Display MoreOf course you know what it is. Of course you can give bounds. It is right there in Fig. 4. The velocity is uniform across 60 mm of the 66 mm orifice. The velocity cannot possibly drop abruptly to zero in the last 3 mm. Make a reasonable estimate based on common sense and basic physics. You don't have to know exactly. Just look at the velocity profile for similar round, smooth pipes with turbulent air flowing through them. Or you can do it the rigorous way. Here:
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This ends with the equation right there on the screen. Go for it!
Or, see the figures and equations here. If you can't do the maths, I think you can use Fig. 4:
https://jingweizhu.weebly.com/…bulent_flow_modelling.pdf
2 Velocity profiles: the inner, outer, and overlap layers
We have seen in Fig. 3 that there are three regions in turbulent flow near a wall:
1. Wall layer: Viscous shear dominates.
2. Outer layer: Turbulent shear dominates.
3. Overlap layer: Both types of shear are important.Let τw be the wall shear stress, and let δ and U represent the thickness and velocity at the edge of
the outer layer, y = δ. For the wall layer, Prandtl deduced in 1930 that u must be independent of
the shear–layer thickness . . .
You want bounds? The error has to be far less than 17%.
Jed: you have posted the same equations I posted - from which I derived Umax = 1.23V (at Re = 12,000). I am happy to go through these equations with you if you doubt this. That gives an average velocity 19% less than the middle of pipe peak velocity.
So I cannot agree with your bound - if it is based on the equations.
If based on the measurements: I'm trying to work out how you use the CW-60. Have you personally used it - you would know. The spec I've found is
http://custom.company.weiku.co…r-Heat-Wire-14658647.html
The hot wire is as you know in a probe. Could you tell me how you insert the (long) probe in the pipe? Is it meant to measure flow perpendicular to the probe, or flow parallel to the probe, or does it make no difference?
From the anenometer data I get an accuracy of approx +/- 0.3m/s, which corresponds to +/- 8.5% on speed, and therefore power.
So my bound currently would be +0 - 19% (airflow velocity profile) +8.5% - 8.5% (anenometer accuracy).
That gives +8.5% - 26% bounds overall on airflow from the measured result.
The -19% from the air velocity profile can maybe be tightened. I'm just not sure because of the big difference between the equations for turbulent flow and the very flat measurements - which seems anomalous. While there is probably some good explanation I'm not confident.