Fundamentos de Engenharia Aeronáutica - Volume único

278
Substituindo-se as Equações (4.142) e (4.143) na Equação (4.141), tem-se que:
dR
2 ⋅ g ⋅ ρ ⋅
=
dq
n
2
− 1 − 2 ⋅ q ⋅ g ⋅ ρ ⋅ n ⋅ ( n
2
( g ⋅ ρ ⋅ n − 1)
2
2
− 1)
−1
2
⋅ dn
dq
= 0
(4.144)
2 ⋅ g ⋅ ρ ⋅
dR
=
dq
n
2
−1
− 2 ⋅ q ⋅ g ⋅ ρ ⋅ n ⋅ ( n
g
2
2
⋅ ρ ⋅ ( n
2
−1)
2
−1)
−1
2
⋅ dn
dq
= 0
(4.144a)
como o termo g 2 ⋅ ρ 2 ⋅ ( n
2 − 1)
no denominador da função é diferente de zero, pois n>1, a
única forma de se zerar a Equação (4.144a) é que o numerador seja nulo, portanto:
2
n dn
2 ⋅ g ⋅ ρ ⋅ n −1
− 2 ⋅ q ⋅ g ⋅ ρ ⋅ ⋅ = 0
(4.145)
2
( n −1)
dq
2 ⋅ g ⋅ ρ ⋅
2
2
( n −1) − 2 ⋅ q ⋅ g ⋅ ρ ⋅ n dn
⋅ = 0
( n
2
−1)
dq
(4.145a)
novamente o denominador da função é diferente de zero, portanto:
como o termo ( ⋅ g ⋅ ρ)
2
2
dn
( n −1) − 2 ⋅ q ⋅ g ⋅ ρ ⋅ n ⋅ = 0
2 ⋅ g ⋅ ρ ⋅
(4.146)
dq
2
dn
2 ⋅ g ⋅ ρ ⋅ ( n −1)
− 2 ⋅ q ⋅ g ⋅ ρ ⋅ n ⋅ = 0
(4.146a)
dq
2 dn
[(
n −1)
− q ⋅ n] = 0
2 ⋅ g ⋅ ρ ⋅
(4.146b)
dq
2 é uma constante diferente de zero, pode-se escrever que:
2 dn
n −1
− q ⋅ n ⋅ = 0
(4.146c)
dq
A partir da Equação (4.138g), tem-se que:
n
2
T ⋅ ρ ⋅ v
=
⋅ ⋅
⋅ S
ρ ⋅ v
⋅ C
2
2 4
D0
−
2
2
2 K W 4 ⋅ K ⋅W
⋅ S
2
(4.147)
considerando a pressão dinâmica q, a Equação (4.147) pode ser reescrita do seguinte modo: