You can use a specialized wind speed gauge, which I did not have.
You can also use a small scrap of paper and a video camera (which I do
have).
The idea is that the bit of paper will move just about as fast as the
air is moving. To measure how fast that is, you can record some video
and look at one frame showing the paper moving. I used four trials and
averaged the results, for each speed setting.
One standard NTSC video frame is composed of two interlaced fields, each
1/60 second in duration, so the full frame shows the paper's motion over
a time interval of 1/30 second. This assumes you have your camera's shutter
set to the standard video exposure of 1/60 sec, and also that your NLE exports
full combined-field frames (not just a single field with the other field
interpolated). Both of these are true in this case.
I put a six-inch length of masking tape on the back of a chair, to use as
a reference in measuring distance. In the image below, you see the blurred
trail of a scrap of paper moving from right to left just above the chair.
As you can see the paper is also rotating. Since this is a combined-field
frame, you see dark lines where the paper is not present during the period
of the other video field. Note that the bright lines shift from odd scanlines
to even lines as the paper moves from field 1 to field 2. This image is enlarged
to 200% so you can see the scanlines more clearly on your screen.
In this example the paper moved a horizontal distance of about 6 inches
in 1/30 of a second, which is 180 inches/sec, 15 feet/sec or 10.2 mph.
(The chair is a relic from the 70's, in fake-leather-textured
vinyl. No animals were harmed during this experiment.)
If you are interested in measurements on fans, you might
also enjoy
this page
.