Hagen-Poiseuille Viscous Pipe Flow

Mechanical Engineering

How It Works

Hagen-Poiseuille flow describes the fully developed, laminar volumetric flow of a viscous incompressible fluid through a straight circular cylindrical conduit. Enforcing the no-slip boundary condition at the stationary pipe walls results in a parabolic radial velocity distribution, with maximum flow velocity occurring along the central centerline axis and falling quadratically to zero at the walls.

Governing Equation
u(r) = (ΔP / (4 · μ · L)) · (R² - r²) , Q = (π · R⁴ · ΔP) / (8 · μ · L) , u_max = 2 · u_avg