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Muslims did not invent the windmill. Windmills to pump irrigation water may have been in use in Babylonia in the 17th century BC. https://en.wikipedia.org/wiki/History_of_wind_power
Windmills were in use in Persia around the 10th century BC. http://www.solaripedia.com/13/80/persian_windmills_and_wind_towers_from_ancient_times.html
Muslims played no role in the invention of the tower windmill popular in the Netherlands.
Romans in pre-Islamic Chemtou in western Tunisia set 3 horizontal water wheels into the bridge abutments.
The other type of waterwheel was the ship mill, where a water wheel is attached to the hull of a ship moored to a bridge, thus allowing it to operate regardless of the water level. These were popular in Europe during the 6th century, and from Europe spread to the Islamic world.
Image by KVDP, via Wikimedia Commons.
Color saturation of image was adjusted by William Siepmann.