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FenTrans, MecFlu, TransCal e TransMassa - Frank White - Mecânica dos Fluidos- Ed: 8º - Capítulo 9.Problemas - Ex. 154

The F-22 supersonic fi ghter cruises at 11,000 m altitude,

with a weight of 50,000 lbf and thrust of 10,000 lbf. Its

wing area is 840 ft2. Assume the wing is a 6-percent-thick

diamond shape and provides all lift and thrust. Use Ackeret

theory to estimate the resulting Mach number.

Passo 1

Saaaalve, tranquilo? Vamos lá resolver mais uma questão juntos?! 😊

Considere a tabela B. 6Em 11000   m de altitude

p ∞ = 22612   P a

Converter os dados em S I unidades

W = 222400   N F = 44500   N A p = 78   m 2

Escreva a relação para o elevador.

W = 4 α M a 2 - 1 k 2 p ∞ M a 2 A p

Aqui, é o M a número de Mach, é a p ∞ pressão, é A p a área da asa, e é W o peso.

222400 = 4 α M a 2 - 1 1.4 2 22612 × M a 2 × 78 . . . ( 1 )

Passo 2

Calcule o número Mach. Escreva a equação para o arrasto.

F = 4 M a 2 - 1 α 2 + y ‾ ' 2 k 2 p ∞ M a 2 A p

Aqui, é F o empuxo, e y ‾ ' é a espessura da asa.

44500 = 4 M a 2 - 1 α 2 + 0.06 2 1.4 2 × ( 22612 ) M a 2 × 78 . . . ( 2 )

Resolva as equações (1) e (2)

α = 0.02  radians 

Substituir na equação (1)

222400 = 4 × 0.02 M a 2 - 1 1.4 2 22612 × M a 2 × 78 M a = 1.92

Assim, o número Mach é 1.92 .

Resposta

M a = 1.92

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