Air flow dissipation rate

Question

Consider two streams of air flowing through the nozzles to an unlimited volume with atmospheric pressure.

The flow is the same, but the cross section areas of the circular nozzles and the speeds differ, so the flow through the smaller nozzle is proportionally faster.

Intuitively, the stream which is faster at the nozzle would transfer the air farther.

Is there any empirical rule which can be used to measure air stream dissipation rates given the initial speed and nozzle cross section area?

I am aware of Lattice-Bolzmann numerical methods, and can run the experiments too, but as i am new to air dynamics, may be I am overlooking something obvious.

Answer 1

In a gas flow into an open volume there will be a fairly well defined point (at some distance form the nozzle) at which the flow transitions from laminar to turbulent and this is usually where most of the energy dissipation occurs.

This can be seem in the real world in the smoke pattern from a recently extinguished candle wick.

The most common formal definition of this is the Reynolds Number which gives a reasonable approximation of whether flow conditions are dominated by viscous or inertial forces.