FL07Ch12 - SPEED OF SOUND, a AS A NONDIMENSIONALIZING...

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SPEED OF SOUND, a AS A NONDIMENSIONALIZING PARAMETER 1 Dimensional, isentropic flow () () gas ideal an to limited not result general d ρ dp a , continuity and momentum combining 0 d ρ a da ρ da d ρ d ρ a da ρ a ρ a ρ da a d ρ ρ A a A ρ mass mass Equation Continuity conctant s 2 2 1 = = = + + = + = = dT T d dp p da a + ρ + ρ + + T p a ρ () () ( ) () motion steady for Equation Euler da ρ a dp da a A ρ dp A a da a a A ρ dp p p A A p dt dV m a m F pA F Equation Momentum = = = + = = = = a u M
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(4.1) M 1 Sin u a Sin Angle, Mach 1 1 = = υ MACH WAVE - very weak pressure wave drawn as 3.5 M t u × t a × υ Interferometer image
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SPEED OF SOUND IN AN IDEAL GAS 2 t tan cons s γ γ a T R γ d ρ dp T R p gas ideal an for ρ p γ d ρ dp ρ d ρ γ p dp constant ρ ln γ p ln ρ p constant v p process isentropic an for = = = ρ = = = = = = m/sec 1020.5 a 300 kJ kgm/sec 1000 kg/kgmole 4 K kJ/kgmole 8.314 1.67 a 1000 γ RT a a K 300 at helium ft/sec 1096.4 a R 500 sec lbf ft lbm 32 lbmole lbm/ 28.97 R lbf/lbmole ft 1545.15 1.4 a T R g γ a R 500 at air 2 2 = × × × = × = = = × × × = =
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STAGNATION PROPERTIES AS NONDIMENSIONALIZING PARAMETERS properties after a gas is brought to rest isentropically, s=constant properties with u=0, M=0 O p O T constant s 1, s s constant entropy isentropic is process stagnation the since ρ ρ , p p , T T 2c u T T 2 u T c T c 0 u for Equation Energy 2 u h 2 u h O O O O p 2 O 2 p O p 1 2 1 2 2 1 1 = = = + = + = = + = + 1 1, M p 2 2, M p * * M , p s
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1-D ISENTROPIC FLOW OF AN IDEAL GAS [] [] [] u/a M , γ RT a (12.25) C.10, Table M 2 1 γ 1 T T T R γ 2 u 1) ( γ 1 T T constant c 1 γ γ R c since T 2c u 1 T T T c h 2 u T c T c 2 u h h 0 u for required) is equaton energy (only the equation energy 2 u h 2 u h 2 O 2 O p p p 2 O p 2 p O p 2 2 2 O 1 2 2 2 2 1 1 = = + = + = = = + = = + = + = = + = + [ ] ) (12.27 C.10, Table M 2 1 γ 1 ρ ρ (12.28) C.10, Table M 2 1 γ 1 p p (12.26) ρ ρ p p T T constant pv flow, isentropic for since 0 s constant pv 1 γ 1 2 O 1 γ γ 2 O 1 γ 1 2 γ 1 - γ 1 2 1 2 γ γ + = + = = = = = =
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REAL GAS AND IDEAL GAS PROPERTY MODELS REAL GAS AND IDEAL GAS PROPERTY MODELS () () () ( ) ( ) () 1 γ R γ c properties 2 any f s dT pv) (du s p p Rln T T ln c s constant pv 0 s 0 s process isentropic properties 2 any f h dT T c h property 1 f T c h properties 2 any f a ρ p a property 1 f γ RT a a / u M a / u M u h, s, ρ , p, T, Module Property Gas Real Gas Ideal Equation Energy 2 u h h p 1 2 1 2 p γ p p constant s 2 1 O = = + = = = = = = = = = = = = = = = + =
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FL07Ch12 - SPEED OF SOUND, a AS A NONDIMENSIONALIZING...

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