Hagen-Poiseuille Equation

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n (Poiseuille equation) The equation of steady, laminar, Newtonian flow through circular tubes:$$Q = \pi R^{\rm 4} \Delta P/\left( {{\rm 8}\eta L} \right)$$ where Q = the volumetric flow rate, R and L are the tube radius and length, ΔP = 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, τw, = ΔP R/(2 L). By Newton's law of viscosity (see Viscosity), the shear rate at the wall, γw, must equal to the shear stress divided by the viscosity. Solving the above equation for ΔP R/(2 η L), one obtains γw = 4 Q/(π R3). By applying the Rabinowitsch Correcti ...