A model for wind-induced draught
There is a textbook model that relates, approximately, air velocity to change in pressure at an orifice
in the air stream. This is:
𝑃=
1
𝜌𝑣 2
2
(1)
where P is the change in pressure, ρ is the density of air and v its velocity. This is simplest to use with
SI units, viz. Pascal, kg per metre cubed and metres per second. One application of this is in the
prediction of Pitot effect where the orifice is perpendicular to the airflow. This effect was, in times
past, used to measure the relative speed of aircraft. Pitot pressure increases with air speed.
If the orifice is parallel to the airflow the pressure drops as air speed increases. I would conjecture
that (1) could be stated more generally as:
𝑃=
1 2
𝜋
𝜌𝑣 cos(2𝜃) , (0 ≤ 𝜃 ≤ ) , (2)
2
2
I have checked this result experimentally and the variation of pressure drop with the square of
velocity holds true over the range tested (1.9 to 14.3 ms-1). The total effect is slightly less than that
predicted from (2), but not much less. The experimental results for airflow parallel to the orifice are
graphed below. These results are consistent with an air density of 1.14 kgm-3 whereas the true value
should be approximately 1.3
Experimental system.
A 3mm. steel tube was set in a vice 15 mm. in front of an anemometer. An air blower was placed so
that the air stream blew over the top of the steel tube to the anemometer. The distance of the
blower to the tube was varied randomly prior to each reading. The bottom of the steel tube was
connected to a manometer by flexible tube. A branch in this tube connected to a closed container
that acted as a reservoir and buffer, reducing any spurious effects due to reverberation within the
system.
Observations.
There was some instability in the readings of both anemometer and manometer. These were
reduced but not removed by adding the buffer/reservoir to the system; it seems likely that these
variations were due to turbulence in the air stream.
A first test of the system returned lower than expected pressure drops. Before proceeding the
upper end of the steel tube was ground and smoothed so that its edges were more precisely parallel
to the air stream and that any roughness causing local turbulence was minimised. The R2 statistic on
the regression indicates that 97% of the variance is accounted for by the model. The value of the y
parameter suggests that expression (1) represents an ideal that may be approached, but not
reached in practice.
From (1) this effect would appear to be independent of the orifice size or its depth, but from the
tests conducted, the effect Is sensitive to the orientation of the orifice and to its shape and surface
texture.
Application
Mean wind speed in the UK is about 6 ms-1 in exposed places. It seems likely that, at 6 ms-1, a hilltop
bloomery could work on wind induced draught during a windy period. Presumably wind effect would
have to be added to any chimney effect. It is worth noting that, if the air inlets of such a bloomery
were large and perpendicular to the air flow, that the wind effect could be doubled.
It seems implausible that this effect was widely employed in the Weald because so many of the
known sites are (even ignoring tree cover) sheltered.
160
140
y = 0.5698x
R² = 0.9717
120
Pressure (Pa)
100
80
60
40
20
0
0
50
100
150
velocity squared
200
250