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In fluid dynamics, the Hagen Poiseuille equation is a physical law that gives the pressure drop in a fluid flowing through a long cylindrical pipe. The assumptions of the equation are that the flow is laminar viscous and incompressible and the flow is through a constant circular cross-section that is substantially longer than its diameter. The equation is also known as the Hagen Poiseuille law, Poiseuille law and Poiseuille equation. ... In standard fluid dynamics notation: \Delta P = \frac{8 \mu L Q}{ \pi r^4} or \Delta P = \frac{128 \mu L Q}{ \pi d^4} where: P is the pressure drop L is the length of pipe is the dynamic viscosity Q is the volumetric flow rate r is the radius d is the diameter Physics notation \Phi = \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} where: V is a volume of the liquid poured (cubic meters) t is the time (seconds) v is mean fluid velocity along the length of the tube (meters/second) x is a distance in direction of flow (meters) R is the internal radius of the tube (meters) P is the pressure difference between the two ends (pascals) L is the total length of the tube in the x direction (meters). source: http://en.wikipedia.org/wiki/Poiseuille_equation

Poiseuille law

Poiseuille equation

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <apply> <eq/> <apply> <times/> <ci>&Delta;</ci> <ci>P</ci> </apply> <apply> <divide/> <apply> <times/> <cn>8</cn> <ci>&mu;</ci> <ci>L</ci> <ci>Q</ci> </apply> <apply> <times/> <pi/> <apply> <power/> <ci>r</ci> <cn>4</cn> </apply> </apply> </apply> </apply> </math>

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mrow> <mi>&Delta;</mi> <mo>&InvisibleTimes;</mo> <mi>P</mi> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>8</mn> <mo>&InvisibleTimes;</mo> <mi>&mu;</mi> <mo>&InvisibleTimes;</mo> <mi>L</mi> <mo>&InvisibleTimes;</mo> <mi>Q</mi> </mrow> <mrow> <mi>&pi;</mi> <mo>&InvisibleTimes;</mo> <msup> <mi>r</mi> <mn>4</mn> </msup> </mrow> </mfrac> </mrow> </math>

\Delta P = \frac{8 \mu L Q}{ \pi r^4}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mi>&Delta;</mi> <mi>P</mi> <mo>=</mo> <mfrac> <mrow> <mn>8</mn> <mi>&mu;</mi> <mi>L</mi> <mi>Q</mi> </mrow> <mrow> <mi>&pi;</mi> <msup> <mi>r</mi> <mn>4</mn> </msup> </mrow> </mfrac> </mrow> <annotation encoding="SnuggleTeX">\[ \Delta P = \frac{8 \mu L Q}{ \pi r^4} \]</annotation> </semantics> </math>