Simple Method to Detect Pipe Turbulence

Consider a fluid flow through a pipe having length to diameter ratio 7500 (or just too big a number). The flow is driven by a constant pressure head (H) and exits the pipe by gravity ensuring a constant pressure difference along the pipe. How to determine the flow is laminar or turbulent? The diameter is very small so sophisticated cross sectional local velocity measurement using Particle Image Velocimetry or Laser Doppler anemometry is not possible (at least not straight forward) to determine the local turbulence. Also, static pressure measurements along the pipe length could disturb the wall surface, if one needs to carry out sensitive experiments with the flow. So, is there a simple way out? We know for a laminar fully developed flow, at any length along the pipe, the cross sectional velocity variation from the pipe wall to the axis is parabolic (maximum at the pipe axis, zero at the pipe wall). Correspondingly, in tur-bulent flow of the same mass flow rate, the velocity profile would be flatter and more uniform along the cross section. Velocity at the axis, in this case