First important concept: turbulence don't have one length-scale. I suggest reading Chapter 6 of Turbulent Flows from Pope [1]. Summarizing, intuitively (I'll loose some formality to keep it simple): turbulence is a composition of infinite eddies of different sizes(length-scales). Each length-scale has it's own energy-fraction associated, which is ~"the sum of the energies of all the eddies with that size". Most of the energy lies in the "production range" (low wave number, or large length-scale). In the so-called inertial range, energy is transferred from large eddies to smaller ones without energy loss (almost inviscid flow) with the Kolmogorov spectrum that has -5/3 wave-number exponent. And following L.F.Richardson, the energy "flows downscale" down to Kolmogorov length-scale, which is the scale at which Reynolds number becomes low enough such that dissipation prevails on inertial effect, and eddies are dissipated. Summarized from Richardson as follows: Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity.
So, going to your question, yes, it looks quite empirical, though I'm not an expert of pipes. But I suppose the scales which you're interested in are the Kolmogorov length-scale (at which dissipation happens) and the energy-density-spectrum-peak length-scale, which is the scale containing the most of the turbulent kinetic energy (look at the turbulence energy density spectrum on Pope)