IB Physics 2 Research project 
Wheel of Water 
The effect of flow rate on the power output of a water wheel. 

Nicole Janes, Emily Wisler, Sarah Paul, Marissa Rietman 
1/18/2013 
Contents:

Up until the twentieth century, waterwheels were used as a major source of generating power. In our project, we will build an overshot wheel; a vertically mounted wheel that is rotated by falling water. The water is channeled to the top of the wheel and collects in the buckets on that side. This makes it heavier and causes the wheel to turn. Overshot wheels gain an advantage from gravity and the momentum of flowing water. On average, an overshot waterwheel uses 63% of the energy in the flow of the water, as calculated by John Smeaton in the eighteenth century (source 7).
The speed that an ornament is raised by the spinning of the water wheel is an estimate of power output. Many factors affect the power output of a water wheel, such as the water not going directly to the buckets, the buckets being under filled or overfilled, the balance of the water for the wheel to turn properly, the wheel being to tight or too loose, as well as the condition of the elements of the wheel (source 3).
The purpose of our investigation is to find out the speed at which we can raise an ornament with an overshot waterwheel due to the flow rate of the water. This will give information on the power output of the water wheel because the faster it raises the ornament, the more efficient the waterwheel will be (source 5).
We believe that, with the flow rate (cups/second) as the independent variable and the power output (amount of time it takes to raise the ornament a foot) as the dependent variable, when the independent variable increases eventually the dependent variable will begin to decrease. Once a lot of water begins to pour onto the wheel, power output will decrease because there will be more water flowing than the wheel will be able to handle.
The materials we used were: corrugated plastic, glue gun, rod, string, ornament, duct tape, 5gallon bucket, water/hose, measuring cup, and a timer. We cut the water wheel out of corrugated plastics and then glued it together with a glue gun. We cut a hole in the middle of the wheel to put the rod through and then secured the edges of the rod to the side of the bucket. The bucket caught the water that flowed out of the water wheel (see picture). With this setup we started with a hose to obtain different flow rates to test our hypothesis. We timed how long it took to fill a 2 cup measuring cup and then divided that number by 2 to get the flow rate in cups per second. The first flow rates we stared with were very slow and took a long time. We then placed the hose over the edge of the water wheel (see picture) and timed the amount of time it took in seconds for the water wheel to raise a one foot string with an ornament attached at the bottom. This time was used to calculate power output. We repeated this procedure 15 times gradually increasing the flow rate each time. We used the same procedure with the measuring cup to measure the new flow rate for each new trial.
Graph:
Calculations Used:
· Calculated velocity from s=(u+v)t/2 converted to v= 2s/t
· Calculated acceleration from v^{2}=u^{2}+2as converted to a=v^{2}/2s
· Convert flow rate to mL/s (236.588 mL per 1 cup)
· Calculated total mass of water from flow rate and time
· Calculated force using F=ma
· Calculated power using Power=Fv
Our results did show that as the flow rate increased so did the power output. It rose exponentially showing that as the flow rates increased, they had a bigger effect on the power output of the water wheel.
Our data showed that when the flow rate was faster, the power output was bigger. It rose in at an exponential rate demonstrating how when the flow rate was faster, not only did it make a greater power output, it had a greater effect on the power output. The data that we collected did not support our hypothesis. While we did predict that as flow rate increased so would power output, our idea that at some point it would eventually drop off was not supported by our data. This might have been because we were not to test a high enough flow rate or because our mode l was just too small. It makes sense that as the flow rate increased so would power output, because as we increased the flow rate, it added more force to the wheel which then was able to turn faster, or in other words generate more power.
One main source of error was in the timing. We timed the flow rate used for calculations by hand which may have been highly inaccurate, because when the flow rate was faster it was hard to stop at exactly the right moment. Another source of error was that in using the hose there was no way to verify that the flow rate remained the same throughout the duration of each trial meaning that there could have been variations affecting power output of the water wheel. Another source of error was that the hose was not placed in the exact same spot for every trial which may have affected the angle at which it hit the water wheel and consequently skewed the power output.
To improve this lab we could have used equations like mgh to calculate the flow rate instead of trying to time it by hand. The water would have to be a set amount in a bucket above with a small hole for the water to run through. Also the use of a bucket with a hole and calculating flow rate through equations would eliminate the uncertainty of the hose. Lastly, if neither the source of water or water wheel were moved inbetween trials it would help to eliminate the uncertainty if the water stream hitting the water wheel at different angles.
1. http://autonopedia.org/renewable_energy/Water/Overshot_Water_Wheel.html This site was very helpful, because it provided information on overshot water wheels to help us start the project.
2. http://www.energyeducation.tx.gov/technology/section_1/topics/calculatingefficiency/index.html This website helped us figure out how to calculate the efficiency of our water wheel.
3. http://www.waterhistory.org/histories/waterwheels This taught us a lot about the history of water wheels.
4. http://permaculturewest.org.au/ipc6/ch08/shannon/index.html This showed us about the mechanics of the water wheel.
5. http://www.sciencebuddies.org/sciencefairprojects/project_ideas/Energy_p021.shtml This gave us an example project to learn from.