Visual angle - Revision history

en>Jacobolus: /* Measuring and computing / um, 2 tan (x/2) is approx tan(x) for small x. It's not approx tan(x/2). Can't just throw away that factor of 2

2014-09-25T23:34:11Z

Measuring and computing: um, 2 * tan (x/2) is approx tan(x) for small x. It's *not* approx tan(x/2). Can't just throw away that factor of 2

← Older revision		Revision as of 01:34, 26 September 2014
Line 1:		Line 1:
	~~{{ref improve\|date=February 2012}}~~		Hi there. Allow me start by introducing the writer, her title is Sophia. What me and my family love is doing ballet but I've been using on new issues recently. My day job is an invoicing officer but I've already applied for an additional 1. Some time ago she selected to live in Alaska and her parents live close [http://kpupf.com/xe/talk/735373 psychic solutions by lynne].
	~~The '''Fanning friction factor''', named after John Thomas Fanning (1837–1911), is a [[dimensionless number]] used in fluid flow calculations~~. ~~It is related to the [[shear stress]] at the wall as:~~

	~~:<math>~~
	~~\tau = \frac{ f \rho v^2}{2}~~
	~~</math>~~

	~~where:~~

	*<math>\tau</math> is the shear stress at the wall
	*'''<math>f</math>''' is the Fanning friction factor of the pipe
	*'''<math>v</math>''' is the fluid velocity in the pipe
	*'''<math>\rho</math>''' is the density of the fluid

	The wall shear stress can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area (<math>2 \pi R L</math> for a pipe) and dividing by the cross-sectional flow area (<math> \pi R^2</math> for a pipe).

	~~The friction [[Head (hydraulic)\|head]] can be related to the pressure loss due to friction by dividing the pressure loss~~ by the ~~product of the acceleration due to gravity and the density of the fluid. Accordingly~~, ~~the relationship between the friction head and the Fanning friction factor is:~~

	~~:<math>~~
	~~h_f = \frac{ 2fv^2L}{gD}~~
	~~</math>~~

	~~where:~~

	*<math>h_f</math> is ~~the friction loss (in head) of the pipe~~.
	*'''<math>f</math>''' is ~~the Fanning friction factor of the pipe.~~
	*'~~''<math>v</math>''' is the fluid velocity in the pipe~~.
	*'''<math>L</math>''' is ~~the length of pipe.~~
	*'~~''<math>g</math>''' is the local acceleration of gravity.~~
	*'''<math>D</math>''' is the pipe diameter.

	~~== Fanning friction factor formulæ ==~~

	~~This friction factor is one-fourth of the [[Darcy friction factor]], so attention must be paid~~ to ~~note which one of these is meant~~ in ~~the "friction factor" chart or equation consulted. Of the two, the Fanning friction factor is the more commonly used by Chemical Engineers~~ and ~~those following the British convention.~~

	~~The formulae below may be used to obtain the Fanning friction factor for common applications.~~

	~~The friction factor for laminar flow in round tubes is often taken to be~~:

	~~<math>f= \frac{16}{Re} <~~/~~math>~~

	~~where Re is the [[Reynolds number]] of the flow.~~

	~~For a square channel the value used is:~~

	~~<math>f = \frac{ 14.227}{Re} <~~/~~math>~~

	~~The Darcy friction factor can also be expressed as<ref>Yunus, Cengel~~. ~~Heat and Mass Transfer. New York: Mc Graw Hull, 2007.</ref>~~

	~~<math>f = \frac{8 \tau_w}{\rho V_{avg} ^ 2} <~~/~~math>~~

	~~where:~~

	* <math>\tau_w</~~math> is the shear stress at the wall~~
	* <math>\rho</~~math> is the density of the fluid~~
	* <math>V_{avg} </math> is the average fluid velocity

	~~For the turbulent flow regime, the relationship between the Fanning friction factor and the Reynolds number is more complex and is governed~~ by ~~the [[Colebrook equation]] <ref>Colebrook, C.F. and White, C.M. 1937, "Experiments with Fluid friction roughened pipes.", ''Proc. R.Soc.(A)'', '''161'''</ref> which is implicit in <math>f</math>:~~

	~~:<math>{1 \over \sqrt{\mathit{f}}}= -4.0 \log_{10} \left(\frac{\frac{\epsilon}{d}}{3.7} + {\frac{1.256}{Re \sqrt{\mathit{f} } } } \right) , \text{turbulent flow}</math>~~

	~~Various [[Darcy friction factor formulae\|explicit approximations~~]~~] of the related Darcy friction factor have been developed for turbulent flow.~~

	~~Stuart W. Churchill<ref>Churchill, S.W~~.~~, 1977, "Friction factor equation spans all fluid-flow regimes", ''Chem.~~
	~~Eng.'', '''91''' </ref> developed a formula that covers the friction factor for both laminar and turbulent flow (note that <math> f </math> represents the Moody friction factor).~~

	~~:<math> f = 8 \left(~~
	~~\left( \frac {8} {Re} \right) ^ {12}~~
	~~+ \left( A+B \right) ^ {-1.5}~~
	~~\right) ^ {\frac {1} {12} } </math>~~
	~~:<math>A = \left( 2.457 \ln \left( \left( \left( \frac {7} {Re} \right) ^ {0.9} + 0.27 \frac {\epsilon} {D} \right)^ {-1}\right) \right) ^ {16} </math>~~
	~~:<math>B = \left( \frac {37530} {Re} \right) ^ {16} </math>~~

	~~== References ==~~
	~~<references/>~~

	~~{{DEFAULTSORT:Fanning Friction Factor}}~~
	~~[[Category:Dimensionless numbers of fluid mechanics]]~~
	~~[[Category:Equations of fluid dynamics]]~~
	~~[[Category:Fluid dynamics]]~~
	~~[[Category:Piping]]~~

en>BG19bot: /* Measuring and computing */WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9838)

2014-01-06T18:18:47Z

Measuring and computing: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9838)

← Older revision		Revision as of 20:18, 6 January 2014
Line 1:		Line 1:
	~~Jayson Berryhill~~ is ~~how I~~'~~m called and my wife doesn~~'~~t like it at all. Invoicing~~ is ~~what I do.~~ The ~~preferred pastime~~ for ~~him~~ and ~~his kids is~~ to ~~perform lacross~~ and he'~~ll be starting some thing else alongside with it~~. I'~~ve always cherished residing~~ in ~~Kentucky but now I~~'~~m contemplating other choices~~.<br><br>~~my site; certified psychics~~ - [~~http~~://~~165~~.~~132~~.39.93/xe/~~visitors~~/~~372912 just click~~ the ~~next webpage~~],		{{ref improve\|date=February 2012}}
			The '''Fanning friction factor''', named after John Thomas Fanning (1837–1911), is a [[dimensionless number]] used in fluid flow calculations. It is related to the [[shear stress]] at the wall as:

			:<math>
			\tau = \frac{ f \rho v^2}{2}
			</math>

			where:

			*<math>\tau</math> is the shear stress at the wall
			*'''<math>f</math>''' is the Fanning friction factor of the pipe
			*'''<math>v</math>''' is the fluid velocity in the pipe
			*'''<math>\rho</math>''' is the density of the fluid

			The wall shear stress can, in turn, be related to the pressure loss by multiplying the wall shear stress by the wall area (<math>2 \pi R L</math> for a pipe) and dividing by the cross-sectional flow area (<math> \pi R^2</math> for a pipe).

			The friction [[Head (hydraulic)\|head]] can be related to the pressure loss due to friction by dividing the pressure loss by the product of the acceleration due to gravity and the density of the fluid. Accordingly, the relationship between the friction head and the Fanning friction factor is:

			:<math>
			h_f = \frac{ 2fv^2L}{gD}
			</math>

			where:

			*<math>h_f</math> is the friction loss (in head) of the pipe.
			*'''<math>f</math>''' is the Fanning friction factor of the pipe.
			*'''<math>v</math>''' is the fluid velocity in the pipe.
			*'''<math>L</math>''' is the length of pipe.
			*'''<math>g</math>''' is the local acceleration of gravity.
			*'''<math>D</math>''' is the pipe diameter.

			== Fanning friction factor formulæ ==

			This friction factor is one-fourth of the [[Darcy friction factor]], so attention must be paid to note which one of these is meant in the "friction factor" chart or equation consulted. Of the two, the Fanning friction factor is the more commonly used by Chemical Engineers and those following the British convention.

			The formulae below may be used to obtain the Fanning friction factor for common applications.

			The friction factor for laminar flow in round tubes is often taken to be:

			<math>f= \frac{16}{Re} </math>

			where Re is the [[Reynolds number]] of the flow.

			For a square channel the value used is:

			<math>f = \frac{ 14.227}{Re} </math>

			The Darcy friction factor can also be expressed as<ref>Yunus, Cengel. Heat and Mass Transfer. New York: Mc Graw Hull, 2007.</ref>

			<math>f = \frac{8 \tau_w}{\rho V_{avg} ^ 2} </math>

			where:

			* <math>\tau_w</math> is the shear stress at the wall
			* <math>\rho</math> is the density of the fluid
			* <math>V_{avg} </math> is the average fluid velocity

			For the turbulent flow regime, the relationship between the Fanning friction factor and the Reynolds number is more complex and is governed by the [[Colebrook equation]] <ref>Colebrook, C.F. and White, C.M. 1937, "Experiments with Fluid friction roughened pipes.", ''Proc. R.Soc.(A)'', '''161'''</ref> which is implicit in <math>f</math>:

			:<math>{1 \over \sqrt{\mathit{f}}}= -4.0 \log_{10} \left(\frac{\frac{\epsilon}{d}}{3.7} + {\frac{1.256}{Re \sqrt{\mathit{f} } } } \right) , \text{turbulent flow}</math>

			Various [[Darcy friction factor formulae\|explicit approximations]] of the related Darcy friction factor have been developed for turbulent flow.

			Stuart W. Churchill<ref>Churchill, S.W., 1977, "Friction factor equation spans all fluid-flow regimes", ''Chem.
			Eng.'', '''91''' </ref> developed a formula that covers the friction factor for both laminar and turbulent flow (note that <math> f </math> represents the Moody friction factor).

			:<math> f = 8 \left(
			\left( \frac {8} {Re} \right) ^ {12}
			+ \left( A+B \right) ^ {-1.5}
			\right) ^ {\frac {1} {12} } </math>
			:<math>A = \left( 2.457 \ln \left( \left( \left( \frac {7} {Re} \right) ^ {0.9} + 0.27 \frac {\epsilon} {D} \right)^ {-1}\right) \right) ^ {16} </math>
			:<math>B = \left( \frac {37530} {Re} \right) ^ {16} </math>

			== References ==
			<references/>

			{{DEFAULTSORT:Fanning Friction Factor}}
			[[Category:Dimensionless numbers of fluid mechanics]]
			[[Category:Equations of fluid dynamics]]
			[[Category:Fluid dynamics]]
			[[Category:Piping]]

137.222.80.157: /* Measuring and computing */

2012-08-10T15:08:23Z

Measuring and computing

New page

Jayson Berryhill is how I'm called and my wife doesn't like it at all. Invoicing is what I do. The preferred pastime for him and his kids is to perform lacross and he'll be starting some thing else alongside with it. I've always cherished residing in Kentucky but now I'm contemplating other choices.<br><br>my site; certified psychics - [http://165.132.39.93/xe/visitors/372912 just click the next webpage],

Visual angle - Revision history

en>Jacobolus: /* Measuring and computing */ um, 2 * tan (x/2) is approx tan(x) for small x. It's *not* approx tan(x/2). Can't just throw away that factor of 2

en>BG19bot: /* Measuring and computing */WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9838)

137.222.80.157: /* Measuring and computing */

en>Jacobolus: /* Measuring and computing / um, 2 tan (x/2) is approx tan(x) for small x. It's not approx tan(x/2). Can't just throw away that factor of 2