1. What is Betz's law?
Betz's law states that the maximum efficiency of a wind-powered machine is 59%. It was derived over one hundred years ago by the German physicist Albert Betz and his contemporaries. Their derivation has been discussed by van Kuik (2007) and Okulov and van Kuik (2012). They disregard viscosity in order to use Bernoulli's principle in their derivation. Assuming inviscid flow leads to a useful model. However, a different approach recognizes the key role that viscosity plays in the interaction of a wind-powered machine with the atmosphere. This model provides a better understanding of how a machine captures energy from the wind, treating the machine as a black box with no knowledge of the mechanism. The machine is held in place by a tower to prevent it from moving downwind when exposed to the wind.
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2. What is the relationship between thrust and the velocity of air flowing through a wind turbine?
Thrust is the force applied by the wind on the machine that tends to push and pull the machine downwind. It is equal to the force applied by the machine on the air mass that flows through it, according to Newton's third law of motion. The first part of thrust, T u, is a reaction to the force applied to the incoming air mass by the machine, decelerating the air mass that flows through it. The second part of thrust, T d, is the force applied by the wind that pulls the air mass through the machine. The velocity change experienced by the air mass that exits the machine and is pulled downwind through the wake is EQUATION, and the velocity at the end of the wake, v f, will always be less than the wind velocity, v o, due to the law of conservation of energy. However, the wake continues downwind for a long distance, and the length of the wake is finite. The machine captures energy from the wind by applying a force on the air mass that resists the flow, and the power captured by the machine can be expressed as P m = (Force) x (Velocity). The mechanical efficiency of the machine is the ratio of the power captured by the machine to the wind power available to it, and the power coefficient is a dimensionless number used to express efficiency. Betz's coefficient, C p, is the maximum value of the power coefficient, which is 0.5926.
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