f15_sp - Fluids – Lecture 15 Notes 1 Mach Number...

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Unformatted text preview: Fluids – Lecture 15 Notes 1. Mach Number Relations 2. Normal-Shock Properties Reading: Anderson 8.4, 8.6 Mach Number Relations Local Mach number For a perfect gas, the speed of sound can be given in a number of ways. γp a = γRT = = ( γ − 1) h (1) ρ The dimensionless local Mach number can then be defined. 2 V ρ ( u 2 + v 2 + w 2 ) u 2 + v 2 + w M ≡ = = a γp ( γ − 1) h It’s important to note that this is a field variable M ( x, y, z ), and is distinct from the freestream Mach number M ∞ . Likewise for V and a . V a M V(x,y,z) a(x,y,z) M(x,y,z) The local stagnation enthalpy can be given in terms of the static enthalpy and the Mach number, or in terms of the speed of sound and the Mach number. 1 1 V 2 γ − 1 h o = h + V 2 = h 1 + = h 1 + γ − 1 M 2 = a 2 1 + M 2 (2) 2 2 h 2 γ − 1 2 This now allows the isentropic relations p o ρ o γ h o γ/ ( γ − 1) = = p ρ h to be put in terms of the Mach number rather than the speed as before. ρ o γ − 1 1 / ( γ − 1) = 1 + M 2 ρ 2 p o γ − 1 γ/ ( γ − 1) = 1 + M 2 p 2 The following relation is also sometimes useful....
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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f15_sp - Fluids – Lecture 15 Notes 1 Mach Number...

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