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

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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. p a = RT = = ( 1) h (1) The dimensionless local Mach number can then be defined. 2 V ( u 2 + v 2 + w 2 ) u 2 + v 2 + w M = = a p ( 1) h Its 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 1 h o = h + V 2 = h 1 + = h 1 + 1 M 2 = a 2 1 + M 2 (2) 2 2 h 2 1 2 This now allows the isentropic relations p o o h o / ( 1) = = p h to be put in terms of the Mach number rather than the speed as before. o 1 1 / ( 1) = 1 + M 2 2 p o 1 / ( 1) = 1 + M 2 p 2 The following relation is also sometimes useful....
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f15_sp - Fluids Lecture 15 Notes 1. Mach Number Relations...

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