RMH Theory

I was calculating the pressure drop in various sections of the RMH when I when I was surprised to find that the dynamic viscosity of air actually increases with temperature to approximately the 1.5 power.  (This figure in MKS units:  https://www.researchgate.net/profile/Sanjeev_Sanghi/publication/272983817/figure/fig1/AS:294713933484047@1447276685803/Figure-1-Variation-of-dynamic-viscosity-and-thermal-conductivity-of-air-with.png).  Secondly, as you know, the volume of an ideal gas expands proportionally with absolute-temperature (in other words to the 1 power.   Assuming a constant mass flow rate, this basically means that the volumetric flow rate in any part of the RMH is proportional to absolute-temperature.)  Amazingly, all of this taken together says that the pressure-loss goes as roughly the absolute-temperature to the 2.5 power.  Assuming constant cross-sectional area throughout the RMH, it appears that the pressure loss in the burn tunnel and riser is roughly twice that of the bench duct, despite the bench duct being several times longer!  

I'm not proposing any formal design changes, since I know your designs are tested, and there are benefits with higher Reynolds number flow (faster, more "turbulent" flow), better mixing, and maybe benefits with a smaller core being slightly easier to insulate (log-function of diameter).  I just thought it was an interesting observation.  If you ever are short on draft pressure, this theory suggests that increasing the diameter of these hot sections slightly, by even a half inch or an inch could reduce the pressure-drop significantly.  Noticing that cross-section area increases with the diameter to the 2nd power, which is close to 2.5 , one could almost size the diameter in proportion to the absolute-temperature, and this ought to give nearly constant pressure drop per unit length.  I know I shouldn't assume this is optimal since there are many other design considerations.  Nevertheless, it seems useful to have some idea of where the pressure losses are.  

Heat transfer by convection is also proportional to the pressure drop, at least in a normal straight, closed pipe.  I'll suppose that having high thermal convection in the heat riser isn't too important, since at such high temperatures I presume most of the heat transfer is by radiation, especially if the gases contain much tar, soot and/or ash.  Reducing pressure losses in the riser would mean more pressure drop is available to expend in the bench duct.  This could be a slight design advantage allowing more heat transfer into the bench for a given length duct.  So in theory the bench could be made either slightly more efficient or slightly shorter for the same heat transfer.  

Sorry for the untested, blue-sky theories...I could be completely wrong, I was just excited to find this and wanted to tell somebody.