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Hagen-Poiseuille Equation

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# Hagen-Poiseuille Equation

*n*(Poiseuille equation) The equation of steady, laminar, Newtonian flow through circular tubes:

*Q*= the volumetric flow rate,

*R*and

*L*are the tube radius and length, Δ

*P*= the pressure drop (including any gravity head) in the direction of low, and

*η*= the fluid viscosity. With the roles of

*Q*and

*η*interchanged, this is the basic equation of capillary viscometry. Any

*consistent*system of units may be used. This important equation was first derived theoretically in 1839 by G. Hagen and, a year later, inferred from experimental measurements by J.L. Poisuille. In a laminar flow through a circular tube, a simple force balance shows that the shear stress at the wall,

*τ*

_{w}, = Δ

*P R*/(2

*L*). By Newton's law of viscosity (see Viscosity), the shear rate at the wall,

*γ*

_{w}, must equal to the shear stress