Waterwheel Experiments for Students--- A Teachers' Guide, Rev. 0.0
Waterwheel Experiments for StudentsThis guide is provided to permit local school teachers in or near Melbourne, Florida to introduce their students to waterwheel concepts. A visit to our Botanical Gardens will show a water wheel in action.
History
Water wheels were used by Romans (1, p.467). While early mill wheels were horizontal, the Romans devised the vertical wheel on a horizontal axis, reaching 15 kWe power (1, 468). The New England colonists had abundant streams, and water wheels hastened the industrial age (1,468). Water wheels were superseded by higher speed turbines like the Pelton turbine where heads of 30 feet or more were possible.
Principles
Waterwheels convert the energy of moving water to mechanical motion. When high water pressures are available, a water jet can spin a Pelton turbine wheel at high speeds of several hundred revolutions per minute. If only a low height of water (head( 8s available a slow moving water wheel is used. Most waterwheels rely upon the weight of water in buckets forcing the wheel to rotate. If the water strikes the top nearer side of the wheel, it rotates towards the water source, When the water falls from a flume (through) over the tip of the wheel, the "overshot" wheel rotates away from the source, An "undershot" wheel can run in a stream with just the bottom few inches submerged, and the stream kinetic energy is converted into rotational energy. In some instances, a surrounding shroud holds water up against the undershot while holding the water in to extract more energy.
Florida Tech's Waterwheel
This small waterwheel is located in the Botanical Gardens of Florida Institute of Technology northwest of Babcock Street and University Boulevard in Melbourne Florida. For more information and assistance, contact Frank Leslie in the Link Building, Dept. of Marine and Environmental Systems.
The renewal of the Botanical Gardens cleared a significant area of "jungle", greatly enhancing the appearance. I felt that a small waterwheel would add a moving, splashing feature that would also serve to introduce local students to the principles of water power. Florida Tech has a strong commitment to community outreach programs, and this educational unit is a small part of that effort.
At the opposite end of the power range, Cornell university spent $1.25 million to renovate a 1.3 MWe hydroplant on campus and reached pay-off in 5 years (1, 474)!
Experiments
First, a warning, as this waterwheel often turns at 50 to 60 rpm, and can be hazardous! There are potential pinch-points, and users must be careful. At low water flows when there is about one inch of water over the spillway, the wheel can be brought to a stop by grasping the shaft firmly. Users accept responsibility for any injury. The wood wheel may tend to develop splinters, and a possibility of infection exists. (Remember that the stream is storm runoff from approximately a square mile of residential community west of Country Club Road.)
Elementary school students should likely be only observers of experiments, while high school students may have active involvement with supervision. Middle school students' participation is at the discretion of their teacher.
Classic Power Measurements
The power of the wheel varies with the weight of water flowing into the wheel per unit time. The wheel opening is 24 inches wide, and the spillway depth of the water forms a cross-sectional area. Measure the depth at several locations along the spillway in front of the wheel and average them to get the average water depth. The speed of flow forms a length of water each second. This length times the area and dividing by 1728 cubic inches/cubic foot yields a volume in cubic feet that flows each second. Multiplying by 62.4 pounds per cubic foot yields the weight of water per second.
This wheel has six closed buckets that catch the water on the side towards the spillway. This type is known as the "breastshot" wheel since the water strikes about 70% of the diameter from the bottom. An overshot wheel receives water on the top from a flume, while an undershot wheel is placed in a stream and i8s pushed from the bottom. Since the water can only fall a maximum of some 25 inches, we used a breast shot wheel.
If the wheel shaft is held to stop the wheel, the water can completely fill the horizontal bucket and retain some water in the next lower bucket. A spring scale measured the holding force as 25 pounds at a 12-inch radius from the shaft center. The torque, or twisting moment, was 12 inches times 25 pounds or 300 inch-pounds or 25 ft-lbs.
Power
Power is the rate of doing work and is proportional to the rotation speed, Ń, times the restraining torque, T. The classic English measurement is the horsepower (hp), which James Watt defined as 550 ft-lbs per second. When the wheel runs without load or is held stationary, the extracted power is zero. At intermediate speeds, power is extracted, reaching a maximum power point (MPP) at some speed. As the spillway water depth rises, the MPP shifts to a higher speed.
We change the speed by applying a mechanical brake and measuring the speed and torque. There are three simple ways to do this: double-scale braking, Prony brake, and weight lifting.
Double-Scale Technique
Wrap three or four turns of 1/4-inch rope around the pipe shaft and connect the ends to two spring scales. Take care not to let the rope lap over itself and grab the shaft. If the shaft were stationary, pulling on the scales would show the same force on each, and the net difference would be zero. If the wheel is turning, there will be a net difference between the scale readings proportional to the friction force on the shaft. Hold the scales steady, read and record each while measuring the time for ten turns of the wheel. Repeat this for some eight different levels of friction. These values might be for approximately 12, 14, 16, 18, 20, 22, & 24 pounds of net force. Multiply each net force by turns per second and divide by 550 ft-lbs/second to yield horsepower. Plot these points to estimate where the MPP occurs for this water depth.
Prony Brake Method
The Prony brake simplifies the torque measurement since only one force reading gage is necessary. A friction brake is formed by half-round sections in a long piece of wood and a short one. These pieces clamp around the pipe shaft. When the bolts are loose, there is zero drag, and a spring scale attached to the end reads zero. When the bolts are tightened, frictional forces then to rotate the long piece, and the scale reads the force at the fixed radius. (One could place the eyebolt for the scale hook at precisely 10 inches to simply torque calculations.) As with the double-scale method, the friction is varied to make torque-speed measurements while the speed is recorded. A plot will show the MPP for the spillway depth.
Weight Lift Method
The original measurement of horsepower was made using a weight lifted by a block-and-tackle as a horse pulled the rope. We can duplicate this experiment by wrapping several turns of rope around the wheel shaft and timing the rise of a large rock of known weight. If 30 pounds rises 6 ft in 5 seconds, that's 180 ft-lbs in 5 seconds, or 36 ft-lb/s. Since 1 hp equals 550 ft-lb/s, 0.065 hp was generated.
Conclusion
Hydropower is one of the earliest forms of industrial power. From water pumping in mines to the early grist mills that ground grain, water power has proven to be an excellent choice for developing countries. Through these experiments, you have seen how a simple machine can accomplish work, even where the water falls a short distance.
Glossary
Head The vertical height of water above the wheel or turbine that drives the rotor.
Kinetic Energy KE = 1/2 mv2
Microhydro A hydropower system with a rated power less than 100 kilowatts.
Potential Energy PE or Ug = mgh
Power (kW) = 5.9 x flow (cu. m/s) x head (m)
Spouting Velocity Speed of water from a jet or hole in a tank = √( 2gh) = ~8 times square root of h ft/sec.
Watershed The area of land that supplies water to the dam.
Units
1 psi = 2.31 ft head = 7 kilopascal. 1 horsepower = 746 watts = 550
ft-lb/sec.
1 cubic ft water = 62.4 pounds. 1 liter water = 1 kilogram. 1 m head = 100g/cm2.
g = 9.8 m/s2 = 32.2 ft/s2. 1 joule = 0.734 ft-lbs. 1 Btu =
778 ft-lbs. 1 kWh = 3.6 x 106 J.
References
1. Aubrecht, Gordon. Energy. Second Edition. Upper Saddle River NJ: Prentice-Hall, 1995.
2. Davis, Scott. Microhydro: Clean Power from Water. Canada: New Society Publishers, 158 pp., 2003.
3. Harrison-Smith, J.L. Practical Water Power. Tauranca, New Zealand, by author, 120 pp., 1985.
Websites
Commercial wheel builders http://www.waterwheelfactory.com/
Society of Old Mills http://www.spoom.org
Cornell University Hydroplant http://eco.pdc.cornell.edu/sustain/energy-hydro.htm
History http://www.angelfire.com/journal/pondlilymill/clark.html
Student Microturbine Generator Project http://www.re-energy.ca/pdf/cp2.pdf
Florida Watersheds http://cfpub.epa.gov/surf/state.cfm?statepostal=FL
Back to Frank Leslie's home page
GardensWheel/waterwheeleducation.htm updated 040706
