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Problem P. 4536. (April 2013)

P. 4536. The theoretical limit of the efficiency of wind turbines is the so called Betz-limit is 59.3%. There are other losses, but the most modern wind turbines efficiency is approximately 84% of the Betz-limit.

a) How many megajoule kinetic energy is carried during 1 second by an air flow of speed of 27 km/h to that wind turbine which is at a height of 100 m, and which has 44 m-long blades?

b) What is the maximum output power of the turbine at this wind speed?

(4 pont)

Deadline expired on May 10, 2013.


Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. \(\displaystyle a)\) 1,6 MJ.

\(\displaystyle b)\) 0,8 MW.


Statistics:

48 students sent a solution.
4 points:Alabér Ádám, Antalicz Balázs, Bencsik Bálint, Berta Dénes, Bingler Arnold, Büki Máté, Csáky Pál, Csathó Botond, Demeter Dániel, Dinev Georgi, Emri Tamás, Epinger Bálint, Hegyi 555 Anna, Horváth András Levente, Huszár Emese, Juhász Péter, Kasza Bence, Kollarics Sándor, Kovács-Deák Máté, Lévai 482 Nikolett, Majoros Bence, Medek Ákos, Nagy 119 Dóra, Nagy Zsolt, Olosz Balázs, Öreg Botond, Papp Roland, Pázmán Zalán, Rózsa Tibor, Seress Dániel, Szász Norbert Csaba, Tanner Martin, Tarjányi 158 Dániel, Tóth Bálint, Tóth Bence, Varju Ákos, Virágh Anna, Wiandt Péter, Zsiros Ádám.
3 points:Berczi Benjámin, Csernák Tamás, Kenderes Anett, Kovács 625 Dorina, Kozár Eszter, Mészáros Gabriella, Tóth Ádám Bars.
2 points:2 students.

Problems in Physics of KöMaL, April 2013