Chapter09

# Mechanics of Fluids

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200 CHAPTER 9 Compressible Flow 9.1 Btu ft-lb lbm ft-lb 0.24 778 32.2 6012 Btu slug lbm- R slug- R p c = = o o c c R v p = - = - = = 6012 1716 4296 4296 1 778 1 32 2 ft -lb slug- R ft -lb slug- R Btu ft - lb slug lbm o o . Btu 0.171 lbm- R = o 9.2 c c R c kc c c k R c k R p v p v p p p = + = = + -  = . . . or 1 1 = - c Rk k p /( ). 1 9.3 If s = 0, Eq. 9.1.9 can be written as c n T T R n p p n T T n p p p c R p l l l l 2 1 2 1 2 1 2 1 = = or It follows that, using c c R c c k p v p v = + = and / , T T p p p p R c k p 2 1 2 1 2 1 1 1 = = - / . Using Eq. 9.1.7, T T p p p p p p k k 2 1 2 1 2 1 2 1 1 1 1 2 2 1 1 = = = - - r r r r or / . Finally, this can be written as p p k 2 1 2 1 = r r . 9.4 Substitute Eq. 4.5.18 into Eq. 4.5.17 and neglect potential energy change: & & & ~ ~ . Q W m V V p p u u S - = - + - + - 2 2 1 2 2 2 1 1 2 1 2 r r

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