Hagen-Poiseuille Equation

n (Poiseuille equation) The equation of steady, laminar, Newtonian flow through circular tubes: 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, τ _w , = ΔP 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