A teaching exercise on renewable energy
Learn how to calculate wind turbine power output through a worked example on formula substitution. Join Dr. Roger Dargaville from Monash University in this resourceful engineering session.
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A teaching exercise on renewable energy A worked example on Formula substitution (MathsAlgebra ACMEM035 and ACMEM036) to help understand how to compute wind turbine power output Dr Roger Dargaville, Resources Engineering, Monash University roger.dargaville@monash.edu
How much energy is there in the wind? Question: a) Write a formula for the energy that a turbine sees every second in terms of the density of the air, the velocity of the wind and the radius of the turbine: ??/?=1 The kinetic energy of an object (i.e. the energy that it possesses due to its motion) is equal to half of an object's mass multiplied by the velocity squared. ?? =1 2??2 2 ? ?2 ??/?=1 2??? ?2 1 2 ???3 1 2 ??2??3 (Area of a circle ? = ??2) The mass of air passing through the swept area of a turbine per unit of time is: velocity area density ? = ??? ??/?= ??/?= Swept Area 1 2 ??2??3 ??/?=
How much energy is there in the wind? b) Assume a 50m radius turbine, air density of 1.23 kg/m3 and a wind speed of 12m/s. What is the total energy available every second? Round your answer to 3 s.f. then write it in scientific notation Workout out the unit of the answer (?2)(?? ?3)(? ?)3 =?5?? ?3?3 ??/?=1 ??/?=1 ??/? 8,340,000 ??/? 8.34 106 2 ??2??3 2 3.14 (502)(1.23) (123) ??/? 8.34 106 W =?2?? ?2? ? ? = = ?
