Water wheels and turbines
Water has been used to power simple and complex mills since antiquity. In colonial America, mills were powered by wooden waterwheels, but as technologies and manufacturing changed during the 19th century, water turbines began to be used more and more. In the period of 1850-1880 dozens of American manufacturers made cast iron turbines of nearly every conceivable configuration. Turbines could be readily ordered in different sizes that were suited for the specific water flow, shafting, and gearing needed for a particular mill. Turbines aren’t as susceptible to reduced flow when the water levels in the turbine pit are high or flooded. Perhaps best of all, turbines were iron and therefore did not require constant repair of a wooden waterwheel that began to rot from intermittent soaking even before installation was complete.
Overshot water wheel
The familiar, picturesque image of an overshot water wheel is the type of water wheel that first comes to mind for a water-powered mill.
The weight of the water in the buckets provide the force to turn an overshot wheel, so larger circumference wheels are desirable. This requires a large fall – the height difference of the water at the top and bottom (also called the “head”). Of course, a larger wheel turns slowly and so gearing may be necessary to increase rpms to suit the mill equipment.
Overshot wheels were constructed of wood for hundreds of years, but there were companies in the last half of the 19th century that made steel wheels. There is a fine example of a large Fitz steel overshot wheel that powers the sawmill at the Taylor Mill in Derry, New Hampshire.
If the head of water is not sufficient for an overshot wheel, a breast wheel might be used where the water strikes the buckets below the top of the wheel. The water passes under the wheel instead of over it, and so rotating in the opposite direction of an overshot wheel.
A breast wheel in which the water strikes the buckets near the top is called a pitchback wheel.
Undershot water wheel
The water strikes the wheel at or near the bottom. Can be used with very low or even no head of water.
Prior to the widespread use of water turbines beginning about 1850-1860, sash sawmills were commonly driven by a type of undershot wheel called a flutter wheel.
Hiscox, Gardner. (1903). Mechanic. movements, powers, devices, and appliances. New York : N.W. Henley & Co. Pages 131-138 have an illustrated and useful glossary of turbine and water wheel types (although unfortunately he doesn't quite correctly know what a flutter wheel is).
Emerson, J. (1892). Treatise Relative to the Testing of Water-wheels and Machinery. Willimansett, MA: published by the author. Evans, O. (1795). The Young Mill-Wright and Miller’s Guide. Philadelphia: Lea & Blanchard. This classic includes material in Part V, The Practical Millwright from a Pennsylvania millwright named Thomas Ellicott. The waterwheel figures shown here are from Ellicott’s section of Evans’ book.Hunter, L. C. (1979). History of Industrial Power in the United States. Volume 1. Waterpower in the Century of the Steam Engine. Charlottesville: Eleutherian Mills-Hagley.Hunter, L. C. (1986). History of Industrial Power in the United States. Volume 2. Steam Power. Charlottesville: Eleutherian Mills-Hagley.Reynolds, T. S. (1979). Scientific Influences on Technology: The Case of the Overshot Waterwheel, 1752-1754. Technology and Culture, 20(2), 270–295.Reynolds, T. S. (1983). Stronger Than a Hundred Men: A History of the Vertical Water Wheel. Baltimore: Johns Hopkins.Reynolds, T. S. (1984). Medieval Roots of the Industrial Revolution. Scientific American, 251(1), 122–130.
More turbine sources listed at Water turbine references.