This form of Bernoulli's equation is only appropriate for ...
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Transcript of This form of Bernoulli's equation is only appropriate for ...
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This form of Bernoulli's equation is only appropriate for incompressible fluids
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Air is compressible
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Water is incompressible
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In a compressible fluid like air, both T and V (density, i.e. n/V) change when pressure changes
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In an incompressible fluid like water, neither T nor density change when pressure changes
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As water flows through the inlet spiral, some part of that flow is directed radially in to the runner and then is lost down the draft tube. Because water is being lost, the diameter of the inlet spiral must shrink to keep velocity and pressure constant.
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Wind turbines are large because the density of air is much less than that of water... and even large as they are, a wind turbine outputs much less power than a hydro turbine. Turbines have gotten larger over time in part for economy of scale: the bigger the turbine, the more power from the wind it can capture, and that increase outweighs the additional cost of a taller tower. But wind speed is also greater at altitude, so turbines have become taller to take advantage of stronger winds.
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This is "Betz's law"
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This is in fact about the optimum tsr - the guess of 5 seconds per rotation (12 rpm) was very close to being correct
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for structural reasons - tips of blades would be going faster than the speed of sound. No turbine could survive spinning that fast.
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~
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power
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Note that the rated power of a wind turbine is not the average power a turbine puts out, it is ~ the maximum power a turbine could put out. The actual power of a turbine is the capacity factor x its rated power. That is, in practice you'd dived the rated power by a factor of 3 to get the actual power (e.g. 3 MW rated -> 1 MW actual)
