The Poiseuille's law (or the Hagen-Poiseuille law also named after Gotthilf Heinrich Ludwig Hagen (1797-1884) for his experiments in 1839) is the physical law concerning the voluminal laminar stationary flow ΦV of incompressible uniform viscous liquid (so called Newtonian fluid) through a cylindrical tube with the constant circular cross-section, experimentally derived in 1838, formulated and published in 1840 and 1846 by Jean Louis Marie Poiseuille (1797-1869), and defined by:
The law is also very important specially in hemorheology and hemodynamics, both fields of physiology.
The Poiseuilles' law was later in 1891 extended to turbulent flow by L. R. Wilberforce, based on Hagenbach's work.
The law itself shows how an interesting field this is, because the Darcy-Weisbach equation should be properly named in full as the Chézy-Weisbach-Darcy-Poiseuille-Hagen-Reynolds-Fanning-Prandtl-Blasius-von Kármán-Nikuradse-Colebrook-White-Rouse-Moody equation or CWDPHRFPBKNCWRM equation in 'short'.
Poiseuille's law corresponds to the Ohm's law for electrical circuits, where pressure drop Δp* is somehow replaced by voltage V and voluminal flow rate ΦV by current I. According to this a term 8η l/πr4 is an adequate substitution for the electrical resistance R.Curiosity
Relation to electrical circuit