An Olympic discus thrower (~100 kg) launches the 2.0 kg discus by spinning rapidly (~4 times per second) with arm outstretched (
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Answer:
- The specific mechanical energy of the air in the specific location is 40.5 J/kg.
- The power generation potential of the wind turbine at such place is of 2290 kW
- The actual electric power generation is 687 kW
Explanation:
- The mechanical energy of the air per unit mass is the specific kinetic energy of the air that is calculated using:
where V is the velocity of the air.
- The specific kinetic energy would be:
.
- The power generation of the wind turbine would be obtained from the product of the mechanical energy of the air times the mass flow that moves the turbine.
- To calculate mass flow it is required first to calculate the volumetric flow. To calculate the volumetric flow the next expression would be:
- Then the mass flow is obtain from the volumetric flow times the density of the air:
- Then, the Power generation potential is:
- The actual electric power generation is calculated using the definition of efficiency:
, where η is the efficiency,
is the energy actually produced and,
is the energy input. Then solving for the energy produced: