Ok, so as my swansong here before a bit of a break I'll just pursue this a bit.

(1) The Reynolds number calculation is definite.

(2) The fact that average speed < max speed is definite, and the difference is of order of 20% for turbulent flow, and 50% for laminar flow. Specifically:

*The ***velocity profile for laminar flow** is the well-known parabolic form

*u(r)/umax=2(1-r^2/R^2)*

*The resulting average velocity is one half of the maximum velocity*

*uav/umax=0.5*

*For ***turbulent pipe flow** among the numerous **empirica**l velocity profiles, the simplest and the best known is the **power-law velocity profile** expressed as

*u(r)/umax=(1-r/R)^1/n*

*where R is the pipe radius and n is a parameter (exponent) which depends of the Reynolds number i.e. n=n(Re).*

*An empirical approximation of this dependence can be expressed as*

*n(Re)=c·ln(Re)*

*where c=0.62 for Re≤2·Re^5 and c=0.65 for Re>2·Re^5*

*Based on this approach on obtained the following relationship between the average velocity and maximum velocity for turbulent flow*

*uav/umax=2n^2/(n+1)(2n+1)*

*It is to mention that*

*-the value n=7 is applicable to a wide range of pipe flows and is the one commonly used resulting ***uav/umax=0,817**

For a better reference: http://www.itcmp.pwr.wroc.pl/~…bulent_flow_Modelling.pdf

Section 2.1

From which we get the empirical value of n = 5.3 (Re=10,000) and uAv/uMax = 0.77 for Re=10,000.

Alternate approximation (for Re = 10,000), using f = (100Re)^-0.25

Umax ≈ V(1+1.33 sqrt(f)) = V*(1 + 1.33/sqrt((100Re)^0.25)

V = (1/(1+UMax * 0.81

So we get a average mean velocity (and hence power) is 81% or 77% (depending on which approximation is used) of the measured centre of pipe mean velocity

For lower Re (and we can go down to 6800 at 2m/s, or lower at high temperatures, this number will be smaller.

T |
density |
dynamic viscosity |
change in Re ~ rho / mu |

25 |
1.18 |
18.37 |
1 |

100 |
0.947 |
21.7 |
0.68 |

The temperature correction for 100C relative to 25C decreases Re to 68% of its previous value. The change in V relative to UMax from this comes from:

Re' = 0.68 Re

f' = 1.10f

V'= 0.99V

OK this correction is very small due to the relative insensitivity of average velocity on Re.

So, given this, and given that Re ranges from 4000 - 12,000 (worst case) unless air temp is very high, the correction factor here does not change more than 2% over the range as long as air velocity > 2 m/s, T < 100C.

I think my previous post using the f calculation was not quite right, as I said then, but these calculations are now all consistent and show the effect (significant) and its dependence on T an V (not significant).

If as Jed says he has accurate data showing that V/UMax ~ 100% here then we have an inconsistency. But the overall heat loss calculation in this system is more complex than the relatively well known difference between centre mean and average mean velocity on pipe turbulent flow.

Working out flowrate from smoke travel speed will not be accurate because again flow rate through a duct will vary across the duct, and only the true average will be correct.

I'm still not considering the R20 results until that sample result is replaced by comprehensive testing. If the sample data is correct then R20 will unlock $100M + from IH etc etc, and careful testing becomes irrelevant.

THH