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| − | == Wind Power == | + | == Wind Power == |
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| − | The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by | + | The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by |
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| − | <math>P=\frac{1}{2}\rho A v^3</math><br> | + | [[File:]] |
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| − | It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''. | + | It varies proportional to air density <span class="texhtml">ρ</span>, to the crossed area ''A ''and to the cube of wind velocity ''v''. |
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| − | The Power ''P ''is the kinetic energy | + | The Power ''P ''is the kinetic energy |
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| − | <math>E=\frac{1}{2}mv^2</math>
| + | [[File:]] |
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| − | of the air-mass ''m ''crossing the area ''A ''during a time interval <br> | + | of the air-mass ''m ''crossing the area ''A ''during a time interval |
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| − | <math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>.
| + | [[File:]]. |
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| − | Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation | + | Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation |
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| − | <math>P=\dot{E}=\frac{1}{2}\dot{m}v^2=\frac{1}{2}\rho A v^3</math>
| + | [[File:]] |
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| − | The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<math>v_1</math>) and behind the rotor area (<math>v_2</math>) is <math>v_1/v_2=1/3</math>. The maximum power extracted is then given by<br> | + | The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (<span class="texhtml">''v''<sub>1</sub></span>) and behind the rotor area (<span class="texhtml">''v''<sub>2</sub></span>) is <span class="texhtml">''v''<sub>1</sub> / ''v''<sub>2</sub> = 1 / 3</span>. The maximum power extracted is then given by |
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| − | <math>P_{Betz}=\frac{1}{2} \rho A v^3 c_{P.Betz}</math>
| + | [[File:]] |
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| − | where <math>c_{p.Betz}=0,59</math> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of <math>c_{p.Betz}=0,5</math>. | + | where <span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,59</span> is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of <span class="texhtml">''c''<sub>''p''.''B''''e''''t''''z''</sub> = 0,5</span>. |
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| − | == Unit abbreviations ==
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| − | {| width="399" cellspacing="1" cellpadding="1" border="0" align="left" style="" | + | |
| | + | == Unit Abbreviations<br/> == |
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| | + | {| style="" align="left" width="399" border="0" cellpadding="1" cellspacing="1" |
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| − | | m = metre = 3.28 ft.<br> | + | | m = metre = 3.28 ft.<br/> |
| − | | HP = horsepower<br> | + | | HP = horsepower<br/> |
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| − | | s = second<br> | + | | s = second<br/> |
| − | | J = Joule<br> | + | | J = Joule<br/> |
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| − | | h = hour<br> | + | | h = hour<br/> |
| − | | cal = calorie<br> | + | | cal = calorie<br/> |
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| − | | N = Newton<br> | + | | N = Newton<br/> |
| − | | toe = tonnes of oil equivalent<br> | + | | toe = tonnes of oil equivalent<br/> |
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| − | | W = Watt<br> | + | | W = Watt<br/> |
| − | | Hz = Hertz (cycles per second)<br> | + | | Hz = Hertz (cycles per second)<br/> |
| | |} | | |} |
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| − | <br>
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| − | <br>
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| − | <br>
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| − | <br>
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| − | <math>10^{-12}</math> = p pico = 1/1000,000,000,000
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| − | <math>10^{-9}</math> = n nano = 1/1000,000,000
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| − | <math>10^{-6}</math> = µ micro = 1/1000,000
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| − | <math>10^{-3}</math> = m milli = 1/1000
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| − | <math>10^{3}</math> = k kilo = 1,000 = thousands | + | <span class="texhtml">10<sup>− 12</sup></span> = p pico = 1/1000,000,000,000 |
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| − | <math>10^{6}</math> = M mega = 1,000,000 = millions | + | <span class="texhtml">10<sup>− 9</sup></span> = n nano = 1/1000,000,000 |
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| − | <math>10^{9}</math> = G giga = 1,000,000,000 | + | <span class="texhtml">10<sup>− 6</sup></span> = µ micro = 1/1000,000 |
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| − | <math>10^{12}</math> = T tera = 1,000,000,000,000 | + | <span class="texhtml">10<sup>− 3</sup></span> = m milli = 1/1000 |
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| − | <math>10^{15}</math> = P peta = 1,000,000,000,000,000 | + | <span class="texhtml">10<sup>3</sup></span> = k kilo = 1,000 = thousands |
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| | + | <span class="texhtml">10<sup>6</sup></span> = M mega = 1,000,000 = millions |
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| | + | <span class="texhtml">10<sup>9</sup></span> = G giga = 1,000,000,000 |
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| − | [[Portal:Wind]]
| + | <span class="texhtml">10<sup>12</sup></span> = T tera = 1,000,000,000,000 |
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| | + | <span class="texhtml">10<sup>15</sup></span> = P peta = 1,000,000,000,000,000 |
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| | + | |
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| | + | [[Portal:Wind]] |
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| | [[Category:Wind]] | | [[Category:Wind]] |
Revision as of 10:05, 16 May 2012
Wind Power
The power P of a wind-stream, crossing an area A with velocity v is given by
[[File:]]
It varies proportional to air density ρ, to the crossed area A and to the cube of wind velocity v.
The Power P is the kinetic energy
[[File:]]
of the air-mass m crossing the area A during a time interval
[[File:]].
Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
[[File:]]
The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses. Betz and Lanchester found, that the maximum energy can be extracted from a wind-stream by a wind turbine, if the relation of wind velocities in front of (v1) and behind the rotor area (v2) is v1 / v2 = 1 / 3. The maximum power extracted is then given by
[[File:]]
where cp.B'e't'z = 0,59 is the power coefficient giving the ratio of the total amount of wind energy which can be extracted theoretically, if no losses occur. Even for this ideal case only 59% of wind energy can be used. In practice power coefficients are smaller: todays wind turbines with good blade profiles reach values of cp.B'e't'z = 0,5.
Unit Abbreviations
m = metre = 3.28 ft.
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HP = horsepower
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s = second
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J = Joule
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h = hour
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cal = calorie
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N = Newton
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toe = tonnes of oil equivalent
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W = Watt
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Hz = Hertz (cycles per second)
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10− 12 = p pico = 1/1000,000,000,000
10− 9 = n nano = 1/1000,000,000
10− 6 = µ micro = 1/1000,000
10− 3 = m milli = 1/1000
103 = k kilo = 1,000 = thousands
106 = M mega = 1,000,000 = millions
109 = G giga = 1,000,000,000
1012 = T tera = 1,000,000,000,000
1015 = P peta = 1,000,000,000,000,000
Portal:Wind
