Well for the IB Extended Essay I have gathered some theory on the overshot water wheel but the problem is I have all this theory, and a general idea of what I want to do, but things just don't seem to come together on paper to do an experiment.
-I have an equation derived for the total available work which basically took the initial kinetic energy of water entering and then we keep subtracting various sources of power losses, and then once these numbers become too small we just multiply the equation by 'm' which is the efficiency of the wheel regardless of what's already been subtracted (meant to be a pretty high number right as of now)
-So that's theoretical power output. Experimentally it is popular to hang a weight from the shaft to calculate the work done by the wheel.
-Also, differentiating the theoretical equation tells us the maximum power out put would occur when the periphery of the wheel is half the speed of entering water. However, this (and the theoretical equation) assumes that no power is lost because of impact, meaning the water simply slips into the wheel for it to turn by its weight rather than impact.
-Breaking up the wheel into vectors shows the changing the angle of the blades could increase or decrease this 'impact' (obviously), and ultimately, this could change the ratio of the maximum power available for the wheel. So instead of the peripheral velocity being half the initial velocity of water, the equation would be more like [Peripheral Velocity=0.5*water velocity*cos(theta-of the blade)]
I have all this information now I need to go on about an experiment either confirming this or use this to take a slightly different approach. (keep in mind I'll be building a prototype of a water-wheel). Any ideas?
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