Notes #6 MAE 533, Fluid Mechanics
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چکیده
1 Different Ways of Representing T • The speed of sound, a, is formally defined as (∂p/∂ρ) s. It is a function of that thermodynamic state variables of the gas. The stagnation enthalphy of a steady flow streamtube is defined by " h • ≡ h + 1 2 u 2. (1) It depends not only of the thermodynamic state of the gas, but also on the magnitude of the flow velocity u. Using the perfect gas approximation (h = C p T , C p = γR/(γ − 1), a 2 = γRT), we have: h • = C p T (1 + γ − 1 2 M 2). (2) where M = u/a is the Mach Number. We now define a o to be the stagnation speed of sound—i.e. the speed of sound when the gas is hypothetically brought to rest adiabatically. For a perfect gas, we have h • = C p T o. Hence a 2 o = γRT • = a 2 (1 + γ − 1 2 M 2). (3) In other words, a o is a measure of the stagnation temperature of the gas.
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