Linear response function - Revision history

en>Yobot: WP:CHECKWIKI error fixes using AWB (10503)

2014-11-25T08:36:02Z

WP:CHECKWIKI error fixes using AWB (10503)

← Older revision		Revision as of 10:36, 25 November 2014
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en>BD2412: Fixing links to disambiguation pages using AWB

2014-02-22T19:48:38Z

Fixing links to disambiguation pages using AWB

← Older revision		Revision as of 21:48, 22 February 2014
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	~~[[File:Ubbelohde lepkosciomierz.PNG\|right\|thumb\|Ubbelohde viscometer]]~~		Hello, my name is Andrew and my spouse doesn't like it at all. Credit authorising is how he tends to make cash. Some time ago he chose to live in North Carolina and he doesn't plan on altering it. To play lacross is 1 of the things she enjoys most.<br><br>my blog ... love psychic readings ([http://clothingcarearchworth.com/index.php?document_srl=441551&mid=customer_review Discover More Here])
	~~[[File:Leo Ubbelohde.jpg\|right\|thumb\|Dr. Leo Ubbelohde~~, ~~the inventor of the Ubbelohde viscometer.]]~~

	~~A '''Ubbelohde type viscometer''' or '''suspended-level viscometer'''~~ is ~~a [[measuring instrument]] which uses a capillary based method of measuring [[viscosity]].<ref>~~'~~'Introduction to Polymers'' R.J. Young ISBN 0-412-22170-5</ref> It is recommended for higher viscosity [[cellulose\|cellulosic polymer]] solutions~~. ~~The advantage of this instrument~~ is ~~that the values obtained are independent of the total volume. The device was invented by the German chemist [[Leo Ubbelohde]] (1877-1964).~~

	~~[[ASTM]] and other test methods are: ISO 3104, ISO 3105, ASTM D 445, ASTM D 446, IP 71, BS 188 <ref>[http://www.rheotek.com/scat.asp?id=69 ASTM Ubbelohde Viscometer<!-- Bot generated title -->]</ref>~~

	~~The Ubbelohde viscometer is closely related~~ to ~~the [[Ostwald viscometer]]~~. Both are u-shaped pieces of glassware with a reservoir on one side and a measuring bulb with a [[capillary]] on the other. A liquid is introduced into the reservoir then sucked through the capillary and measuring bulb. The liquid is allowed to travel back through the measuring bulb and the time ~~it takes for the liquid~~ to ~~pass through two calibrated marks is a measure for viscosity. The Ubbelohde device has a third arm extending from the end of the capillary~~ and ~~open to the atmosphere. In this way the pressure head only depends on a fixed height and no longer on the total volume of liquid.~~

	~~==Determination of viscosity==~~

	~~The determination of viscosity is based on [[Poiseuille~~'~~s law]]:~~

	~~:<math> \frac{dV}{dt} = v \pi R^{2} = \frac{\pi R^{4}}{8 \eta} \left( \frac{- \Delta P}{\Delta x}\right) = \frac{\pi R^{4}}{8 \eta} \frac{ \|\Delta P\|}{L}, </math>~~

	~~where~~ t ~~is the [[time]]~~ it ~~takes for a [[volume]] V to elute~~. ~~The ratio <math>\frac{dv}{dt}</math> depends on R as the capillary [[radius]], on~~ the ~~average applied [[pressure]] P, on its length L and on the dynamic [[viscosity]] [[Eta (letter)\|η]]~~.

	~~The average pressure head is given by:~~

	:<~~math~~>~~\Delta P = \rho g \Delta H \,~~<~~/math~~>

	~~with [[Rho (letter)\|ρ]] the [[density]] of the liquid, g the [[Standard gravity]] and H the average head of the liquid~~. ~~In this way the viscosity of a fluid can be determined~~.

	~~Usually the viscosity of a liquid is compared to a liquid with an analyte for example a polymer dissolved in it~~. ~~The~~ [~~[relative viscosity]] is given by~~:

	~~:<math>\eta_r = \frac{\eta}{\eta_0} = \frac{t \rho}{t_0 \rho_0},</math>~~

	~~where t<sub>0<~~/~~sub> and ρ<sub>0<~~/~~sub> are the elution time and density of the pure liquid~~. ~~When the solution is very diluted~~

	~~:<math>\rho \simeq \rho_0 \,<~~/~~math>~~

	~~the so-called '''specific viscosity''' becomes:~~

	~~:<math>\eta_{sp} = \eta_r - 1 = \frac{t - t_0}{t_0}~~. ~~\,</math>~~

	~~This specific viscosity is related to the [[concentration]] of the analyte through the [[Intrinsic viscosity]] [η] by the [[power series]]:~~

	~~:<math>\eta_{sp}~~ = ~~[\eta] c + k [\eta]^2 c^2 + \cdots\,</math>~~

	or

	~~:<math>\frac{\eta_{sp}}{c}~~ = ~~[\eta] + k [\eta]^2 c + \cdots,\,</math>~~

	~~where <math>\frac{\eta_{sp}}{c}</math> is called the '''viscosity number'''.~~

	~~The intrinsic viscosity can be determined experimentally by measuring the viscosity number as function of concentration as the Y-axis intercept.~~

	~~== References ==~~
	~~{{Reflist}}~~

	~~[[Category:Measuring instruments]]~~
	~~[[Category:Laboratory glassware]]~~
	~~[[Category:Polymer chemistry]~~]

en>Zueignung: /* Example */ more explicit; also, a damped oscillator is not a band-pass filter

2013-08-10T18:30:26Z

Example: more explicit; also, a damped oscillator is not a band-pass filter

← Older revision		Revision as of 20:30, 10 August 2013
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	~~Alyson~~ is ~~the title individuals use~~ to ~~contact me and I believe it seems fairly great when you say it~~. ~~My day occupation~~ is ~~an info officer but I've currently utilized~~ for ~~an additional one~~. ~~My spouse~~ and ~~I reside in Mississippi but now I'm contemplating~~ other ~~choices.~~ [http://~~afeen~~.~~Fbho~~.~~net~~/~~v2/index~~.~~php~~?do=/~~profile~~-~~210/info/ best psychics~~] ~~My spouse doesn't like~~ it the way ~~I do but what I truly like performing~~ is ~~caving but I don~~'t ~~have~~ the time ~~lately~~.<br><br>~~Also visit my web page; telephone~~ [~~http~~://~~conniecolin~~.~~com~~/xe/~~community~~/~~24580 real psychic readings~~]; [~~http:~~//~~findyourflirt~~.~~net/index~~.~~php?m~~=~~member_profile&p~~=~~profile&id~~=~~117823 findyourflirt.net~~],		[[File:Ubbelohde lepkosciomierz.PNG\|right\|thumb\|Ubbelohde viscometer]]
			[[File:Leo Ubbelohde.jpg\|right\|thumb\|Dr. Leo Ubbelohde, the inventor of the Ubbelohde viscometer.]]

			A '''Ubbelohde type viscometer''' or '''suspended-level viscometer''' is a [[measuring instrument]] which uses a capillary based method of measuring [[viscosity]].<ref>''Introduction to Polymers'' R.J. Young ISBN 0-412-22170-5</ref> It is recommended for higher viscosity [[cellulose\|cellulosic polymer]] solutions. The advantage of this instrument is that the values obtained are independent of the total volume. The device was invented by the German chemist [[Leo Ubbelohde]] (1877-1964).

			[[ASTM]] and other test methods are: ISO 3104, ISO 3105, ASTM D 445, ASTM D 446, IP 71, BS 188 <ref>[http://www.rheotek.com/scat.asp?id=69 ASTM Ubbelohde Viscometer<!-- Bot generated title -->]</ref>

			The Ubbelohde viscometer is closely related to the [[Ostwald viscometer]]. Both are u-shaped pieces of glassware with a reservoir on one side and a measuring bulb with a [[capillary]] on the other. A liquid is introduced into the reservoir then sucked through the capillary and measuring bulb. The liquid is allowed to travel back through the measuring bulb and the time it takes for the liquid to pass through two calibrated marks is a measure for viscosity. The Ubbelohde device has a third arm extending from the end of the capillary and open to the atmosphere. In this way the pressure head only depends on a fixed height and no longer on the total volume of liquid.

			==Determination of viscosity==

			The determination of viscosity is based on [[Poiseuille's law]]:

			:<math> \frac{dV}{dt} = v \pi R^{2} = \frac{\pi R^{4}}{8 \eta} \left( \frac{- \Delta P}{\Delta x}\right) = \frac{\pi R^{4}}{8 \eta} \frac{ \|\Delta P\|}{L}, </math>

			where t is the [[time]] it takes for a [[volume]] V to elute. The ratio <math>\frac{dv}{dt}</math> depends on R as the capillary [[radius]], on the average applied [[pressure]] P, on its length L and on the dynamic [[viscosity]] [[Eta (letter)\|η]].

			The average pressure head is given by:

			:<math>\Delta P = \rho g \Delta H \,</math>

			with [[Rho (letter)\|ρ]] the [[density]] of the liquid, g the [[Standard gravity]] and H the average head of the liquid. In this way the viscosity of a fluid can be determined.

			Usually the viscosity of a liquid is compared to a liquid with an analyte for example a polymer dissolved in it. The [[relative viscosity]] is given by:

			:<math>\eta_r = \frac{\eta}{\eta_0} = \frac{t \rho}{t_0 \rho_0},</math>

			where t<sub>0</sub> and ρ<sub>0</sub> are the elution time and density of the pure liquid. When the solution is very diluted

			:<math>\rho \simeq \rho_0 \,</math>

			the so-called '''specific viscosity''' becomes:

			:<math>\eta_{sp} = \eta_r - 1 = \frac{t - t_0}{t_0}. \,</math>

			This specific viscosity is related to the [[concentration]] of the analyte through the [[Intrinsic viscosity]] [η] by the [[power series]]:

			:<math>\eta_{sp} = [\eta] c + k [\eta]^2 c^2 + \cdots\,</math>

			or

			:<math>\frac{\eta_{sp}}{c} = [\eta] + k [\eta]^2 c + \cdots,\,</math>

			where <math>\frac{\eta_{sp}}{c}</math> is called the '''viscosity number'''.

			The intrinsic viscosity can be determined experimentally by measuring the viscosity number as function of concentration as the Y-axis intercept.

			== References ==
			{{Reflist}}

			[[Category:Measuring instruments]]
			[[Category:Laboratory glassware]]
			[[Category:Polymer chemistry]]

en>Cydebot: Robot - Moving category Fundamental physics concepts to :Category:Concepts in physics per CFD at Wikipedia:Categories for discussion/Log/2012 July 12.

2012-07-19T00:30:37Z

Robot - Moving category Fundamental physics concepts to Category:Concepts in physics per CFD at Wikipedia:Categories for discussion/Log/2012 July 12.

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