Luís Gonzaga dos Reis Ramos
Licenciado em Ciências da Engenharia Mecânica
Desenvolvimento de um Sistema de
Deslocamento Bi-axial para Aplicação em
Túnel Aerodinâmico
Dissertação para Obtenção do Grau de Mestre em Engenharia Mecânica
Orientador:
Doutor Luís Miguel Chagas da Costa Gil, Professor Auxiliar da Faculdade de Ciências e Tecnologia da Universidade Nova de LisboaJúri
Presidente:
Doutor Daniel Cardoso Vaz, Professor Auxiliar daFaculdade de Ciências e Tecnologias da Universidade Nova de Lisboa
Arguente:
Doutor Telmo Jorge Gomes dos Santos, Professor Associado da Faculdade de Ciências e Tecnologias da Universidade Nova de LisboaVogal:
Doutor Luís Miguel Chagas da Costa Gil, Professor Auxiliar da Faculdade de Ciências e Tecnologias da Universidade Nova de Lisboa
Luís Gonzaga dos Reis Ramos
Licenciado em Ciências da Engenharia Mecânica
Desenvolvimento de um Sistema de
Deslocamento Bi-axial para Aplicação em
Túnel Aerodinâmico
Dissertação para Obtenção do Grau de Mestre em Engenharia Mecânica
Orientador:
Doutor Luís Miguel Chagas da Costa Gil, Professor Auxiliar da Faculdade de Ciências e Tecnologia da Universidade Nova de LisboaJúri
Presidente:
Doutor Daniel Cardoso Vaz, Professor Auxiliar daFaculdade de Ciências e Tecnologias da Universidade Nova de Lisboa
Arguente:
Doutor Telmo Jorge Gomes dos Santos, Professor Associado da Faculdade de Ciências e Tecnologias da Universidade Nova de LisboaVogal:
Doutor Luís Miguel Chagas da Costa Gil, Professor Auxiliar da Faculdade de Ciências e Tecnologias da Universidade Nova de Lisboa
❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ❙✐st❡♠❛ ❞❡ ❉❡s❧♦❝❛♠❡♥t♦ ❇✐✲❛①✐❛❧ ♣❛r❛ ❆♣❧✐❝❛çã♦ ❡♠ ❚ú♥❡❧ ❆❡r♦❞✐♥â♠✐❝♦
❈♦♣②r✐❣❤t ➞ ✷✵✶✽ ▲✉ís ●♦♥③❛❣❛ ❞♦s ❘❡✐s ❘❛♠♦s
❆ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❡ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛ tê♠ ♦ ❞✐r❡✐t♦✱ ♣❡r♣ét✉♦ ❡ s❡♠ ❧✐♠✐t❡s ❣❡♦❣rá✜❝♦s✱ ❞❡ ❛rq✉✐✈❛r ❡ ♣✉❜❧✐❝❛r ❡st❛ ❞✐ss❡rt❛çã♦ ❛tr❛✈és ❞❡ ❡①❡♠♣❧❛r❡s
❆●❘❆❉❊❈■▼❊◆❚❖❙
❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ♦ Pr♦❢❡ss♦r ▲✉ís ●✐❧✱ ♣❡❧❛ ♣r♦♣♦st❛ ❞♦ t❡♠❛ ❞❛ ♣r❡s❡♥t❡ ❞✐s✲ s❡rt❛çã♦✳ ❊st❡ t❡♠❛ ❡①♣❛♥❞✐✉ ♦ ♠❡✉ ❝♦♥❤❡❝✐♠❡♥t♦ ♥❛s ♠❛✐s ❞✐✈❡rs❛s ár❡❛s✱ ❡ t♦r♥♦✉✲♠❡ ✉♠❛ ♣❡ss♦❛ ♠❛✐s ♣♦❧✐✈❛❧❡♥t❡✳ ❚✐✈❡ ❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ♣❛ss❛r ♣❡❧♦ ♣r♦❝❡ss♦ ❞❡ ♣r♦❥❡t♦✱ ❢❛❜r✐❝❛çã♦ ❡ t❡st❡ ❞❡ ✉♠❛ ♠áq✉✐♥❛✱ ❡ t❡r♠✐♥❛r ❛ ❞✐ss❡rt❛çã♦ t❡♥❞♦ ❝♦♥str✉í❞♦ ✉♠❛ ♠áq✉✐♥❛ ❢✉♥❝✐♦♥❛❧✱ ❝♦♠ ✉♠❛ ✉t✐❧✐❞❛❞❡ ✈❡r❞❛❞❡✐r❛✳
❆❣r❛❞❡ç♦ ❛✐♥❞❛✱ ❞❡ ♠♦❞♦ ❣❡r❛❧✱ ❛♦s ♣r♦❢❡ss♦r❡s q✉❡ ♠❡ ❛❝♦♠♣❛♥❤❛r❛♠ ❛♦ ❧♦♥❣♦ ❞♦ ♠❡✉ ♣❡r❝✉rs♦ ❛❝❛❞é♠✐❝♦✱ ♠✉✐t♦s ❞♦s q✉❛✐s ♣♦ss✉❡♠ ✉♠❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❡♥s✐♥❛r ❡ ❞❡ ❝❛t✐✈❛r ♦ ❛❧✉♥♦ ❡①❝❡❝✐♦♥❛❧✳
❆❣r❛❞❡ç♦✱ ♣♦r ✜♠✱ ❛♦s ♠❡✉s ♣❛✐s ❡ ❛♦s ♠❡✉s ❛♠✐❣♦s ♣♦r t♦❞♦ ♦ ❛♣♦✐♦ ❛♦ ❧♦♥❣♦ ❞❡st❡s ❛♥♦s✳
❘❊❙❯▼❖
◆❡st❡ ❞♦❝✉♠❡♥t♦ é r❡❧❛t❛❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥str✉çã♦ ❞❡ ✉♠ ❡♥❣❡♥❤♦ q✉❡✱ ❝♦♠ r❡❝✉rs♦ ❛ ❞✉❛s ♠❡s❛s ❧✐♥❡❛r❡s ❡ ❞♦✐s ♠♦t♦r❡s ❞❡ ♣❛ss♦ ❛ ♣❛ss♦✱ s❡ ♠♦✈✐♠❡♥t❛ s❡❣✉♥❞♦ ❞♦✐s ❡✐①♦s✳ ❆ ❡st❛ ♠♦♥t❛❣❡♠ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ ❛❝♦♣❧❛❞♦ ✉♠ s✉♣♦rt❡ ♣❛r❛ ✉♠ t✉❜♦ ❞❡ P✐t♦t✱ ♠❛s ♣♦❞❡♠ s❡r ❢❛❝✐❧♠❡♥t❡ ❛❞❛♣t❛❞♦s ♦✉tr♦s ✐♥str✉♠❡♥t♦s ❞❡ ♠❡❞✐çã♦✳ ❆ ✉t✐❧✐③❛çã♦ ♣r❡t❡♥❞✐❞❛ ♣❛r❛ ❛ ♠♦♥t❛❣❡♠ é ❛ ♠❡❞✐çã♦ ❞❡ ♣r❡ssõ❡s✴✈❡❧♦❝✐❞❛❞❡s ♥♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s ❞❛ ❋❈❚✳
❋♦r❛♠ r❡❧❛t❛❞♦s ✈ár✐♦s ❛s♣❡t♦s r❡❧❡✈❛♥t❡s ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♠♦♥t❛❣❡♠✱ ❝♦♠♦ ❛ ❡s❝♦❧❤❛ ❡ ❛❞❛♣t❛çã♦ ❞❡ ✉♠❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦✱ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦s ❞r✐✈❡rs ❝♦♥tr♦❧❛❞♦r❡s ❞♦s ♠♦t♦r❡s ♣❛ss♦ ❛ ♣❛ss♦✱ ❛ ♠♦♥t❛❣❡♠ ❞♦s s❡♥s♦r❡s ❞❡ ✜♠ ❞❡ ❝✉rs♦ ♥♦s sít✐♦s ❞❡✈✐❞♦s✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ❝❛✐①❛ ♣❛r❛ ❣✉❛r❞❛r ❡ ♣r♦t❡❣❡r ♦s ❝♦♠♣♦♥❡♥t❡s ❡ ❣❛r❛♥t✐r ✉♠❛ ✐♥t❡r❢❛❝❡ ❝♦♠ ♦ ✉t✐❧✐③❛❞♦r✱ ❡♥tr❡ ♦✉tr♦s ❛s♣❡t♦s✳
❋♦✐ t❛♠❜é♠ r❡❧❛t❛❞♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❝ó❞✐❣♦ ♣❛r❛ ❛ ♣❧❛❝❛ ❝♦♥tr♦❧❛❞♦r❛ ❆r❞✉✐♥♦✳ ❊st❡ s♦❢t✇❛r❡ ♣❡r♠✐t❡ ❛ ✐♥s❡rçã♦ ❞❡ ❞✐✈❡rs❛s ❝♦♦r❞❡♥❛❞❛s ♥❛ ♠❡♠ór✐❛ ❞♦ ❆r❞✉✐♥♦ ❡ ♦ ♣♦st❡r✐♦r ❝♦♥tr♦❧♦ ❞♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞❛ ♠❡s❛ ❛tr❛✈és ❞❡ ❞♦✐s ❜♦tõ❡s q✉❡ ❛✈❛♥ç❛♠ ♣❛r❛ ❛ ♣♦s✐çã♦ s❡❣✉✐♥t❡ ♦✉ ✈♦❧t❛♠ à ❛♥t❡r✐♦r✳ ❆❧t❡r♥❛t✐✈❛♠❡♥t❡✱ ❛s ♣♦s✐çõ❡s ♣r❡t❡♥❞✐❞❛s ♣♦❞❡♠ s❡r ✐♥s❡r✐❞❛s ♠❛♥✉❛❧♠❡♥t❡ ♥♦ ❝♦♠♣✉t❛❞♦r✱ ❛tr❛✈és ❞❛ ❥❛♥❡❧❛ ❞❡ ❝♦♠✉♥✐❝❛çã♦ s❡r✐❛❧ ❞♦ ❆r❞✉✐♥♦✳
❖ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❛ ♠♦♥t❛❣❡♠ ❢♦✐ ✈❛❧✐❞❛❞♦ ❝♦♠ s✉❝❡ss♦ ❛tr❛✈és ❞❡ ✉♠ t❡st❡ ❛♦ ♣♦s✐❝✐♦♥❛✲ ♠❡♥t♦ ❞❛ ♠❡s❛✱ ❡ ❛tr❛✈és ❞❛ ♠❡❞✐çã♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s à s❛í❞❛ ❞❡ ✉♠❛ ❝♦♥❞✉t❛✱ q✉❡ ♣❡r♠✐t✐r❛♠ ❞❡t❡r♠✐♥❛r ♣❡r✜s ❞❡ ✈❡❧♦❝✐❞❛❞❡ à s❛í❞❛ ❞❛ ❝♦♥❞✉t❛✱ ❜❡♠ ❝♦♠♦ ✈❛❧♦r❡s ❞❡ ❝❛✉❞❛❧✳
P❛❧❛✈r❛s ❈❤❛✈❡
❼ ▼❡s❛ ▲✐♥❡❛r
❼ ▼♦t♦r❡s P❛ss♦ ❛ P❛ss♦ ❼ ❆r❞✉✐♥♦
❼ ❚ú♥❡❧ ❆❡r♦❞✐♥â♠✐❝♦
❆❇❙❚❘❆❈❚
■♥ t❤✐s ♠❛st❡r t❤❡s✐s ❞♦❝✉♠❡♥t t❤❡ ♣r♦❝❡ss ♦❢ ❝♦♥str✉❝t✐♦♥ ♦❢ ❛ ♠❛❝❤✐♥❡ ✐s ❞❡s❝r✐❜❡❞✳ ❚❤✐s ♠❛❝❤✐♥❡ ✉s❡s t✇♦ ❧✐♥❡❛r ♠♦❞✉❧❡s ❛♥❞ t✇♦ st❡♣♣❡r ♠♦t♦rs ✐♥ ♦r❞❡r t♦ ♠♦✈❡ ❛❧♦♥❣ t✇♦ ❛①✐s✳ ❆ ♠♦✉♥t ❢♦r ❛ P✐t♦t t✉❜❡ ✇❛s ♠❛❞❡ ❛♥❞ ❝♦✉♣❧❡❞ t♦ t❤✐s ♠❛❝❤✐♥❡✱ ❜✉t ♦t❤❡r ♠❡❛s✉r❡♠❡♥t ❞❡✈✐❝❡s ❝❛♥ ❡❛s✐❧② ❜❡ ❝♦♥♥❡❝t❡❞ ❛s ✇❡❧❧✳ ❚❤❡ ✉s❛❣❡ ❝❛s❡ s❝❡♥❛r✐♦ ❢♦r t❤✐s ♠❛❝❤✐♥❡ ✐s ♣r❡ss✉r❡✴✈❡❧♦❝✐t② ♠❡❛s✉r❡♠❡♥t ✐♥ ❋❈❚ ✇✐♥❞ t✉♥♥❡❧s✳
❱❛r✐♦✉s ❛s♣❡❝ts t❤❛t ✇❡r❡ r❡❧❡✈❛♥t t♦ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ♠❛❝❤✐♥❡ ✇❡r❡ ❞❡s❝r✐❜❡❞✱ s✉❝❤ ❛s t❤❡ ❝❤♦✐❝❡ ❛♥❞ ❝✉st♦♠✐③❛t✐♦♥ ♦❢ t❤❡ ♣♦✇❡r s✉♣♣❧②✱ t❤❡ ✇♦r❦✐♥❣s ♦❢ t❤❡ st❡♣♣❡r ♠♦t♦r ❞r✐✈❡rs✱ t❤❡ ♠♦✉♥t✐♥❣ ♦❢ t❤❡ ❡♥❞ st♦♣ s✇✐t❝❤❡s ✐♥ t❤❡ ❝♦rr❡❝t ♣❧❛❝❡s✱ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛♥ ❛❞❡q✉❛t❡ ❝❛s❡ ❢♦r t❤❡ st♦r❛❣❡ ❛♥❞ ♣r♦t❡❝t✐♦♥ ♦❢ t❤❡ ❝♦♠♣♦♥❡♥ts ❛♥❞ ♣❧❛❝❡♠❡♥t ♦❢ t❤❡ ✉s❡r ✐♥t❡r❢❛❝❡ ❜✉tt♦♥s✱ ❛♠♦♥❣st ♦t❤❡r ❛s♣❡❝ts✳
❆❧s♦ ❞❡s❝r✐❜❡❞ ✇❛s t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ s♦❢t✇❛r❡ ❢♦r t❤❡ ❝♦♥tr♦❧ ❞❡✈✐❞❡✱ ❛♥ ❆r❞✉✐♥♦✳ ❚❤✐s s♦❢t✇❛r❡ ❛❧❧♦✇s ❢♦r t❤❡ ✐♥♣✉t ♦❢ ✈❛r✐♦✉s ❝♦♦r❞✐♥❛t❡ ✈❛❧✉❡s ✐♥ t❤❡ ❆r❞✉✐♥♦✬s ♠❡♠♦r②✱ ❛♥❞ ❧❛t❡r t❤❡ ❝♦♥tr♦❧ ♦❢ t❤❡ ❧✐♥❡❛r ♠♦❞✉❧❡✬s ♣♦s✐t✐♦♥✐♥❣ t❤r♦✉❣❤ t✇♦ ❜✉tt♦♥s t❤❛t ❛❞✈❛♥❝❡ ✐t t♦ t❤❡ ♥❡①t ♣♦s✐t✐♦♥ ♦r r❡t✉r♥ ✐t t♦ t❤❡ ♣r❡✈✐♦✉s ♣♦s✐t✐♦♥✳ ❆❧t❡r♥❛t✐✈❡❧②✱ ❛ ♣♦s✐t✐♦♥ ✈❛❧✉❡ ❝❛♥ ❜❡ ♠❛♥✉❛❧❧② t②♣❡❞ ✐♥ t❤❡ ❆r❞✉✐♥♦✬s s❡r✐❛❧ ♠♦♥✐t♦r ✇✐♥❞♦✇✳
❚❤❡ ♠❛❝❤✐♥❡✬s ❝♦rr❡❝t ✇♦r❦✐♥❣ ✇❛s ✈❛❧✐❞❛t❡❞ ❜② ❛ t❡st t♦ t❤❡ ♣♦s✐t✐♦♥✐♥❣ ♦❢ t❤❡ ❧✐♥❡❛r ♠♦❞✉❧❡s✱ ❛♥❞ ❛❧s♦ t❤r♦✉❣❤ t❤❡ ♠❡❛s✉r❡♠❡♥t ♦❢ ✈❡❧♦❝✐t② ✈❛❧✉❡s ❛t t❤❡ ❡♥❞ ♦❢ ❛ ❞✉❝t✱ ✇❤✐❝❤ ❛❧❧♦✇❡❞ ❢♦r t❤❡ ✜♥❞✐♥❣ ♦❢ ✈❡❧♦❝✐t② ♣r♦✜❧❡s ❛t t❤❡ ❡♥❞ ♦❢ t❤❡ ❞✉❝t✱ ❛s ✇❡❧❧ ❛s ✈♦❧✉♠❡ ✢♦✇ r❛t❡ ✈❛❧✉❡s✳
❑❡②✇♦r❞s
❼ ▲✐♥❡❛r ▼♦❞✉❧❡ ❼ ❙t❡♣♣❡r ▼♦t♦rs ❼ ❆r❞✉✐♥♦
❼ ❲✐♥❞ ❚✉♥♥❡❧
❮◆❉■❈❊ ❉❊ ❈❖◆❚❊Ú❉❖❙
❆❣r❛❞❡❝✐♠❡♥t♦s ✈✐✐
❘❡s✉♠♦ ✐①
❆❜str❛❝t ①✐
❮♥❞✐❝❡ ❞❡ ❈♦♥t❡ú❞♦s ①✐✐✐
❮♥❞✐❝❡ ❞❡ ❋✐❣✉r❛s ①✈
❮♥❞✐❝❡ ❞❡ ❚❛❜❡❧❛s ①✈✐✐
◆♦♠❡♥❝❧❛t✉r❛ ①①
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ❈♦♥t❡①t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✸ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✹ ❊str✉t✉r❛ ❞❛ ❞✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷
✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✺
✷✳✶ ❇r❡✈❡ ❤✐stór✐❛ ❞♦ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✶ ❯s♦ ❛t✉❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❚✉❜♦ ❞❡ P✐t♦t ❡ s✉❛ ✉t✐❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷✳✶ ❈✉✐❞❛❞♦s✱ ✈❛♥t❛❣❡♥s ❡ ❞❡s✈❛♥t❛❣❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷✳✷ ▼❡❞✐çã♦ ❞❡ ❝❛✉❞❛❧ ♣♦r ❛tr❛✈❡ss❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✸ ▼♦t♦r❡s ❞❡ ♣❛ss♦ ❛ ♣❛ss♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✶ ▼♦t♦r ✐❞❡❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✷ ▼♦t♦r r❡❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✸ ❈✉r✈❛ ✈❡❧♦❝✐❞❛❞❡✲❜✐♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✹ P❡r❞❛s ❞❡✈✐❞♦ ❛ ❞❡t❡♥t t♦rq✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸✳✺ ❊s❝♦❧❤❛ ❞❡ ✈❛❧♦r❡s ❞❡ t❡♥sã♦ ❡ ❝♦rr❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✸✳✻ ❚✐♣♦s ❞❡ ♠♦t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✹ ▼✐❝r♦st❡♣♣✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✹✳✶ ❋✉❧❧ st❡♣♣✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✹✳✷ ❍❛❧❢ st❡♣♣✐♥❣ ❡ ♦✉tr♦s ♠♦❞♦s ❞❡ ♠✐❝r♦st❡♣♣✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✸ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❙✐st❡♠❛ ❞❡ ❉❡s❧♦❝❛♠❡♥t♦ ✶✼ ✸✳✶ ▼♦t♦r❡s ♣❛ss♦ ❛ ♣❛ss♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✷ ❉r✐✈❡rs ❞♦s ♠♦t♦r❡s ♣❛ss♦ ❛ ♣❛ss♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✸ ❋♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✹ P❧❛❝❛ ◆■ ❯❙❇✲✻✵✵✽ ❡ ❙♦❢t✇❛r❡ ▲❛❜❱■❊❲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✺ ❆r❞✉✐♥♦ ❡ r❡s♣❡t✐✈♦ ❝ó❞✐❣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✺✳✶ ❈ó❞✐❣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✻ ❈❛✐①❛ ♣❛r❛ ♦s ❝♦♠♣♦♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✼ ❙❡♥s♦r❡s ❞❡ ✜♠ ❞❡ ❝✉rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✽ ▲✐❣❛çã♦ ❡♥tr❡ ❛ ♠❡s❛ ❧✐♥❡❛r ❡ ♦ t✉❜♦ ❞❡ P✐t♦t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹ ❚❡st❡s ❊①♣❡r✐♠❡♥t❛✐s ✸✸
✹✳✶ ❚❡st❡ ❛♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✹✳✷ ❆tr❛✈❡ss❛♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✷✳✶ ❖❜❥❡t✐✈♦s ❞❛ ❡①♣❡r✐ê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✷✳✷ ❊q✉✐♣❛♠❡♥t♦ ❡ ♣r♦❝❡❞✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✷✳✸ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✷✳✹ ❉✐s❝✉ssã♦ ❞♦s r❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✺ ❈♦♥❝❧✉sã♦ ✹✺
✺✳✶ ❚r❛❜❛❧❤♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
❇✐❜❧✐♦❣r❛✜❛ ✹✼
❆♥❡①♦s ✺✶
❆ ❊s♣❡❝✐✜❝❛çõ❡s ❞♦ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ❇ ❉♦❝✉♠❡♥t❛çã♦ ❞♦s ❞r✐✈❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ❈ ❊sq✉❡♠❛ ❞❡ ❧✐❣❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ❉ ❈ó❞✐❣♦ ✐♠♣❧❡♠❡♥t❛❞♦ ♥♦ ❆r❞✉✐♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
❮◆❉■❈❊ ❉❊ ❋■●❯❘❆❙
✷✳✶ ❘❡❝r✐❛çã♦ ❞❡ ✉♠ ❞♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s ❝♦♥str✉í❞♦s ♣❡❧♦s ✐r♠ã♦s ❲r✐❣❤t ❬✷❪ ✳ ✳ ✻ ✷✳✷ ❚❡st❡ ❡♠ tú♥❡❧ ❝❧✐♠át✐❝♦ ❬✸❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✸ ❚✉❜♦ ❞❡ P✐t♦t ✭❛✮ ❡ r❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ t✉❜♦ ❞❡ Pr❛♥❞t❧ ❬✻❪ ✭❜✮ ✳ ✳ ✳ ✳ ✼ ✷✳✹ ❉✐❛❣r❛♠❛ ❞❛ ♠♦♥t❛❣❡♠ ❞❡ ✉♠ t✉❜♦ ❞❡ P✐t♦t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✺ ❊rr♦ ❞❡ ♠❡❞✐çã♦ ❡♠ ❢✉♥çã♦ ❞♦ â♥❣✉❧♦ ❞❡ ❞❡s✈✐♦ ❬✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✻ ❈❛✉❞❛❧ ✈♦❧ú♠✐❝♦ ❛tr❛✈és ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡✿ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ❞❡ ár❡❛dA ✭❛✮ ❡
❡❧❡♠❡♥t♦ ❞❡ ✈♦❧✉♠❡ ❞❡ ✢✉✐❞♦ q✉❡ ❛tr❛✈❡ss❛ ❛ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ♥✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦dt ✭❜✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✼ ❉❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛✉❞❛❧ ♣♦r ✈❛rr✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✽ ❈✉r✈❛ ✈❡❧♦❝✐❞❛❞❡✲❜✐♥ár✐♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✾ ❈✉r✈❛ ❞❡ ✉♠ ♠♦t♦r ❧✐♠✐t❛❞♦ ❡♠ ❝♦rr❡♥t❡ ❬✶✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✶✵ ❈✉r✈❛s ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ♣rát✐❝❛s ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✶✶ ■♥✢✉ê♥❝✐❛ ❞♦ ❛✉♠❡♥t♦ ❞❡ t❡♥sã♦ ♥♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪ ✶✷ ✷✳✶✷ ■♥✢✉ê♥❝✐❛ ❞♦ ❛✉♠❡♥t♦ ❞♦ ❧✐♠✐t❡ ❞❡ ❝♦rr❡♥t❡ ♥♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦
❛ ♣❛ss♦ ❬✶✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✶✸ ❚✐♣♦s ❞❡ ❧✐❣❛çõ❡s ❡❧étr✐❝❛s ❞♦s ♠♦t♦r❡s ✉♥✐♣♦❧❛r❡s ❬✶✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✶✹ ❊sq✉❡♠❛ ❞❡ ❧✐❣❛çõ❡s ❡❧étr✐❝❛s ❞♦s ♠♦t♦r❡s ❜✐♣♦❧❛r❡s ❬✶✶❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✶✺ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❡ ✈❛r✐❛çã♦ ❞❛ ❝♦rr❡♥t❡ ♥♦ ♠♦❞♦ ❢✉❧❧ st❡♣♣✐♥❣ ❬✶✹❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✶✻ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❡ ✈❛r✐❛çã♦ ❞❛ ❝♦rr❡♥t❡ ♥♦ ♠♦❞♦ ❤❛❧❢ st❡♣♣✐♥❣ ❬✶✹❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✶✼ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡ ❡ ✈❛r✐❛çã♦ ❞❛ ❝♦rr❡♥t❡ ♥♦ ♠♦❞♦1/4 st❡♣ ❬✶✹❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸✳✶ ❉r✐✈❡r P✐❇♦t st❡♣♣❡r ♠♦t♦r ❞r✐✈❡r r❡✈✳ ✷✳✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✷ ❋♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦ ❡s❝♦❧❤✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✸ ❈❛r❛❝t❡ríst✐❝❛s ❞❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦ ❡s❝♦❧❤✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✹ ▼♦❞✐✜❝❛çã♦ ❞❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✺ P❧❛❝❛ ◆■ ❯❙❇✲✻✵✵✽ ❬✷✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✻ ▼♦♥t❛❣❡♠ ❞❡ t❡st❡ ❞♦s ❝♦♠♣♦♥❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✼ ❉❡♠♦♥str❛çã♦ ❞♦ ♠♦❞♦ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ✧▼♦❞♦ ▼❛♥✉❛❧✧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✽ ❉❡♠♦♥str❛çã♦ ❞♦ ♠♦❞♦ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ✧▼♦❞♦ ❙❡r✐❛❧✧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✸✳✾ ❈❛✐①❛ ✲ ✈✐st❛ ❞♦ t♦♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✶✵ ❈❛✐①❛ ✲ ✈✐st❛ ❞♦ ✐♥t❡r✐♦r✱ ❞❛ ♣❛rt❡ ❞❡ trás ❡ ❞❛ ❧❛t❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✶✶ ▼♦❞❡❧♦ ❡♠ ❙♦❧✐❞❲♦r❦s ❞❡ ✉♠ ❛♣♦✐♦ ♣❛r❛ ✉♠ s❡♥s♦r ❞❡ ✜♠ ❞❡ ❝✉rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶✷ ❙❡♥s♦r❡s ❞❡ ✜♠ ❞❡ ❝✉rs♦ ♠♦♥t❛❞♦s ❡ ❛ ❢✉♥❝✐♦♥❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✶✸ ❉❡t❛❧❤❡ ❞♦ t✉❜♦ ❡♠ ❛ç♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✹ ❆❝❡ssór✐♦s ❞❡ ❧✐❣❛çã♦ ❞♦ P✐t♦t ❛♦ t✉❜♦ ❞❡ ❡①t❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✹✳✶ ▼❡❞✐çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ♠❡s❛ ❞♦ ❡✐①♦ ❞♦s ①① ✭❛✮ ❡ ②② ✭❜✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✷ ❱❡r✐✜❝❛çã♦ ❞♦ ♥✐✈❡❧❛♠❡♥t♦ ❞❛ ❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✹✳✸ ▼♦♥t❛❣❡♠ ❡①♣❡r✐♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✹ ▲✐♥❤❛ ♣❡r❝♦rr✐❞❛ ♣❡❧♦ t✉❜♦ ❞❡ P✐t♦t ♥♦ ❛tr❛✈❡ss❛♠❡♥t♦ ❞✐❛❣♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✺ P❡r✜❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣❛r❛ ❡s❝♦❛♠❡♥t♦ ❧❛♠✐♥❛r ✭❛✮ ❡ t✉r❜✉❧❡♥t♦ ✭❜✮ ❬✼❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✻ P❡r✜❧ ❞❡ ❱❡❧♦❝✐❞❛❞❡s à s❛í❞❛ ❞♦ t✉❜♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✹✳✼ ❆❞♠✐ssã♦ ❞♦ ✈❡♥t✐❧❛❞♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✽ P❡r✜❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s à s❛í❞❛ ❞♦ t✉❜♦ ♥❛ s❡❣✉♥❞❛ ♠❡❞✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
❮◆❉■❈❊ ❉❊ ❚❆❇❊▲❆❙
✹✳✶ ❘❡❣✐st♦ ❞♦s ✈❛❧♦r❡s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♣❛r❛ ❛ ♠❡❞✐çã♦ ❞✐❛❣♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✹✳✷ ❈á❧❝✉❧♦ ❞♦ ❝❛✉❞❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✹✳✸ ❘❡❣✐st♦ ❞♦s ✈❛❧♦r❡s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♣❛r❛ ❛ s❡❣✉♥❞❛ ♠❡❞✐çã♦ ❞✐❛❣♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✹ ❈á❧❝✉❧♦ ❞♦ ❝❛✉❞❛❧ ♣❛r❛ ❛ s❡❣✉♥❞❛ ♠❡❞✐çã♦ ❞✐❛❣♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✺ ❘❡❣✐st♦ ❞♦s ✈❛❧♦r❡s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♣❛r❛ ❛ ♠❡❞✐çã♦ ❝✐r❝✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✻ ❆♥á❧✐s❡ ❡st❛tíst✐❝❛ ❞♦s ✈❛❧♦r❡s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❞❛ ♠❡❞✐çã♦ ❝✐r❝✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
◆❖▼❊◆❈▲❆❚❯❘❆
❙í♠❜♦❧♦s ❧❛t✐♥♦s
■ ❈♦rr❡♥t❡ ❡❧étr✐❝❛ ❬A❪
▲ ■♥❞✉tâ♥❝✐❛ ❬H❪
P P♦tê♥❝✐❛ ❬W❪
◗ ❈❛✉❞❛❧ ✈♦❧ú♠✐❝♦ ❬m3
·s−1❪
❘ ❘❡s✐stê♥❝✐❛ ❡❧étr✐❝❛ ❬Ω❪
❘❡ ◆ú♠❡r♦ ❞❡ ❘❡②♥♦❧❞s
t ❚❡♠♣♦ ❬s❪
❚ ❇✐♥ár✐♦ ❬N ·m❪
❯ ❉✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❬V❪ ❱ ❱❡❧♦❝✐❞❛❞❡ ❬m·s−1❪
❙í♠❜♦❧♦s ❣r❡❣♦s
µ ❱✐s❝♦s✐❞❛❞❡ ❬P a·s❪
ω ❱❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ❬rad·s−1❪
ρ ▼❛ss❛ ✈♦❧ú♠✐❝❛ ❬kg·m3❪
❙✐❣❧❛s
❆❚❳ ❆❞✈❛♥❝❡❞ ❚❡❝❤♥♦❧♦❣② ❡❳t❡♥❞❡❞ ❆❉❈ ❆♥❛❧♦❣✲t♦✲❞✐❣✐t❛❧ ❝♦♥✈❡rt❡r
❉❈ ❉✐r❡❝t ❈✉rr❡♥t
❉❊▼■ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ▼❡❝â♥✐❝❛ ❡ ■♥❞✉str✐❛❧ ❋❈❚ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛
▲❊❉ ▲✐❣❤t ❡♠✐tt✐♥❣ ❞✐♦❞❡ ▼❉❋ ▼❡❞✐✉♠ ❞❡♥s✐t② ✜❜❡r✇♦♦❞
◆❊▼❆ ◆❛t✐♦♥❛❧ ❊❧❡tr✐❝ ▼❛♥✉❢❛❝t✉r❡rs ❆ss♦❝✐❛t✐♦♥
P❈ P❡rs♦♥❛❧ ❈♦♠♣✉t❡r
❯◆▲ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛ ❯❙❇ ❯♥✐✈❡rs❛❧ ❙❡r✐❛❧ ❇✉s
✶✳ ■◆❚❘❖❉❯➬➹❖
✶✳✶✳ ❈♦♥t❡①t♦
❖ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦✱ ✐♥✈❡♥t❛❞♦ ❡♠ ✶✽✼✶✱ ❢♦✐ ✐♥✐❝✐❛❧♠❡♥t❡ ✉s❛❞♦ ♥♦ r❛♠♦ ❞❛ ❛❡r♦♥á✉t✐❝❛ ♥♦ ❡st✉❞♦ ❞♦ ❡s❝♦❛♠❡♥t♦ ❞❡ ❛r s♦❜r❡ s✉♣❡r❢í❝✐❡s✳ ❘❡✈❡❧♦✉✲s❡ ✉♠ ❡q✉✐♣❛♠❡♥t♦ ❞❡ ❣r❛♥❞❡ ✉t✐❧✐❞❛❞❡✱ t❡♥❞♦ s✐❞♦ ❝♦♥s❡❣✉✐❞♦s ❞✐✈❡rs♦s ❛✈❛♥ç♦s té❝♥✐❝♦s✱ ♠❡s♠♦ ❛♥t❡s ❞♦ ♣r✐♠❡✐r♦ ✈♦♦ tr✐♣✉❧❛❞♦ ❛ ♠♦t♦r ✭q✉❡ só s❡ ✈✐r✐❛ ❛ r❡❛❧✐③❛r ❡♠ ✶✾✵✸✮✳
❆t✉❛❧♠❡♥t❡ ❛ ✉t✐❧✐❞❛❞❡ ❞♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s ♥ã♦ s❡ r❡str✐♥❣❡ à ✐♥❞✉str✐❛ ❛❡r♦♥á✉t✐❝❛✳ ❙ã♦ ✉t✐❧✐③❛❞♦s ♣♦r ❝♦♥str✉t♦r❡s ❛✉t♦♠ó✈❡✐s ♣❛r❛ ❡st✉❞❛r ♦ ❡s❝♦❛♠❡♥t♦ s♦❜r❡ ❛ ❝❛rr♦ç❛r✐❛ ❞♦ ❛✉t♦♠ó✈❡❧ ❡ ♣❛r❛ ❛✈❛❧✐❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ❡♠ ❝♦♥❞✐çõ❡s ❝❧✐♠át✐❝❛s ❛❞✈❡rs❛s✳ ❙ã♦ ✉t✐❧✐③❛❞♦s✱ t❛♠❜é♠✱ ♥♦ ❡st✉❞♦ ❞♦ ✐♠♣❛❝t♦ ❞♦ ✈❡♥t♦ ❡♠ ❡❞✐❢í❝✐♦s ❡ ♦✉tr❛s ❣r❛♥❞❡s ❝♦♥str✉çõ❡s✱ ♠❡❞✐♥❞♦ ❡❢❡✐t♦s ❞❡ r❡ss♦♥â♥❝✐❛ ❡♠ ❡str✉t✉r❛s ❛❧t❛s✱ ♦✉ ❛ ♣♦❧✉✐çã♦ s♦♥♦r❛ ♣❡rt♦ ❞❡ ❡❞✐❢í❝✐♦s✳
❈♦♠ ♦s rá♣✐❞♦s ❛✈❛♥ç♦s ♥❛ t❡❝♥♦❧♦❣✐❛✱ ❛ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ t♦r♥♦✉✲s❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❡ss❡♥❝✐❛❧ ♣❛r❛ ❛ ❞✐♥â♠✐❝❛ ❞♦s ✢✉✐❞♦s✱ ❡ ♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s tê♠ ✈✐♥❞♦ ❛ s❡r ✉t✐❧✐③❛❞♦s ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❢❡rr❛♠❡♥t❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ s❡♥❞♦ ❢r❡q✉❡♥t❡♠❡♥t❡ ✐♥str✉♠❡♥t❛❞♦s ❝♦♠ s✐st❡♠❛s ❞❡ ❛q✉✐s✐çã♦ ❡ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s✱ ❡ ❛ s✉❛ ♦♣❡r❛çã♦ ♣♦r ✈❡③❡s ❝♦♠♣✉t♦r✐③❛❞❛✳
❊st❡s s✐st❡♠❛s✱ ❛♥❛❧ó❣✐❝♦s ♦✉ ❞✐❣✐t❛✐s✱ sã♦ ♥♦r♠❛❧♠❡♥t❡ ✐♥str✉♠❡♥t♦s ❡s♣❡❝✐❛❧✐③❛❞♦s✱ ♣r♦❥❡✲ t❛❞♦s ♣❛r❛ ❞❡s❡♠♣❡♥❤❛r ✉♠❛ ❢✉♥çã♦ ❡s♣❡❝í✜❝❛✳ P♦r ❡st❛ r❛③ã♦ tê♠✱ ♥♦r♠❛❧♠❡♥t❡✱ ✉♠ ❝✉st♦ ❡❧❡✈❛❞♦✳
❊①✐st❡♠✱ ♥♦ ❡♥t❛♥t♦✱ ♣❧❛t❛❢♦r♠❛s ❝♦♠♦ ♦ ❆r❞✉✐♥♦ ❡ ♦ ❘❛s❜❡r② P✐ q✉❡ s❡ ❛♣r❡s❡♥t❛♠ ❝♦♠♦ ♣❧❛❝❛s ❞❡ ❜❛✐①♦ ❝✉st♦ ❝♦♠ ✉♠ ❡❧❡✈❛❞♦ ♣♦❞❡r ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✱ ❡ ✉♠❛ ❣r❛♥❞❡ ✈❡rs❛t✐❧✐❞❛❞❡ ❞❡ ❧✐❣❛çã♦ ❝♦♠ ♦✉tr♦s ❝♦♠♣♦♥❡♥t❡s✱ ❛♥❛❧ó❣✐❝♦s ♦✉ ❞✐❣✐t❛✐s✳ ❙ã♦✱ ♣♦r ✐ss♦✱ ❛❞❡q✉❛❞❛s ❝♦♠♦ ❛❧t❡r♥❛t✐✈❛s ❛ ❞❡t❡r♠✐♥❛❞♦s s✐st❡♠❛s ♠❛✐s ❝❛r♦s✳
✶✳✷✳ ❖❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ❞❛ ❞✐ss❡rt❛çã♦ ♣♦❞❡✲s❡ r❡s✉♠✐r ❛✿
❼ Pr♦❥❡t❛r ❡ ❝♦♥str✉✐r ✉♠❛ ♠♦♥t❛❣❡♠ ❛ s❡r ❝♦❧♦❝❛❞❛ ♥♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s ❡①✐s✲ t❡♥t❡s ♥♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ▼❡❝â♥✐❝❛ ❡ ■♥❞✉str✐❛❧ ❞❛ ❋❈❚✲❯◆▲✱ ♥✉♠❛ ❞❡t❡r♠✐♥❛❞❛ s❡❝çã♦ ❞❡st❡s✱ ❡ ❝❛♣❛③ ❞❡ ❞❡s❧♦❝❛r ✉♠ s❡♥s♦r ✭t✉❜♦ ❞❡ P✐t♦t✱ ❛♥❡♠ó✲ ♠❡tr♦ ❞❡ ✜♦ q✉❡♥t❡✱ ❛♥❡♠ó♠❡tr♦ ❧❛s❡r✲❉♦♣♣❧❡r ♦✉ ❡q✉✐♣❛♠❡♥t♦ s❡♠❡❧❤❛♥t❡✮ ♣❛r❛ q✉❛❧q✉❡r ♣♦♥t♦ ♥❛ s❡❝çã♦ ❡s❝♦❧❤✐❞❛✳
❊①✐st❡♠✱ ❛✐♥❞❛✱ ♦✉tr♦s ♦❜❥❡t✐✈♦s q✉❡ s❡ ❡♥q✉❛❞r❛♠ ♥♦ ♣r✐♥❝✐♣❛❧✳ ❊st❡s sã♦✿
❼ ❊❢❡t✉❛r ♦ ❝♦♥tr♦❧♦ ❞♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ s❡♥s♦r ♣♦r ✈✐❛ ❡❧❡tró♥✐❝❛✱ r❡❝♦rr❡♥❞♦ ❛ ✉♠❛ ♣❧❛❝❛ ❆r❞✉✐♥♦ ♦✉ ❛ ✉♠ ❡q✉✐♣❛♠❡♥t♦ ❞❡ ❛q✉✐s✐çã♦ ❞✐❣✐t❛❧ ❞❛ ◆❛t✐♦♥❛❧ ■♥str✉♠❡♥ts✳
❼ ❯t✐❧✐③❛r ♠♦t♦r❡s ♣❛ss♦ ❛ ♣❛ss♦ ❡ ♠❡s❛s ❧✐♥❡❛r❡s ❛❞q✉✐r✐❞❛s ❝♦♠ ❛ ✐♥t❡♥çã♦ ❞❡ s❡r❡♠ ✉t✐❧✐③❛❞♦s ♥❡st❛ ♠♦♥t❛❣❡♠✳
❼ Pr♦❥❡t❛r ✉♠❛ ❜❛s❡ ♣❛r❛ ❛ ♠♦♥t❛❣❡♠ ❝♦♠ ✈❡r✐✜❝❛çã♦ ❡ ❛❥✉st❡ ❞❡ ♥✐✈❡❧❛♠❡♥t♦✱ ❞❡ ♠♦❞♦ ❛ ❣❛r❛♥t✐r ♦ ❝♦rr❡t♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞♦ s❡♥s♦r ♥❛ s❡❝çã♦ ❞♦ tú♥❡❧✳
❼ ●❛r❛♥t✐r ✉♠❛ ❢á❝✐❧ ✐♥t❡r❢❛❝❡ ❝♦♠ ♦ ✉t✐❧✐③❛❞♦r✳
❼ ❚❡st❛r ❛ ♠♦♥t❛❣❡♠✱ ❞❡ ♠♦❞♦ ❛ ✈❡r✐✜❝❛r ♦ s❡✉ ❝♦rr❡t♦ ❢✉♥❝✐♦♥❛♠❡♥t♦✳
✶✳✸✳ ▼♦t✐✈❛çã♦
❊st❡ tr❛❜❛❧❤♦ r❡✈❡❧♦✉✲s❡ ✉♠❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❛❝r❡s❝❡♥t❛r à s❡❝çã♦ ❞❡ ❉✐♥â♠✐❝❛ ❞♦s ❋❧✉✐❞♦s ❡ ❚❡r♠♦❞✐♥â♠✐❝❛ ❆♣❧✐❝❛❞❛ ❞♦ ❉❊▼■ ❞❛ ❋❈❚✲❯◆▲ ✉♠ ❡q✉✐♣❛♠❡♥t♦ q✉❡ t♦r♥❛r✐❛ ♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s ❞❛ ❢❛❝✉❧❞❛❞❡ ♠❛✐s út❡✐s✱ ❛♦ ♣❡r♠✐t✐r ❡❢❡t✉❛r ♠❡❞✐çõ❡s q✉❡ ❛♥t❡s ♥ã♦ ❡r❛♠ ♣♦ssí✈❡✐s ♦✉ ❡r❛♠ ❝♦♠♣❧✐❝❛❞❛s ❞❡ r❡❛❧✐③❛r✳
❊r❛ t❛♠❜é♠ ✉♠❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❛t✉❛❧✐③❛r ♦ tú♥❡❧✱ ❛♦ ❛❝r❡s❝❡♥t❛r✲❧❤❡ ❡q✉✐♣❛♠❡♥t♦ ❛❝t✉❛❧✱ q✉❡ ✉t✐❧✐③❛r✐❛ ❝♦♠♣♦♥❡♥t❡s ❡ s♦❢t✇❛r❡ ♠♦❞❡r♥♦s✳
❆s ♣❧❛❝❛s ◆■ ❯❙❇✲✻✵✵✽ ❥á t✐♥❤❛♠ s✐❞♦ ✉t✐❧✐③❛❞❛s ♥♦✉tr♦s ♣r♦❥❡t♦s ❞♦ ❉❊▼■✱ ♥♦♠❡❛❞❛♠❡♥t❡ ❡♠ ♠áq✉✐♥❛s ❞❡ ✐♠♣r❡ssã♦ ✸❉✱ ♣❡❧♦ q✉❡ ♦ s❡✉ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❡r❛ ❝♦♥❤❡❝✐❞♦s ♣♦r ✈ár✐♦s ❛❧✉♥♦s ❞♦ ❞❡♣❛rt❛♠❡♥t♦✳
❉❡ ✉♠ ♣♦♥t♦ ❞❡ ✈✐st❛ ♣❡ss♦❛❧✱ ♦ ❛✉t♦r t❡♠ ✉♠ ❡❧❡✈❛❞♦ ✐♥t❡r❡ss❡ ♣♦r ❡❧❡tró♥✐❝❛✱ ♠❡❝â♥✐❝❛ ❡ ♣r♦❥❡t♦s ❞♦ ✐t ②♦✉rs❡❧❢ ❞❡ ✉♠ ♠♦❞♦ ❣❡r❛❧✱ ❡ ♦ tr❛❜❛❧❤♦ ♣❡r♠✐t✐✉ ❛♣r♦❢✉♥❞❛r ❝♦♥❤❡❝✐♠❡♥t♦s ♥❡st❛s ár❡❛s✳
✶✳✹✳ ❊str✉t✉r❛ ❞❛ ❞✐ss❡rt❛çã♦
❆ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦ ❡♥❝♦♥tr❛✲s❡ ❞✐✈✐❞✐❞❛ ❡♠ ❝✐♥❝♦ ❝❛♣ít✉❧♦s✳
◆♦ ♣r✐♠❡✐r♦ ❡ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦ ❛❜♦r❞❛✲s❡ ♦ ❝♦♥t❡①t♦✱ ♦❜❥❡t✐✈♦s✱ ♠♦t✐✈❛çã♦ ❡ ❡str✉t✉r❛ ❞❛ ❞✐ss❡rt❛çã♦✳
◆♦ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦ é ❛♣r❡s❡♥t❛❞❛ ❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❡❢❡t✉❛❞❛ ♣❡❧♦ ❛✉t♦r✱ q✉❡ ❝♦♠❡ç❛ ❝♦♠ ✉♠ r❡s✉♠♦ ❞❛ ❤✐stór✐❛ ❞♦ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦ ❡ s✉❛s ✉t✐❧✐③❛çõ❡s✳ ➱ ❛❜♦r❞❛❞❛ ❛ t❡♦r✐❛ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ t✉❜♦ ❞❡ P✐t♦t✱ ✉♠ ✐♥str✉♠❡♥t♦ ❞❡ ♠❡❞✐çã♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♣♦♥t✉❛❧ ♥✉♠ ❡s❝♦❛♠❡♥t♦✱ ❡ ❛❧❣✉♥s ❛s♣❡t♦s ✐♠♣♦rt❛♥t❡s r❡❢❡r❡♥t❡s à s✉❛ ✉t✐❧✐③❛çã♦✳
❙ã♦ ❛✐♥❞❛ ❛♥❛❧✐s❛❞❛s ♥❡st❡ ❝❛♣ít✉❧♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦✱ ❜❡♠ ❝♦♠♦ ♦ ♠✐❝r♦st❡♣♣✐♥❣✱ ✉♠ ♠♦❞♦ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ♠♦t♦r ✐♠♣❧❡♠❡♥t❛❞♦ ♣❡❧♦ s❡✉ ❞r✐✈❡r q✉❡ ♣❡r♠✐t❡ ❛t✐♥❣✐r ♠❛✐s ♣♦s✐çõ❡s ❛♥❣✉❧❛r❡s ❞♦ ♠♦t♦r✱ ❜❡♠ ❝♦♠♦ ✉♠❛ r♦t❛çã♦ ♠❛✐s s✉❛✈❡✳
◆♦ ❝❛♣ít✉❧♦ t❡r❝❡✐r♦ é ❞❡s❝r✐t♦ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ♠♦♥t❛❣❡♠✳ ❙ã♦ ❛❜♦r❞❛❞❛s ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s r❡❧❡✈❛♥t❡s ❞♦ ❡q✉✐♣❛♠❡♥t♦ ✉t✐❧✐③❛❞♦✱ ❡ é ❞❡s❝r✐t❛ ❛ ❡s❝♦❧❤❛ ❡ ♠♦❞✐✜❝❛çã♦ ❞❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦✳ ➱ t❛♠❜é♠ ❞❡s❝r✐t❛ ❛ ❢❛❜r✐❝❛çã♦ ❞❡ ❛❧❣✉♥s ❡❧❡♠❡♥t♦s✱ ❝♦♠♦ ❛ ❝❛✐①❛ ♣❛r❛ ♦s ❝♦♠♣♦♥❡♥t❡s ❡ ♦s ❛♣♦✐♦s ♣❛r❛ ♦s s❡♥s♦r❡s ❞❡ ✜♠ ❞❡ ❝✉rs♦✱ ❡ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❧✐❣❛çõ❡s ❡❧étr✐❝❛s ❡♥tr❡ ❝♦♠♣♦♥❡♥t❡s✳ ➱ ❞❡❞✐❝❛❞♦ ✉♠ s✉❜✲❝❛♣ít✉❧♦ ❛♦ ❝ó❞✐❣♦ ❞♦ ❆r❞✉✐♥♦ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ❡st❛ ❛♣❧✐❝❛çã♦✳
◆♦ q✉❛rt♦ ❝❛♣ít✉❧♦ ❞❡s❝r❡✈❡♠✲s❡ ♦s t❡st❡s ❛ q✉❡ ❛ ♠♦♥t❛❣❡♠ ❢♦✐ s✉❥❡✐t❛✳ ◆♦ ♣r✐♠❡✐r♦ ❢♦✐ ♠❡❞✐❞♦ ♦ ♣♦s✐❝✐♦♥❛♠❡♥t♦ ❞❛s ♠❡s❛s ❧✐♥❡❛r❡s ❛♣ós ❡st❛ t❡r ♣❡r❝♦rr✐❞♦ ✉♠❛ ♠❛❧❤❛ ❞❡ ♣♦s✐çõ❡s✳ ◆♦ s❡❣✉♥❞♦ sã♦ ❡❢❡t✉❛❞♦s ❛tr❛✈❡ss❛♠❡♥t♦s à s❛í❞❛ ❞❡ ✉♠❛ ❝♦♥❞✉t❛✳ ➱ ❞❡s❝r✐t♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ❡①♣❡r✐♠❡♥t❛❧ ✉t✐❧✐③❛❞♦ ♥❛ ♠❡❞✐çã♦ ❞♦s ✈ár✐♦s ✈❛❧♦r❡s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♥❛ ❝♦♥❞✉t❛✱ ❡ sã♦ ❛♣r❡s❡♥✲ t❛❞♦s ♦s ✈❛❧♦r❡s ♦❜t✐❞♦s ❡ ♦ s❡✉ r❡s♣❡t✐✈♦ tr❛t❛♠❡♥t♦✱ q✉❡ ♣❡r♠✐t✐✉ r❡t✐r❛r ❝♦♥❝❧✉sõ❡s s♦❜r❡ ♦ ❡s❝♦❛♠❡♥t♦ ❡st✉❞❛❞♦✳ ❊st❛s ❝♦♥❝❧✉sõ❡s sã♦ ❛♣r❡s❡♥t❛❞❛s ❡ ❞✐s❝✉t✐❞❛s✳
❖ ú❧t✐♠♦ ❝❛♣ít✉❧♦ ❝♦♥té♠ ❛ ❝♦♥❝❧✉sã♦✱ ♦♥❞❡ é ❢❡✐t❛ ✉♠❛ ❛♥á❧✐s❡ ❝rít✐❝❛ ❞♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✲ ✈✐❞♦ ❡ ❞❛ ♠♦♥t❛❣❡♠ ❡♠ s✐✱ ❡ ♦♥❞❡ sã♦ ♣r♦♣♦st♦s tr❛❜❛❧❤♦s ❢✉t✉r♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❛ ♠♦♥t❛❣❡♠✳
✷✳ ❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆
◆❛ ♣r❡s❡♥t❡ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❛❜♦r❞❛♠✲s❡ ❛❧❣✉♥s t❡♠❛s r❡❧❡✈❛♥t❡s ♣❛r❛ ❛ ❞✐ss❡rt❛çã♦✳ ❈♦♠❡ç❛✲s❡ ♣♦r ❞❡s❝r❡✈❡r ❛ ❤✐stór✐❛ ❞♦ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦ ❡ ❛ s✉❛ ✉t✐❧✐③❛çã♦ ❛t✉❛❧✱ ❝♦♠♦ ❢♦r♠❛ ❞❡ ❛♣r❡s❡♥t❛r ❛ ❡✈♦❧✉çã♦ ❡ ❛ ✉t✐❧✐❞❛❞❡ ❞❡st❡ ❡q✉✐♣❛♠❡♥t♦✳
❆ ❝♦♠♣♦♥❡♥t❡ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ ❞✐ss❡rt❛çã♦ t❡♠ ❝♦♠♦ ú♥✐❝♦ ♦❜❥❡t✐✈♦ t❡st❛r ❛ ♠♦♥t❛❣❡♠ ❞❡s❡♥✈♦❧✈✐❞❛✱ ❡ ❝♦♠♦ t❛❧ ❛❜♦r❞♦✉✲s❡ ❜r❡✈❡♠❡♥t❡ ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ t✉❜♦ ❞❡ P✐t♦t✱ ❛ ❝♦rr❡t❛ ✉t✐❧✐③❛çã♦ ❞❡st❡ ✐♥str✉♠❡♥t♦ ❞❡ ♠❡❞✐çã♦ ❡ ♦ ❝á❧❝✉❧♦ ❞❡ ❝❛✉❞❛✐s ♣♦r ❛tr❛✈❡ss❛♠❡♥t♦✳
➱ ❛❜♦r❞❛❞❛✱ ♣♦r ✜♠✱ ❛ t❡♦r✐❛ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦s ♠♦t♦r❡s ♣❛ss♦ ❛ ♣❛ss♦✱ ♦ ❝♦♠♣♦♥❡♥t❡ q✉❡ ✐rá ✐♠♣♦r ♠♦✈✐♠❡♥t♦ à ♠❡s❛ ❧✐♥❡❛r✱ ❝✉❥♦ ❝♦♠♣❧❡①♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ é ❞❡s❝r✐t♦ ❡♠ ✈ár✐♦s s✉❜✲ s✉❜✲❝❛♣ít✉❧♦s✳
✷✳✶✳ ❇r❡✈❡ ❤✐stór✐❛ ❞♦ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦
❆♣ós ✈ár✐❛s t❡♥t❛t✐✈❛s ❞❡ ✈♦♦ tr✐♣✉❧❛❞♦ ❢❛❧❤❛❞❛s✱ ♦s ♣✐♦♥❡✐r♦s ❞❛ ❛✈✐❛çã♦ ❛♣❡r❝❡❜❡r❛♠✲s❡ ❞❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❡st✉❞❛r ♦ ❡s❝♦❛♠❡♥t♦ ❞❡ ❛r s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠ ♣❧❛♥❛❞♦r ♥✉♠ ❛♠❜✐❡♥t❡ ❝♦♥tr♦❧❛❞♦✳
Pr✐♠❡✐r♦ ❢♦r❛♠ ❢❡✐t♦s ❡st✉❞♦s ♥♦ ❡①t❡r✐♦r✱ ❡♠ ❧♦❝❛✐s ♦♥❞❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ❢♦ss❡ ❡stá✲ ✈❡❧ ❡ ❝♦♥❤❡❝✐❞❛✱ ❡ ♣♦st❡r✐♦r♠❡♥t❡ ❝♦♥str✉✐r❛♠✲s❡ ❡♥❣❡♥❤♦s q✉❡ ❝♦❧♦❝❛✈❛♠ ♦ ♦❜❥❡t♦ ❡♠ ❡st✉❞♦ ❡♠ ♠♦✈✐♠❡♥t♦ ❞❡ r♦t❛çã♦✱ à ✈♦❧t❛ ❞❡ ✉♠ ❡✐①♦ ✜①♦ ❛♦ s♦❧♦✱ ✐♠♣♦♥❞♦✲❧❤❡ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ ♣ré✲ ❡st❛❜❡❧❡❝✐❞❛ ❬✶❪✳ ❊st❛s ♠áq✉✐♥❛s r❡♠♦♥t❛♠ ❛♦ sé❝✳ ❳❱■■■✳
❆ ✐♥✈❡♥çã♦ ❞♦ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦ é ❝r❡❞✐t❛❞❛ ❛ ❋r❛♥❦ ❍✳ ❲❡♥❤❛♠ ✭✶✽✷✹✲✶✾✵✽✮✱ ❡♥❣❡♥❤❡✐r♦ ♥❛✈❛❧ ❜r✐tâ♥✐❝♦ ❡ ♠❡♠❜r♦ ❞❛ ❙♦❝✐❡❞❛❞❡ ❆❡r♦♥á✉t✐❝❛ ❞❛ ●rã✲❇r❡t❛♥❤❛✳ ❖ s❡✉ ❡♥❣❡♥❤♦✱ ❝♦♥str✉í❞♦ ❡♠ ✶✽✼✶✱ ❝♦♥s✐st✐❛ ♥✉♠ ✈❡♥t✐❧❛❞♦r ❝♦❧♦❝❛❞♦ ❡♠ r♦t❛çã♦ ♣♦r ✉♠ ♠♦t♦r ❛ ✈❛♣♦r✱ q✉❡ ♠♦✈✐❛ ❛r ♣♦r ✉♠❛ ♣❛ss❛❣❡♠ q✉❛❞r❛❞❛ ❝♦♠ ❝❡r❝❛ ❞❡45 cm ❞❡ ❧❛❞♦ ❡3,5 m❞❡ ❝♦♠♣r✐♠❡♥t♦✳
❖s t❡st❡s ❝♦♥❞✉③✐❞♦s ♣♦r ❲❡♥❤❛♠ ♥♦ s❡✉ tú♥❡❧ ♣❡r♠✐t✐r❛♠ ✈ár✐♦s ❛✈❛♥ç♦s t❡ór✐❝♦✲♣rát✐❝♦s✱ ❡♥tr❡ ❡❧❡s ❡❧❡s ❛ ❞❡✜♥✐çã♦ ❞❡ ❛❧♦♥❣❛♠❡♥t♦ ❞❡ ✉♠❛ ❛s❛✶✱ ❡ ❛ r❡❧❛çã♦ ❡♥tr❡ ❛ ❢♦rç❛ ❞❡ s✉st❡♥t❛çã♦
❡ ♦ ❛❧♦♥❣❛♠❡♥t♦✳
❆♣❡s❛r ❞❡st❡s ❛✈❛♥ç♦s✱ ♦ ❢❛♠♦s♦ ✈♦♦ tr✐♣✉❧❛❞♦ ❛ ♠♦t♦r ❞♦s ✐r♠ã♦s ❲r✐❣❤t só s❡ r❡❛❧✐③❛r✐❛ ❡♠ ❞❡③❡♠❜r♦ ❞❡ ✶✾✵✸✱ ✸✷ ❛♥♦s ❛♣ós ❛ ✐♥✈❡♥çã♦ ❞♦ tú♥❡❧ ❛❡r♦❞✐♥â♠✐❝♦✳ ❚❛♠❜é♠ ♦s ✐r♠ã♦s ❲r✐❣❤t r❡❝♦rr❡r❛♠ ❛ ❡st❡ ❡q✉✐♣❛♠❡♥t♦✱ t❡♥❞♦ ❝♦♥str✉í❞♦ ❞♦✐s tú♥❡✐s ✭♥❛ ✜❣✉r❛ ✷✳✶ ♦❜s❡r✈❛✲s❡ ❛ r❡❝r✐❛çã♦ ❞❡ ✉♠ ❞❡❧❡s✮✳ ❘❡❝♦rr❡♥❞♦ ❛ s❡♥s♦r❡s ❝♦♠ ✉♠ ❢✉♥❝✐♦♥❛♠❡♥t♦ s❡♠❡❧❤❛♥t❡ ❛ ❞✐♥❛♠ó♠❡tr♦s✱ ❡❢❡t✉✲ ❛r❛♠ ♠❡❞✐çõ❡s ❞❡ s✉st❡♥t❛çã♦ ❡♠ ♣❡r✜s ❛❧❛r❡s r❡❧❛t✐✈❛♠❡♥t❡ ❛ ♦✉tr♦s ♣❡r✜s ❛❧❛r❡s ❝❛❧✐❜r❛❞♦s✱ ♦ q✉❡ ❧❤❡s ♣❡r♠✐t✐❛ ✉♠❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❝é❧❡r❡ ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♣❡r✜s ❬✶❪✳
✷✳✶✳✶ ❯s♦ ❛t✉❛❧
❆t✉❛❧♠❡♥t❡ ♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s sã♦ ❢❡rr❛♠❡♥t❛s ❞❡ ❣r❛♥❞❡ ✉t✐❧✐❞❛❞❡ ♣❛r❛ ❞✐✈❡rs♦s r❛♠♦s ❞❡ ❡♥❣❡♥❤❛r✐❛✱ ♥ã♦ s❡♥❞♦ ♦ s❡✉ ✉s♦ r❡str✐♥❣✐❞♦ ❛♣❡♥❛s à ❛❡r♦♥á✉t✐❝❛✳
✶❆❧♦♥❣❛♠❡♥t♦✿ r❡❧❛çã♦ ❡♥tr❡ ❛ ❡♥✈❡r❣❛❞✉r❛ ❡ ❛ ❝♦r❞❛ ❞❡ ✉♠❛ ❛s❛✳
❋✐❣✉r❛ ✷✳✶✿ ❘❡❝r✐❛çã♦ ❞❡ ✉♠ ❞♦s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s ❝♦♥str✉í❞♦s ♣❡❧♦s ✐r♠ã♦s ❲r✐❣❤t ❬✷❪
❙ã♦ ✉t✐❧✐③❛❞♦s ♣❡❧♦s ❝♦♥str✉t♦r❡s ❛✉t♦♠ó✈❡✐s ♥ã♦ só ♣❛r❛ ❡st✉❞❛r ♦ ❡s❝♦❛♠❡♥t♦ ♣❡❧❛ ❝❛rr♦ç❛r✐❛ ❞♦ ❛✉t♦♠ó✈❡❧ ✭r❡❝♦rr❡♥❞♦ ❛ ♠♦❞❡❧♦s✱ ♦✉ ❛ ♣r♦tót✐♣♦s à ❡s❝❛❧❛ r❡❛❧✮✱ ♠❛s t❛♠❜é♠ ♣❛r❛ ❛✈❛❧✐❛r ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❝♦♠♣♦♥❡♥t❡s ❡♠ ❝♦♥❞✐çõ❡s ❝❧✐♠át✐❝❛s ❞✐✈❡rs❛s ❡♠ tú♥❡✐s ❝❧✐♠át✐❝♦s ✭✜❣✉r❛ ✷✳✷✮✱ ❞❡s❡♥✈♦❧✈✐❞♦s ❡①❝❧✉s✐✈❛♠❡♥t❡ ♣❛r❛ ❡st❡ ❡❢❡✐t♦✳
❋✐❣✉r❛ ✷✳✷✿ ❚❡st❡ ❡♠ tú♥❡❧ ❝❧✐♠át✐❝♦ ❬✸❪
❙ã♦ t❛♠❜é♠ ✉t✐❧✐③❛❞♦s ♥♦ ❡st✉❞♦ ❞♦ ✐♠♣❛❝t♦ ❞♦ ✈❡♥t♦ ❡♠ ❝♦♥str✉çõ❡s✱ ♠❡❞✐♥❞♦ ♦ ✐♠♣❛❝t♦ ❞❡ ❞✐❢❡r❡♥t❡s ✈❡❧♦❝✐❞❛❞❡s ❞♦ ✈❡♥t♦ ♥❛ r❡s✐stê♥❝✐❛ ❡str✉t✉r❛❧ ❞♦ ❡❞✐❢í❝✐♦s✱ ♠❡❞✐♥❞♦ ❡❢❡✐t♦s ❞❡ r❡s✲ s♦♥â♥❝✐❛ ♦✉ ❞❡s♣r❡♥❞✐♠❡♥t♦ ❞❡ ✈órt✐❝❡s ❡♠ ❡str✉t✉r❛s ❛❧t❛s ❡ ♣♦♥t❡s✱ ♠❡❞✐♥❞♦ ❛ ♣♦❧✉✐çã♦ s♦♥♦r❛ ♣❡rt♦ ❞❡ ❡❞✐❢í❝✐♦s✱ ❡♥tr❡ ♦✉tr❛s ✉t✐❧✐③❛çõ❡s ❬✹❪✳
❈♦♠ ♦s rá♣✐❞♦s ❡ ❝♦♥s✐❞❡rá✈❡✐s ❛✈❛♥ç♦s ✐♥❢♦r♠át✐❝♦s✱ ❛ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ t♦r♥♦✉✲ s❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❡ss❡♥❝✐❛❧ ♣❛r❛ ❛ ❞✐♥â♠✐❝❛ ❞♦s ✢✉✐❞♦s✳ ❖s tú♥❡✐s ❛❡r♦❞✐♥â♠✐❝♦s sã♦ ❛❣♦r❛ ✉t✐❧✐③❛❞♦s ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❛s ❢❡rr❛♠❡♥t❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ ✈❛❧✐❞❛♥❞♦ ❛ q✉❛❧✐❞❛❞❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r ❡st❛ ✈✐❛✳ P❛r❛ t❛❧✱ ♦s tú♥❡✐s sã♦ ❢r❡q✉❡♥t❡♠❡♥t❡ ❛t✉❛❧✐③❛❞♦s ❝♦♠ ✐♥str✉♠❡♥t♦s ❞❡ ❛q✉✐s✐çã♦ ❡ ❛♥á❧✐s❡ ❞❡ ❞❛❞♦s✱ ❡ ❛ s✉❛ ♦♣❡r❛çã♦ é ❝♦♠♣✉t♦r✐③❛❞❛ ❬✺❪✳
✷✳✷✳ ❚✉❜♦ ❞❡ P✐t♦t ❡ s✉❛ ✉t✐❧✐③❛çã♦
❖ t✉❜♦ ❞❡ P✐t♦t✱ ✐♥✈❡♥t❛❞♦ ♣❡❧♦ ❡♥❣❡♥❤❡✐r♦ ❢r❛♥❝ês ❍❡♥r✐ P✐t♦t ❡♠ ✶✼✸✷ ❡ r❡♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✷✳✸❛✱ é ✉♠ ✐♥str✉♠❡♥t♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♠❡❞✐r ❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ❡s❝♦❛♠❡♥t♦ s♦❜r❡ ✉♠❛ ár❡❛ ♠✉✐t♦ ♣❡q✉❡♥❛ ✭❝♦♥s✐❞❡r❛❞❛ ♣♦♥t✉❛❧✮✳ ❯♠ ✐♥str✉♠❡♥t♦ s❡♠❡❧❤❛♥t❡ é ♦ t✉❜♦ ❞❡ Pr❛♥❞t❧ ♦✉ P✐t♦t✲ ❡stát✐❝♦✱ ❝✉❥❛ r❡♣r❡s❡♥t❛çã♦ s❡ ❡♥❝♦♥tr❛ ♥❛ ✜❣✉r❛ ✷✳✸❜✳ ◆❛ ❧✐t❡r❛t✉r❛ ✉s❛✲s❡ ❢r❡q✉❡♥t❡♠❡♥t❡ ♦ ♥♦♠❡ ✧t✉❜♦ ❞❡ P✐t♦t✧♣❛r❛ ❛♠❜♦s ♦s ✐♥str✉♠❡♥t♦s✳
✭❛✮ ✭❜✮
❋✐❣✉r❛ ✷✳✸✿ ❚✉❜♦ ❞❡ P✐t♦t ✭❛✮ ❡ r❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ t✉❜♦ ❞❡ Pr❛♥❞t❧ ❬✻❪ ✭❜✮
❆♠❜♦s sã♦ t✉❜♦s ❞❡ ♣❡q✉❡♥♦ ❞✐â♠❡tr♦✱ ♣♦s✐❝✐♦♥❛❞♦s ❞❡ ♠♦❞♦ ❛ ✜❝❛r❡♠ ❛❧✐♥❤❛❞♦s ❝♦♠ ♦ ❡s❝♦❛♠❡♥t♦✳ ❖s ♦r✐❢í❝✐♦s ♥❛ ♣❛r❡❞❡ ❞♦ t✉❜♦ ❞❡ Pr❛♥❞t❧✱ ♣❡r♣❡♥❞✐❝✉❧❛r❡s ❛♦ t✉❜♦ ❝❡♥tr❛❧✱ ♠❡❞❡♠ ❛ ♣r❡ssã♦ ❡stát✐❝❛✱ps✳ ❖ ♦r✐❢í❝✐♦ ❛ ♠♦♥t❛♥t❡ ♠❡❞❡ ❛ ♣r❡ssã♦ t♦t❛❧✱ ♦✉ ♣r❡ssã♦ ❞❡ ❡st❛❣♥❛çã♦ p0✱
♣♦rq✉❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✢✉✐❞♦ é r❡❞✉③✐❞❛ ❛té ③❡r♦ ♥❡st❡ ♦r✐❢í❝✐♦✳ ❆ ♣r❡ssã♦ t♦t❛❧ é ✐❣✉❛❧ é ❛ s♦♠❛ ❞❛ ♣r❡ssã♦ ❡stát✐❝❛ ❝♦♠ ❛ ♣r❡ssã♦ ❞✐♥â♠✐❝❛✿
p0 =ps+pd ✭✷✳✶✮
❊♠ ✈❡③ ❞❡ ♠❡❞✐rp0❡pss❡♣❛r❛❞❛♠❡♥t❡ r❡❝♦rr❡♥❞♦ ❛ ♠❛♥ó♠❡tr♦s ❧✐❣❛❞♦s à ♦✉tr❛ ❡①tr❡♠✐❞❛❞❡
❞♦ t✉❜♦✱ ♣♦❞❡✲s❡ r❡❝♦rr❡r ❛ ✉♠ tr❛♥s❞✉t♦r ❞✐❢❡r❡♥❝✐❛❧ ❞❡ ♣r❡ssã♦ ❡ ♠❡❞✐r ❛ ♣r❡ssã♦ ❞✐♥â♠✐❝❛ ❞✐r❡t❛♠❡♥t❡ ✭❝♦♠♦ r❡♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✷✳✸❜✮✳
❆ ❡①♣r❡ssã♦ ✷✳✹✱ q✉❡ ♣❡r♠✐t❡ ❝❛❧❝✉❧❛r ❛ ✈❡❧♦❝✐❞❛❞❡ ❛ ♣❛rt✐r ❞❛ ♣r❡ssã♦✱ é ♦❜t✐❞❛ ❞❛ ❡q✉❛çã♦ ❞❡ ❇❡r♥♦✉❧❧✐ ♣❛r❛ r❡❣✐♠❡ ♣❡r♠❛♥❡♥t❡✱ ✐♥❝♦♠♣r❡ssí✈❡❧ ❡ s❡♠ ❛tr✐t♦ ✭❡q✉❛çã♦ ✷✳✷✮✱ ❛♦ ❧♦♥❣♦ ❞❛ ❧✐♥❤❛ ❞❡ ❝♦rr❡♥t❡ ❞❛ ✜❣✉r❛ ✷✳✹✳
p1
ρ + 1 2V
2
1 +gz1 =
p2
ρ + 1 2V
2
2 +gz2 =cte ✭✷✳✷✮
ps+
1 2ρV
2
+ρgzs=p0+
1 2ρ(0)
2
+ρgz0 ✭✷✳✸✮
V =
s
2(p0−ps)
ρ ✭✷✳✹✮
✷✳✷✳✶ ❈✉✐❞❛❞♦s✱ ✈❛♥t❛❣❡♥s ❡ ❞❡s✈❛♥t❛❣❡♥s
❯♠❛ ❞❡s✈❛♥t❛❣❡♠ ❞♦ t✉❜♦ ❞❡ P✐t♦t é q✉❡ ❡st❡ ❞❡✈❡ ❡st❛r ❛❧✐♥❤❛❞♦ ♥❛ ❞✐r❡çã♦ ❞♦ ❡s❝♦❛♠❡♥t♦✱ q✉❡ ♣♦❞❡ ♥ã♦ s❡r ❝♦♥❤❡❝✐❞❛✳ ◆♦ ❡♥t❛♥t♦✱ ♣❛r❛ â♥❣✉❧♦s ❞❡ ❞❡s✈✐♦ ❛té 5◦✱ ♦s ❡rr♦s ❞❡ ♠❡❞✐çã♦ sã♦
❞❡s♣r❡③á✈❡✐s✭✜❣✉r❛ ✷✳✺✮✳
❉❡✈✐❞♦ à r❡s♣♦st❛ ❧❡♥t❛ ❞♦s t✉❜♦s q✉❡ ❢❛③❡♠ ❛ ❧✐❣❛çã♦ ❛♦s ♠❛♥ó♠❡tr♦s✱ ♦ t✉❜♦ ❞❡ P✐t♦t ♥ã♦ é út✐❧ ❡♠ r❡❣✐♠❡ tr❛♥s✐tór✐♦ ❬✼❪✳ ◆ã♦ é✱ ✐❣✉❛❧♠❡♥t❡✱ út✐❧ ❡♠ ❣❛s❡s ❛ ❜❛✐①❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡✈✐❞♦ às ♣❡q✉❡♥❛s ❞✐❢❡r❡♥ç❛s ❞❡ ♣r❡ssã♦ ❡♥✈♦❧✈✐❞❛s✳ P♦r ❡①❡♠♣❧♦✱ ♣❛r❛ ❛r ❛ 1 km/h✱ s✉❜st✐t✉✐♥❞♦ ♦s
❋✐❣✉r❛ ✷✳✹✿ ❉✐❛❣r❛♠❛ ❞❛ ♠♦♥t❛❣❡♠ ❞❡ ✉♠ t✉❜♦ ❞❡ P✐t♦t
❋✐❣✉r❛ ✷✳✺✿ ❊rr♦ ❞❡ ♠❡❞✐çã♦ ❡♠ ❢✉♥çã♦ ❞♦ â♥❣✉❧♦ ❞❡ ❞❡s✈✐♦ ❬✼❪
✈❛❧♦r❡s ❞❡✈✐❞♦s ♥❛ ❡q✉❛çã♦ ✷✳✹✱ ♦❜té♠✲s❡ p0−ps= 0,047 Pa✱ ✈❛❧♦r ❢♦r❛ ❞❛ r❡s♦❧✉çã♦ ❞❛ ♠❛✐♦r✐❛
❞♦s ♠❛♥ó♠❡tr♦s✳
✷✳✷✳✷ ▼❡❞✐çã♦ ❞❡ ❝❛✉❞❛❧ ♣♦r ❛tr❛✈❡ss❛♠❡♥t♦
❖ ❝❛✉❞❛❧ ✈♦❧ú♠✐❝♦ é ❛ q✉❛♥t✐❞❛❞❡✱ ❡♠ ✈♦❧✉♠❡✱ ❞❡ ✢✉✐❞♦ q✉❡ ❛tr❛✈❡ss❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ s✉♣❡r❢í❝✐❡ ♣♦r ✉♥✐❞❛❞❡ ❞❡ t❡♠♣♦✳
❙✉♣♦♥❞♦ q✉❡ ❛ s✉♣❡r❢í❝✐❡S❞❛ ✜❣✉r❛ ✷✳✻❛ é ✉♠❛ ♠❛❧❤❛ ✐♠❛❣✐♥ár✐❛ ♣❡❧❛ q✉❛❧ ♦ ✢✉✐❞♦ ❛tr❛✈❡ss❛ s❡♠ r❡s✐stê♥❝✐❛✳ ❙❡ ❛ ✈❡❧♦❝✐❞❛❞❡ V ✈❛r✐❛r✱ é ♥❡❝❡ssár✐❛ ❛ ✐♥t❡❣r❛çã♦ ♥❛ s✉♣❡r❢í❝✐❡ ❡❧❡♠❡♥t❛r dA ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❝❛✉❞❛❧✳ ❙❡❥❛ θ ♦ â♥❣✉❧♦ ❡♥tr❡V ❡ n✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ✈❡t♦r ♥♦r♠❛❧ ❛ dA✳ ❖ ✈♦❧✉♠❡ ❞❡ ✢✉✐❞♦✱ r❡♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✷✳✻❜✱ q✉❡ ❛tr❛✈❡ss❛ dA ♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ dt ❝♦rr❡s♣♦♥❞❡ ❛✿
dV =V dt dA cosθ= (V ·n) dA dt ✭✷✳✺✮
❊ ♦ ❝❛✉❞❛❧ ✈♦❧ú♠✐❝♦Qq✉❡ ❛tr❛✈❡ss❛ ❛ s✉♣❡r❢í❝✐❡ S é ♦ ✐♥t❡❣r❛❧ ❞❡dV/dt✿
Q=
Z
s
(V ·n) dA=
Z
s
Vn dA ✭✷✳✻✮
❊♠ q✉❡ ♦ ♣r♦❞✉t♦ ✐♥t❡r♥♦ V ·n é ❡q✉✐✈❛❧❡♥t❡ ❛ Vn✱ ❛ ❝♦♠♣♦♥❡♥t❡ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ♥♦r♠❛❧ ❛
dA✳ ❖ ✉s♦ ❞♦ ♣r♦❞✉t♦ ✈❡t♦r✐❛❧ ♣❡r♠✐t❡ q✉❡Q❛ss✉♠❛ ✈❛❧♦r❡s ♣♦s✐t✐✈♦s ♦✉ ♥❡❣❛t✐✈♦s✱ ♣❡r♠✐t✐♥❞♦ ✐♥❢❡r✐r ♦ s❡♥t✐❞♦ ❞♦ ❡s❝♦❛♠❡♥t♦✳
◆✉♠❛ ♠❡❞✐çã♦ ❞❡ ❝❛✉❞❛❧ ♣♦r ❛tr❛✈❡ss❛♠❡♥t♦✱ sã♦ ♠❡❞✐❞♦s ✈❛❧♦r❡s ❞❡ ✈❡❧♦❝✐❞❛❞❡Vi❡♠ ♣♦♥t♦s
❝♦♥✈❡♥✐❡♥t❡♠❡♥t❡ s❡❧❡❝✐♦♥❛❞♦s ❞❡ ✉♠❛ ❝♦♥❞✉t❛ ♦✉ ❝❛♥❛❧✳ ❆ s✉♣❡r❢í❝✐❡ ❞❡ ♣❛ss❛❣❡♠ ❞♦ ✢✉✐❞♦ é ❞✐✈✐❞✐❞❛ ❡♠ ár❡❛s ❞✐s❝r❡t❛s✱ Ai✱ ❞❡ ♠♦❞♦ ❛ q✉❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✢✉✐❞♦ ♣♦ss❛ s❡r ❝♦♥s✐❞❡r❛❞❛
✭❛✮ ✭❜✮
❋✐❣✉r❛ ✷✳✻✿ ❈❛✉❞❛❧ ✈♦❧ú♠✐❝♦ ❛tr❛✈és ❞❡ ✉♠❛ s✉♣❡r❢í❝✐❡✿ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ❞❡ ár❡❛ dA ✭❛✮ ❡ ❡❧❡♠❡♥t♦ ❞❡ ✈♦❧✉♠❡ ❞❡ ✢✉✐❞♦ q✉❡ ❛tr❛✈❡ss❛ ❛ ✉♥✐❞❛❞❡ ❡❧❡♠❡♥t❛r ♥✉♠ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ dt ✭❜✮
❝♦♥st❛♥t❡ ❡♠ q✉❛❧q✉❡r ♣♦♥t♦ ❞❛ ár❡❛✳ ❖ ❝á❧❝✉❧♦ ❞♦ ❝❛✉❞❛❧ é✱ ❡❢❡t✐✈❛♠❡♥t❡✱ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ✐♥t❡❣r❛❧ ❞❛ ❡q✉❛çã♦ ✷✳✻✿
Q=X
i
ViAi ✭✷✳✼✮
❋✐❣✉r❛ ✷✳✼✿ ❉❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛✉❞❛❧ ♣♦r ✈❛rr✐♠❡♥t♦
◆❛ ✜❣✉r❛ ✷✳✼ ♦❜s❡r✈❛✲s❡ ✉♠ ♣❡r✜❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❞❡ ✉♠ ❡s❝♦❛♠❡♥t♦ à s❛í❞❛ ❞❡ ✉♠ t✉❜♦ ❞❡ s❡❝çã♦ ❝✐r❝✉❧❛r✱ q✉❡ ❢♦✐ ❞✐✈✐❞✐❞♦ ❡♠ ❝♦r♦❛s ❝✐r❝✉❧❛r❡s✱ Ai✱ ❢❛③❡♥❞♦✲s❡ ❝♦rr❡s♣♦♥❞❡r ❛ ❝❛❞❛
❝♦r♦❛ ✉♠❛ ✈❡❧♦❝✐❞❛❞❡ Vi✱ ♠❡❞✐❞❛ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ ❯♠❛ ♣♦ssí✈❡❧ ♣r✐♠❡✐r❛ ❛♣r♦①✐♠❛çã♦ ✭♣♦r
❡①❝❡ss♦✮ ❞♦ ✈❛❧♦r ❞♦ ❝❛✉❞❛❧ à s❛í❞❛ ❞♦ t✉❜♦ s❡rá✿
Q=X
i
Vi π(Ri2+1−R 2
i) ✭✷✳✽✮
✷✳✸✳ ▼♦t♦r❡s ❞❡ ♣❛ss♦ ❛ ♣❛ss♦
❯♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ✉♠ ❞✐s♣♦s✐t✐✈♦ ❞❡ ♣♦tê♥❝✐❛ ❝♦♥st❛♥t❡✱ ♦♥❞❡ ❛ ♣♦tê♥❝✐❛ é ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ ♣r♦❞✉t♦ ❞♦ ❜✐♥ár✐♦ ♣❡❧❛ ✈❡❧♦❝✐❞❛❞❡✭❡q✳ ✷✳✾✮✳ ❊st❡ t✐♣♦ ❞❡ ♠♦t♦r❡s ❛ss✉♠❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♥ú♠❡r♦ ❞❡ ♣♦s✐çõ❡s ❛♥❣✉❧❛r❡s ❞✐st✐♥t❛s ✭❞✉③❡♥t❛s✱ t✐♣✐❝❛♠❡♥t❡✮✱ t❡♥❞♦ ✉♠❛ ♣r❡❝✐sã♦ ❡❧❡✈❛❞❛ ♥♦ s❡✉ ♣♦s✐❝✐♦♥❛♠❡♥t♦✳
P =T ×ω ✭✷✳✾✮
✷✳✸✳✶ ▼♦t♦r ✐❞❡❛❧
❯♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ✐❞❡❛❧ ♥ã♦ t❡r✐❛ ❢r✐❝çã♦ ♠❡❝â♥✐❝❛ ❡ ♦ s❡✉ ❜✐♥ár✐♦ s❡r✐❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ♥♦ ❡st❛t♦r ♠✉❧t✐♣❧✐❝❛❞♦ ♣❡❧❛ ❝♦rr❡♥t❡ q✉❡ ❛tr❛✈❡ss❛ ❛s r❡❢❡r✐❞❛s ❡s♣✐r❛s✳ ❆ s✉❛ ú♥✐❝❛ ❝❛r❛❝t❡ríst✐❝❛ ❡❧étr✐❝❛ s❡r✐❛ ❛ ✐♥❞✉tâ♥❝✐❛✷✳
◆✉♠ ♠♦t♦r ✐❞❡❛❧✱ à ♠❡❞✐❞❛ q✉❡ ❛ s✉❛ ✈❡❧♦❝✐❞❛❞❡ s❡ ❛♣r♦①✐♠❛ ❞❡ ③❡r♦✱ ♦ s❡✉ ❜✐♥ár✐♦ ❛♣r♦①✐♠❛r✲ s❡✲✐❛ ❞♦ ✐♥✜♥✐t♦✱ ❡ ❛ ✈❡❧♦❝✐❞❛❞❡ ✐♥✜♥✐t❛ t❡r✐❛ ❜✐♥ár✐♦ ✐❣✉❛❧ ❛ ③❡r♦✳ ❈♦♠♦ ❛ ❝♦rr❡♥t❡ é ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ❜✐♥ár✐♦✱ ❛ ❝♦rr❡♥t❡ s❡r✐❛ ✐♥✜♥✐t❛ ❛ ✈❡❧♦❝✐❞❛❞❡ ③❡r♦✳
✷✳✸✳✷ ▼♦t♦r r❡❛❧
❯♠ ♠♦t♦r r❡❛❧ ❞✐❢❡r❡ ❞❡ ✉♠ ✐❞❡❛❧ ♣♦r t❡r r❡s✐stê♥❝✐❛ ♥ã♦ ♥✉❧❛ ♥❛s ❡s♣✐r❛s✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❛s ♣❧❛❝❛s ❞❡ ❢❡rr♦ ❡stã♦ s✉❥❡✐t❛s ❛ s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛✱ ❛ ♣❡r❞❛s ♣♦r ❝♦rr❡♥t❡ ❞❡ ❋♦✉❝❛✉❧t ❡ ❛ ♣❡r❞❛s ❞❡ ❤✐st❡r❡s❡ ❡♥tr❡ ❛ ✈❛r✐❛çã♦ ❞❡ ❢♦rç❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ ✭❝♦rr❡♥t❡✮ ❡ ❛ ✐♥❞✉çã♦ ♠❛❣♥ét✐❝❛ ✭❞❡♥s✐❞❛❞❡ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦✮ ❬✽❪✳
❆ s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛ ✐♠♣õ❡ ✉♠ ❧✐♠✐t❡ ♥❛ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ✐♥✈❡rs❛ ❡♥tr❡ ❛ ❝♦rr❡♥t❡ ❡ ♦ ❜✐♥ár✐♦✱ ❡♥q✉❛♥t♦ q✉❡ ❛ r❡s✐stê♥❝✐❛ ❞❛s ❡s♣✐r❛s ❡ ❛s ♣❡r❞❛s ♥♦ ❢❡rr♦ ✭♣♦r ❝♦rr❡♥t❡ ❞❡ ❋❛✉❧❝❛✉❧t ❡ ❤✐st❡r❡s❡✮ ♣r♦✈♦❝❛♠ ♦ ❛q✉❡❝✐♠❡♥t♦ ❞♦ ♠♦t♦r✳
✷✳✸✳✸ ❈✉r✈❛ ✈❡❧♦❝✐❞❛❞❡✲❜✐♥ár✐♦
❈❛❞❛ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ t❡♠ ❡s♣❡❝✐✜❝❛❞♦ ✉♠ ✈❛❧♦r ♠á①✐♠♦ ❞❡ ❝♦rr❡♥t❡ q✉❡ ♥ã♦ ♣♦❞❡ s❡r ❡①❝❡❞✐❞♦✳ ❈♦♠♦ ❛ ❝♦rr❡♥t❡ é ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à ✈❡❧♦❝✐❞❛❞❡✱ ♣❛r❛ ❜❛✐①❛s ✈❡❧♦❝✐❞❛❞❡s ❛ ❝♦rr❡♥t❡ t❡♥❞❡ ♣❛r❛ ✈❛❧♦r❡s ❛❧t♦s✳ ❈❛❜❡ ❛♦ ❞r✐✈❡r ❞♦ ♠♦t♦r ❧✐♠✐t❛r ♦ ✈❛❧♦r ♠á①✐♠♦ ❞❡ ❝♦rr❡♥t❡✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ ♦ ❜✐♥ár✐♦ ✜❝❛ t❛♠❜é♠ ❧✐♠✐t❛❞♦ ❛té à ❝♦r♥❡r s♣❡❡❞✱ ✈❡❧♦❝✐❞❛❞❡ ❛ ♣❛rt✐r ❞❛ q✉❛❧ ♦ ✈❛❧♦r ❞❡ ❝♦rr❡♥t❡ ❝♦♠❡ç❛ ❛ ❞✐♠✐♥✉✐r ✭✜❣✉r❛s ✷✳✽ ❡ ✷✳✾✮✳
✷✳✸✳✹ P❡r❞❛s ❞❡✈✐❞♦ ❛ ❞❡t❡♥t t♦rq✉❡
❯♠❛ ❝❛r❛❝t❡ríst✐❝❛ q✉❡ ❞✐❢❡r❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❞❡ ♦✉tr♦s ♠♦t♦r❡s ✭♣❛rt✐❝✉❧❛r♠❡♥❡ s❡r✈♦♠♦t♦r❡s✮✱ é ❛ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❜❧♦q✉❡❛r ♦ r♦t♦r q✉❛♥❞♦ ♣❛r❛❞♦✱ ❛té ✉♠ ❝❡rt♦ ❜✐♥ár✐♦ ❬✾❪✳ ◆❛ ✜❣✉r❛ ✷✳✾ ♦❜s❡r✈❛✲s❡ q✉❡ ♣❛r❛ ✈❡❧♦❝✐❞❛❞❡ ✐❣✉❛❧ ❛ ③❡r♦✱ ♦ ✈❛❧♦r ❞♦ ❜✐♥ár✐♦ ♠❛♥té♠✲s❡ ✐❣✉❛❧ ❛♦ ✈❛❧♦r ♠á①✐♠♦ ❡s♣❡❝✐✜❝❛❞♦✱ ♦ q✉❡ s✐❣♥✐✜❝❛ q✉❡ ✉♠ ❛❣❡♥t❡ ❡①t❡r♥♦ ♣♦❞❡ ❛♣❧✐❝❛r ♥♦ r♦t♦r ✉♠ ❜✐♥ár✐♦ ✐♥❢❡r✐♦r ❛♦ ❡s♣❡❝✐✜❝❛❞♦ s❡♠ q✉❡ ♦ ✈❡✐♦ ❛❧t❡r❡ ❛ s✉❛ ♣♦s✐çã♦✳ ❖ ♠♦t♦r só ❛ss✉♠❡ ❡st❡ ❝♦♠♣♦rt❛♠❡♥t♦ s❡ ❡st✐✈❡r ❛ s❡r ❛❧✐♠❡♥t❛❞♦✳
▼❡s♠♦ ❞❡s❧✐❣❛❞♦✱ ♥♦ ❡♥t❛♥t♦✱ ♦ r♦t♦r ♣♦ss✉✐ ✉♠❛ r❡s✐stê♥❝✐❛ ❛♦ ♠♦✈✐♠❡♥t♦✱ ❝❛✉s❛❞❛ ♣❡❧❛s ❛tr❛çõ❡s ♠❛❣♥ét✐❝❛s ✐♥t❡r♥❛s✳ ❆♦ r♦❞❛r ♦ ✈❡✐♦ ❞❡ s❛í❞❛ ♠❛♥✉❛❧♠❡♥t❡ ❝♦♠ ♦ ♠♦t♦r ❞❡s❧✐❣❛❞♦ é ♣♦ssí✈❡❧ s❡♥t✐r ✉♠❛ r❡s✐stê♥❝✐❛ ❡♠ ❢♦r♠❛ ♣✉❧s❛❞❛✳ ❖ ❜✐♥ár✐♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ✈❡♥❝❡r ❡st❛ r❡s✐s✲ tê♥❝✐❛ é ❝❤❛♠❛❞♦ ❞❡t❡♥t t♦rq✉❡✳
✷■♥❞✉tâ♥❝✐❛✿ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ✉♠ ❝♦♥❞✉t♦r ❡♠ q✉❡ ✉♠❛ ✈❛r✐❛çã♦ ❞❛ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ ❛tr❛✈és ❞❡❧❡ ✐♥❞✉③ ✉♠❛ ❢♦rç❛ ❡❧❡tr♦♠♦tr✐③ ✭❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧✮ ♥❡st❡✳
❊st❡ ❜✐♥ár✐♦ r❡♣r❡s❡♥t❛ ✉♠❛ ♣❡r❞❛ q✉❛♥❞♦ ♦ ♠♦t♦r r♦❞❛ ✭✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ❞♦ s❡♥t✐❞♦✮✱ ❡ ❛ ♣❡r❞❛ ❞❡ ♣♦tê♥❝✐❛ ❞❡✈✐❞♦ ❛ ❡st❡ ❡❢❡✐t♦ é ♣r♦♣♦r❝✐♦♥❛❧ à ✈❡❧♦❝✐❞❛❞❡ ❞❡ r♦t❛çã♦✳ ❆ss✐♠✱ ❡st❛ ♣❡r❞❛ ❞❡✈❡ s❡r s✉❜tr❛í❞❛ à ❝✉r✈❛ ✐❞❡❛❧✳ ◆❛ ✜❣✉r❛ ✷✳✶✵ ♦❜s❡r✈❛♠✲s❡ ❛s ✈❛r✐❛çõ❡s ❞❡ ♣♦tê♥❝✐❛ ❡ ❜✐♥ár✐♦ ❞❡ ✉♠ ♠♦t♦r ❡♠ ❢✉♥çã♦ ❞❛ s✉❛ ✈❡❧♦❝✐❞❛❞❡✱ ❝♦♠ ❡ s❡♠ ❛ s✉❜tr❛çã♦ ❞❛s ♣❡r❞❛s ♣♦r ❞❡t❡♥t t♦rq✉❡✳
❋✐❣✉r❛ ✷✳✽✿ ❈✉r✈❛ ✈❡❧♦❝✐❞❛❞❡✲❜✐♥ár✐♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪
❋✐❣✉r❛ ✷✳✾✿ ❈✉r✈❛ ❞❡ ✉♠ ♠♦t♦r ❧✐♠✐t❛❞♦ ❡♠ ❝♦rr❡♥t❡ ❬✶✵❪
✷✳✸✳✺ ❊s❝♦❧❤❛ ❞❡ ✈❛❧♦r❡s ❞❡ t❡♥sã♦ ❡ ❝♦rr❡♥t❡
❆ ♣♦tê♥❝✐❛ ❡ ❜✐♥ár✐♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à t❡♥sã♦ ❝♦♠ q✉❡ é ❛❧✐♠❡♥t❛❞♦ ❬✶✵❪✱ ❛ ♣❛rt✐r ❞❛ ③♦♥❛ ❡♠ q✉❡ ❛ ❝♦rr❡♥t❡ ♥ã♦ é ❧✐♠✐t❛❞❛ ♣❡❧♦ ❞r✐✈❡r ✭✜❣✉r❛ ✷✳✶✶✮✳ ❆ t❡♥sã♦ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦s ♠♦t♦r❡s ♣❛ss♦ ❛ ♣❛ss♦ ♥ã♦ é ✐♥❞✐❝❛❞❛ ♥❛s ❡s♣❡❝✐✜❝❛çõ❡s✱ ❡ ❞❡✈❡✲s❡ s❡♠♣r❡ t♦♠❛r ❡♠ ❝♦♥t❛ ♦ ❛✉♠❡♥t♦ ❞♦ ❝❛❧♦r ❞✐ss✐♣❛❞♦ r❡s✉❧t❛♥t❡ ❞♦ ❛✉♠❡♥t♦ ❞❛ t❡♥sã♦✳ ❆ ❡q✉❛çã♦ ✷✳✶✵✱ ♦❜t✐❞❛ ❡♠♣✐r✐❝❛♠❡♥t❡ ❬✶✵❪ ✱ s✉❣❡r❡ ✉♠ ❧✐♠✐t❡ ♠á①✐♠♦ ♣❛r❛ ❛ t❡♥sã♦ ❞❛ ❢♦♥t❡ ❞❡ ❛❧✐♠❡♥t❛çã♦✳
U▼❛①= 32×√L
❖♥❞❡ ▲ é ❛ ✐♥❞✉t❛♥❝✐❛ ❞♦ ♠♦t♦r✱ ♥♦r♠❛❧♠❡♥t❡ ✐♥❞✐❝❛❞❛ ♥❛s ❡s♣❡❝✐✜❝❛çõ❡s ❞❡st❡✳ ✭✷✳✶✵✮
❋✐❣✉r❛ ✷✳✶✵✿ ❈✉r✈❛s ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ♣rát✐❝❛s ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪
❋✐❣✉r❛ ✷✳✶✶✿ ■♥✢✉ê♥❝✐❛ ❞♦ ❛✉♠❡♥t♦ ❞❡ t❡♥sã♦ ♥♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪
❋✐❣✉r❛ ✷✳✶✷✿ ■♥✢✉ê♥❝✐❛ ❞♦ ❛✉♠❡♥t♦ ❞♦ ❧✐♠✐t❡ ❞❡ ❝♦rr❡♥t❡ ♥♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ♠♦t♦r ♣❛ss♦ ❛ ♣❛ss♦ ❬✶✵❪
❖ ❛✉♠❡♥t♦ ❞❛ ❝♦rr❡♥t❡ ❧✐♠✐t❡ ❛✉♠❡♥t❛ ♦ ❜✐♥ár✐♦ ❞✐s♣♦♥í✈❡❧ ❛ ❜❛✐①❛s ✈❡❧♦❝✐❞❛❞❡s ❞❡ r♦t❛çã♦✳ ◆❛ ✜❣✉r❛ ✷✳✶✷ ♦❜s❡r✈❛✲s❡ ♦ ❛✉♠❡♥t♦ ❞❛ ❝♦rr❡♥t❡ ❧✐♠✐t❡ ♣❛r❛ ♦ ❞♦❜r♦✳ ❖ ❜✐♥ár✐♦ ♥ã♦ ✐r✐❛✱ ♥♦ ❡♥t❛♥t♦✱ ❞✉♣❧✐❝❛r✱ ❞❡✈✐❞♦ à s❛t✉r❛çã♦ ♠❛❣♥ét✐❝❛ ❬✶✵❪✳ ❖ ♠♦t♦r ✐r✐❛✱ t❛♠❜é♠✱ ❞✐ss✐♣❛r ❝♦♥s✐❞❡r❛✲ ✈❡❧♠❡♥t❡ ♠❛✐s ❝❛❧♦r✳ ❖ ✈❛❧♦r ❞❡ ❝♦rr❡♥t❡ ♠á①✐♠♦ é s❡♠♣r❡ ✐♥❞✐❝❛❞♦ ♥❛s ❡s♣❡❝✐✜❝❛çõ❡s✱ ❡ ❞❡✈❡
