Читать книгу The Rheology Handbook - Thomas Mezger - Страница 19

Assumptions: horizontal pipe, steady-state and laminar flow conditions (for information on laminar and turbulent flow see Chapter 3.3.3), ideal-viscous flow, incompressible liquid. According to the Hagen/Poiseuille relation , the following holds for the maximum shear stress τw and the maximum shear rate γ ̇ w in a pipeline (index w for “at the wall”):

Equation 2.4

τw = (R ⋅ Δp) / (2 ⋅ L)

Equation 2.5

γ ̇ w = (4 ⋅ V ̇ ) / (π ⋅ R3)

With the pipe radius R [m]; the pressure difference Δp [Pa] between inlet and outlet of the pipe or along the length L [m] of the measuring section, respectively (Δp must be compensated by the pump pressure); and the volume flow rate V ̇ [m3/s]. This relation was named in honor to Gotthilf H. L. Hagen (1797 to 1848) [2.6] and Jean L. M. Poiseuille (1799 to 1869) [2.7].