The Earth's rotation and laminar pipe flow

Abstract

A pipe flow facility with a length of 32 m and a diameter of 40 mm has been designed in which a laminar flow of water can be maintained for Reynolds numbers up to 60 000. Velocity measurements taken in this facility show an asymmetric velocity profile both in the vertical as well as horizontal direction with velocities that deviate strongly from the parabolic Hagen–Poiseuille profile. The cause of this asymmetry is traced back to the influence of the Earth's rotation. This is confirmed by means of a comparison of the experimental data with the results from a perturbation solution and from a numerical computation of the full nonlinear Navier–Stokes equations. The physical background of this unforeseen result lies in the fact that a Hagen–Poiseuille flow is governed by a force equilibrium and inertia forces are everywhere negligible. This implies that the Coriolis force can be balanced only by a viscous force. So even the small Coriolis force due to the Earth's rotation causes a large velocity distortion for a case such as ours where the kinematic viscosity is small.