Wonderful experiment and a good question.
I would suggest using a kitchen weighing scale.
More accurate the better. Weigh each shirt three
times: (1) before soaking, (2) right after
soaking, but make sure it is not dripping wet (we
want to accurately measure evaporated water), and
(3) several measurements while the shirt is out in
the sun. From the weight difference between each
step you will be able to calculate accurately the
moisture content by weight. If needed in terms of
volume, use the value for the density of water
(1000 kg/m3) to convert.
You can take extra care to be accurate by also
measuring the weight of the bucket of water into
which the shirt soaked; the decrease in bucket’s
weight should be the increase in shirt’s weight,
if no spilling occurs.
Hope this helps. Enjoy your wonderful
experiment and let me know if it worked.
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