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exam1_solutions - ES330 Section 2 Exam#1 Name You will have...

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ES330 Section 2 Exam#1 Name: You will have 1.5 hours to complete the exam. Please show all work and list any assumptions you are making. You must draw a control volume, free body diagram, and coordinate system if required by the problem to receive credit for your work. Problem #1 (40 points) Wind power is becoming more and more common as energy needs grow. The wind entering and leaving the turbine can be described by the streamlines that bound all of the mass flowing into the blades as shown below. Turbine blades V 1 A 1 V 2 A 2 bounding streamlines
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ES330 Section 2 Exam#1 Name: Starting with the following equation: + + + + + + + = + cs cv net net dA n V gz V P u V d gz V P u t W Q ˆ 2 2 2 2 v ( ( & & ρ ρ ρ ρ (a) Derive an expression for the amount of power that is available from the wind if the wind speed approaching a turbine is V wind , the area of the blades is A b , the exit area A 2 , and there are no losses. A 1 A b , V 1 =V wind . (10 points) (b)
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