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Chapter 15: Problem 14

Is the flow speed behind a wind turbine greater or less than in front? Is the pressure behind the turbine higher or lower than in front? Is this a violation of Bernoulli's principle? Explain.

Short Answer

Expert verified
The flow speed of the wind behind a wind turbine is less than in front of it while the pressure is higher behind the turbine compared to the front. This doesn't violate Bernoulli's principle. Bernoulli's principle, in essence, is a statement of the conservation of energy principle for flowing fluids, and it shows that the energy in a fluid flow remains constant if losses due to friction are neglected.

Step by step solution

01

Understanding the flow of wind behind and in front of a wind turbine

From Bernoulli's principle, we know that if a fluid (in this case, air) flows through a narrower area, it must speed up (to conserve the principle of continuity, which states that the mass flowing per second through a tube is constant along the tube). The same principle will apply to the wind flowing through a wind turbine, and thus the wind speed is lower behind a wind turbine compared to the wind speed in front of the turbine.
02

Understanding the pressure behind and in front of a wind turbine

The pressure behind a wind turbine is higher. When the air slows down (decrease in kinetic energy) after passing along the blades, the pressure will rise (increase in potential energy). This change is in accordance to Bernoulli's principle which states that in a fluid, an increase in speed occurs simultaneously with a decrease in pressure or a change in the fluid's gravitational potential energy. Hence, pressure does increase when the wind slows down after passing through a turbine.
03

Understanding if there is a violation of Bernoulli's principle

There is no violation of Bernoulli's principle in this scenario. The principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. Here, when the wind speed decreases after passing through the turbine, the pressure increases which is in line with Bernoulli's principle, as it implies conservation of energy.

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