I will summarize my views and recommendations in the following way:

1) Flare lines ( besides two phase flow) can be subjected to two different kinds of vibration , both of which are flow related.

2) The first type which is known as acoustic induced vibration is more probable.This does not depend on rhov^2. It depends on the product of Mach No. and Pressure drop at valve stations. It is a high frequency vibration which excites the " circumferential modes" of vibration. This type of vibration is addressed by the paper by Carucci and Mueller and the paper by Francis. Francis's paper puts a D/T restriction of 64 for systems where sound power level exceeds that of what is max. allowable for a D/T ratio.

The other solutions are use of anti-vibration trims,special valves,avoidance of weldolets, use of welding tees, use of full encirclement reinforcement at welded pipe supports ( or use of clamped pipe supports at non axial stop locations ) etc.

MTD also provides guidelines for the same.

3) The other type of vibration ( less probable)due to flow is what is known as Flow induced vibration ( an industry name ). This is a low frequency vibration and excites the planar modes. This is a function of rhov^2 as well as the stiffness of the system. MTD guidelines provides formula for calculation of L.O.F or likelihood of failure ( refer second edition of MTD as first edition provides a conservative estimate for gaseous systems) where the term rhov^2 appears.

This guideline also provides correction actions. However a better approach is to compute the pulsating forces( flow induced vibartion is more related to flow velocity and the pressure pulsation due to flow separation at elbows and valves where as acoustic induced vibartion is more realted to pressure drop at valve stations) and thereby compute the flexural stresses at tee points.These flexural stresses are checked against endurance limit. Computation of such forces are based on empirical relationships which I cannot reproduce in the forum.If this approach is not possible, then MTD guideline recommendations can be followed or to put in more general way, recommendations that are valid for acoustic induced vibration are also valid for flow induced vibration and same can be followed.

Hope this helps.