Tattalin Turbin Kasa da Kyakkyawan Betz

Don samun kula da zafi na gida ta wind turbine muna iya bayar da wani sabon jikin zafi. Ana bayar cewa yadda zafi ya faru a fadin jiki shine V1 kuma yadda zafi ya faru a babin jiki shine V2. Yana da kyau, masa m ya faru a kan wannan jiki daga lokacin rana biyu.
A nan, saboda haka ana sami energy cin kula na zafi a fadin jiki,

Duk da haka, saboda haka ana sami energy cin kula na zafi a babin jiki,


Saboda haka, energy cin kula na zafi ya canza, a lokacin da wannan adadin zafi ya faru daga fadin zuwa babban jiki,

Kamar yadda ake magana, masa m ya faru a kan wannan jiki daga lokacin rana biyu. Saboda haka, power da aka ci zafi shine mafi yawan energy cin kula da ya canza a lokacin da masa m ya faru daga fadin zuwa babban jiki.

A nan, ake magana cewa power shine canzan energy daga lokacin rana biyu. Saboda haka, wannan power da aka ci zafi zai iya rubuta cewa,

Saboda masa m ya faru a lokacin rana biyu, muna iya magana cewa m shine rate ta masa na zafi. Idan muna duba hakan da ma'adanci, za a iya sanin cewa rate ta masa zai kasancewa a fadin, a babin, kuma a duk tushen jiki. Duk da yadda adadin zafi ya faru a fadin, adadin da take faru a babin.
Idan Va, A, da ρ suna nufin velocity na zafi, area ta cross-section na jiki, da density na zafi a blades na turbine, maka rate ta masa na zafi zai iya rubuta cewa

A nan, idan muna bayyana m da ρVaA a equation (1), muna samu,

A nan, saboda an bayar cewa turbine ya shiga a tsakiyar jiki, velocity na zafi a blades na turbine zai iya hasashen velocity na fadin da velocity na babin.

Don samun power mai yawa daga zafi, muna iya ci equation (3) kafin V2 kuma bayar da shi da zero. Wannan shine,

Betz Coefficient

Daga equation na musamman, ana samu cewa power mai yawa da aka ci zafi shine fraction 0.5925 daga energy cin kulan. Wannan fraction shine Betz Coefficient. Wannan power da aka ci shine kamar theory of wind turbine amma power mechanical da generator ya samu ita yana fiye waɗanda ake ci kuma wannan shine saboda losses don friction, rotor bearing, da inefficiencies aerodynamic design na turbine.

Daga equation (4) ana samu cewa power da aka ci

1. Mushaida da density na zafi ρ. Idan density na zafi yana fiye, power na turbine yana fiye.

2. Mushaida da area ta swept na blades na turbine. Idan length na blade yana fiye, radius ta area ta swept yana fiye, saboda haka power na turbine yana fiye.

3. Power na turbine tana yi abuwa da velocity3 na zafi. Wannan na nufin cewa idan velocity na zafi yana duba, power na turbine zai duba zuwa eight folds.

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