they don't either. The days of spending a lot of time and money to have a website built are long gone. Word - Press is an open source content management system which is easy to use and offers many user friendly features. Article Source: Hostgator discount coupons for your Wordpress site here.
 
==Formulation==
 
The use of the depth–slope product — in computing the bed shear-stress — specifically refers to two assumptions that are widely applicable to natural [[river]] channels: that the angle of the channel from horizontal is small enough that it can be approximated as the slope by the [[small-angle formula]], and that the channel is much wider than it is deep, and sidewall effects can be ignored. Although it is a simplistic approach to find the shear stress in what can often be a locally unsteady [[fluvial]] system, when averaged over distances of kilometers, these local variations average and the depth–slope product becomes a useful tool to understand shear stress in open channels such as rivers.
 
===Depth and hydraulic radius===
 
The first assumption is that the channel is much wider than it is deep, and the equations can be solved as if the channel were infinitely wide. This means that side-wall effects can be ignored, and that the [[hydraulic radius]], <math>R_h</math>, can be assumed to be equal to the channel depth, <math>h</math>.
 
:<math>R_h = \frac{A}{P}</math>
 
where <math>A</math> is the [[cross sectional area]] of flow and <math>P</math> is [[wetted perimeter]]. For a semicircular channel, the hydraulic radius would simply be the true [[radius]].
 
For an approximately rectangular channel (for simplicity in the mathematics of the explanation of the assumption),
 
:<math>A = b h </math>,
 
where <math>b</math> is the width (breadth) of the channel, and
 
:<math>P = b+2h</math>.
 
For b>>h,
 
:<math>P \rightarrow b</math>,
 
and therefore
 
:<math>R_h \rightarrow \frac{b h}{b} = h</math>.
 
Formally, this assumption can generally be held to hold when the width is greater than about 20 times the height; the exact amount of error accrued can be found by comparing the height to the hydraulic radius. For channels with a lower width-to-depth ratio, a better solution can be found by using the hydraulic radius instead of the above simplification.
 
===Pressure===
 
The total [[stress (mechanics)|stress]] on the bed of an open channel of infinite width is given by the [[hydrostatic pressure]] acting on the bed. For a fluid of [[density]] <math>\rho</math>, an [[gravitational acceleration|acceleration due to gravity]] <math>g</math>, and a flow depth <math>h</math>, the pressure exerted on the bed is simply the weight of an element of fluid, <math>\rho g</math>, times the depth of the flow, <math>h</math>. From this, we get the expression for the total pressure, <math>P_b</math>, acting on the bed.
 
:<math>P_b=\rho g h \,</math>
 
===Shear stress===
 
In order to convert the pressure into a shear stress, it is necessary to determine the [[Euclidean vector|component]] of the pressure that provides shear on the bed. For a channel that is at an angle <math>\alpha</math> from horizontal, the shear component of the stress acting on the bed <math>/\left(\tau_b\right)</math>, which is the component acting tangentially to the bed, equals the total pressure times the sine of the angle <math>\alpha</math>.
 
:<math>\tau_b=\rho g h \sin{\left(\alpha\right)} \,</math>
 
In natural rivers, the angle <math>\alpha</math> is typically very small. As a result, the small-angle formula states that:
 
:<math>\sin{\left(\alpha\right)}\approx\tan{\left(\alpha\right)}</math>
 
The tangent of the angle <math>\alpha</math> is, by definition, equal to the [[slope]] of the channel, <math>S</math>.
 
:<math>\tan{\left(\alpha\right)}\equiv S</math>
 
From this, we can arrive at the final form of the relation between bed shear stress and depth–slope product:
 
:<math>\tau_b=\rho g h S \,</math>
 
===Scaling===
 
Assuming a single, well-mixed, [[wikt:homogeneous|homogeneous]] fluid and a single acceleration due to gravity (both are good assumptions in natural rivers, and the second is a good assumption for processes on Earth, or any planetary body with a dominant influence on the local graviational field), the only two variables that determine the boundary shear stress are the depth and the slope. This is the significance of the name of the formula.
 
:<math>\tau_b\propto h S</math>
 
For natural streams, in the [[Mks system of units|mks]] or [[International System of Units|SI]] system (units of [[Pascal (pressure)|pascals]] for shear stress), a typical useful relationship to remember is that:
 
:<math>\tau_b=10000 \left[\frac{\mathrm{kg}}{\mathrm{m}^2 \ \mathrm{s}^2}\right] h S</math>
 
for water with a density of 1000&nbsp;kg/m<sup>3</sup> and approximating the acceleration due to gravity as 10&nbsp;m/s<sup>2</sup> (the error in this assumption is typically much smaller than the error from measurements).
 
==Uses==
 
Bed shear stress can be used to find:
* The vertical [[velocity]] profile within the fluid flow
* The ability of the [[fluid]] to [[Sediment transport|carry sediment]]
* The rate of shear [[Dispersive mass transfer|dispersion]] of contaminants and tracers.
 
==See also==
* [[Sediment]]
* [[Fluid mechanics]]
 
==References==
*Leopold, Wolman, and Miller (1964), ''Fluvial Processes in Geomorphology,'' Dover Publications, Mineola, NY, USA, 535 pp.
 
{{DEFAULTSORT:Depth-slope product}}
[[Category:Fluid dynamics]]
[[Category:Geology]]
[[Category:Civil engineering]]
[[Category:Environmental engineering]]

Latest revision as of 20:00, 3 September 2014

Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. You can either install Word - Press yourself or use free services offered on the web today. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster.

Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. There are number of web services that offer Word press development across the world. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. Once you've installed the program you can quickly begin by adding content and editing it with features such as bullet pointing, text alignment and effects without having to do all the coding yourself.

It is very easy to install Word - Press blog or website. Word - Press has ensured the users of this open source blogging platform do not have to troubleshoot on their own, or seek outside help. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. Here is more on wordpress backup check out our website. To turn the Word - Press Plugin on, click Activate on the far right side of the list. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way.

Word - Press installation is very easy and hassle free. But the Joomla was created as the CMS over years of hard work. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. If you just want to share some picture and want to use it as a dairy, that you want to share with your friends and family members, then blogger would be an excellent choice. If your site does well you can get paid professional designer to create a unique Word - Press theme.

A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. I don't want that for my visitors and I'm quite sure they don't either. The days of spending a lot of time and money to have a website built are long gone. Word - Press is an open source content management system which is easy to use and offers many user friendly features. Article Source: Hostgator discount coupons for your Wordpress site here.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Papyrus_39&oldid=262483"