Step by step solution to "At a certain location, wind is blowing steadily..."

ukelangf0

Answered question

2021-11-17

At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60-m-diameter blades at that location. Take the air density to be $1.25 \frac{k g}{m^{3}}$ .

Answer & Explanation

Florence Pittman

Beginner2021-11-18Added 15 answers

Given
$V = 10 \frac{m}{s}$
$D = 60 m$
$p_{a i r} = 1.25 \frac{k g}{m^{3}}$
Required
Power generation potential P
Solution
per mass unit, kinetic energy:
$e = \frac{K E}{m} = \frac{V^{2}}{2}$
$= \frac{10^{2}}{2}$
$= 50 \frac{m^{2}}{s^{2}}$
This result shows how many J of kinetic energy 1kg of air moving at 10\frac{m}{s} has. To calculate power generation potential of the wind turbine one has to calcuta the mass of air that crosses the wind turbine every second:
$m_{a i r} = ρ_{a i r} \cdot A_{t u r b i n e} \cdot V$
$= ρ_{a i r} \cdot \frac{D^{2} π}{4} \cdot V$
$= 1.25 \cdot \frac{60^{2} π}{4} \cdot 10$
$= 35343 \frac{k g}{s}$
Since air has a kinetic energy of 50 J per kilogram, the potential for overall power generation is:
$P = m_{a i r} \cdot e$
$= 35343 \cdot 50$
$= 1767.15 k W$
Result: P=1767.15 kW

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