CHAPTER 9 Compressible Flow
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1 CHPTER 9 Corssibl Flow Inrouion 9. v R. kv. R or R k k Rk k Char 9 / Corssibl Flow S of Soun 9.4 Subsiu Eq ino Eq an ngl onial nrgy hang: Q WS u~ u~. Enhaly is fin in Throynais as h u~ v u~ /. Thrfor, Q WS h h. ssu h flui is an ial gas wih onsan sifi ha so ha h T. Thn Q WS ( T T). Nx, l v R an k / v so ha / R k/( k ). Thn, wih h ial gas law RT, h firs law aks h for Q W S k k 9.6 Th s of soun is givn by /. For an isohral ross TR / K, whr K is a onsan. This an b iffrnia: K RT. Hn, h s of soun is RT Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
2 Char 9 / Corssibl Flow 9.8 For war Bulk oulus = Pa Sin 000 kg/, w s ha /s 9.0 Sin = 450 /s for h sall wav, h i inrn is sons 9. krt /s /s. sin. M sin an L 776 L s. L 9.6 Eq. 9..4: krt fs. Enrgy Eq: ( ) ( ) T ( T T). 0 T. T f/s( 0. f/s) 60 f-lb/slug- R No: Us slug = lb-s /f ( = F/a). (Unis an b a ain!) 0.0 R or 0.0 F Isnroi Flow 9.8 a) s a kpa abs kpa abs. s =0 s Fro s : s s s s / k / kg/ /s Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
3 Char 9 / Corssibl Flow 9.0 Is r ? kpa. a) b) r hok flow. M. krt kpa..4 87T T. T 48. K, 5.8 /s kg/ kg/s r M = kg/ /s kg/s a) r M kpa. T K kg/ /s kg/s. b) r kpa, M 0.8, T 0.884T kg/, /s kg/s kpa abs. T K /s kg/ s sia sia. T R fs. [ / ( )] (.5/) slug/s sia, T 46.6 R, 000 fs. 0 0 [ / ( )] (.5/) slug/s. 0 Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
4 Char 9 / Corssibl Flow T T. T 5 K /0.667 = kpa abs. Nx, T 5 K, kpa; /s = kg/ = kpa / or Trial-an-rror: 9.8 /s. 0.0 kg/ an 99.4 kpa abs. 9.0 W n o rin h Mah nubr a h xi. Sin h M = a h hroa, hn hroa 9.7. Hn, h ara raio a h xi is Using h air abls, w fin wo ossibl soluions, on for subsoni flow, an h ohr for sursoni flow in h ivrging sion of h nozzl. h xi: Subsoni Flow: M 0.5, T T , an Hn, M M krt /s Sursoni Flow: M.76, T T , an Hn, M M krt /s 9. / RT (45 4.7)44 / (76 50) slug/f. / slug/f fs (/) slug/s. 0 Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
5 Char 9 / Corssibl Flow T krt T. T 44.0 K.. /s..4/ kpa abs..76 kg/ = Trial-an-rror:. /s, 659 /s , kg / kpa, 4. 9 kpa abs. 9.6 M sia, T R slug. f f M.04, T R, = 684 fs f Using orssibl flow abls for air, w rin h rssur raio an raur raio for M =.8 o b: T , an T kpaabs an T T 0 5 K M.8 krt /s L M. Ngl visous ffs. M or Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
6 Char 9 / Corssibl Flow 9.4 Isnroi flow. Sin k =.4 for nirogn, h isnroi flow abl ay b us. M, i /s. i kg/ i M > M = M < ~ = 0 i i i M, T 0.57 T0, T0 T 044 K or 77 C kpa abs ssu 0 0 kpa. Thn kg/ F /s M. 4; M.94, T T K, kpa abs F B /s. F B N. Noral Shok 9.48 a) ( 000) kg/ ( ) = /s..774 kg/. 4 0 Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
7 Char 9 / Corssibl Flow Subsiu in an fin 808 kpa abs. M T 746 K or 47 C M T km k ( k ) M ( k )M. T k k ( k )M M (4kM k ) k k M k. (This is Eq. 9.4.). Subsiu ino abov: k ( k ) ( k ) ( k ) ( ) ( ) ( ) 4k k k k k ( k ) / k ( k ) / For a srong shok in whih. k,. k ( k ) ( k ) k ( k ) ( k )( k ). 9.5 If M 0.5, hn M /s kpa abs. 8. kg/ (.85 9) kpa. T. K. M 000 / M kpa. T K. For isnroi flow fro 0: For M = 0.458, = an T T / kpa abs. T / K or 448 C. 5 0 Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
8 Char 9 / Corssibl Flow M kpa abs M kpa. T K. rains a, kg/ /s kg/s. If hroa ara is ru, M kg/ an kg/s. 4.7 sia. 4. M.94, an / sia. M.94, / M, sia. T R fs. M.94,.48 sia. T R fs. M , 4.7 sia. T T R fs sia. aor Flow / kpa. T K kg/ /s. (M.) or 6. 4 T 0./ K kg/ (Enrgy fro 0.) ( 87 J/kg K) 050 /s ( /4) or Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
9 Char 9 / Corssibl Flow /. 8.9 M, sia. T R. 50 Obliqu Shok Wav slug/f fs f. or.9" M Fro Fig. 9.5, 46, 79. a) 46. Mn.9sin Mn M sin(46 0 ). M kpa abs. T K. = 0 o ) /s. a ah shok = 5 o 9.66 Mn.5sin 5.0. Mn T K. M 0.576/ sin(5 0 ) Mn.6sin Mn M sin(47 0 ). M.44. T K. M krt /s M, Mn sin 8.4. Mn kpa abs M kpa abs. sin(8 0 ) ( ) noral kpa abs. 7 0 Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
10 Char 9 / Corssibl Flow Exansion Wavs For M 4, (S Fig. 9.8.) T T T T T T K /s. T 56 C. 9.7 a) Mu.7. u (0/0.0585) = 4.4 kpa abs. For 5 an M.5, 7. Mn.5sin 7.. Mn kpa abs. M M 0.889/ sin(7 5 ) If 5 wih M 4, hn Fig. 9.5 = 8. n M 4sin8.4. M n kpa. shok M M l M u shok 0.88 M.64. sin(8 5 ) M 4, , M u u 0 = 6.6 kpa. C L Lif.5 os 5 0 / 6.6 ( /) os C D Drag.5sin ( /) sin Cngag Larning. ll Righs Rsrv. May no b sann, oi or ulia, or os o a ublily assibl wbsi, in whol or in ar.
CHAPTER 9 Compressible Flow
CHPTER 9 Comrssibl Flow Char 9 / Comrssibl Flow Inroducion 9. c c cv + R. c kcv. c + R or c R k k Rk c k Sd of Sound 9.4 Subsiu Eq. 4.5.8 ino Eq. 4.5.7 and nglc onial nrgy chang: Q WS + + u~ u~. m ρ ρ
CHAPTER 9. Compressible Flow. Btu ft-lb lbm ft-lb c p = = ft-lb slug- R. slug- R. 1 k. p p. p v p v. = ρ ρ
CHPTER 9 Cmrssibl Flw 9 Bu f-lb lbm f-lb c 778 6 lbm- R Bu slug slug- R f-lb cv c R 6 76 96 96 slug- R Bu 7 lbm R f-lb slug- R Bu 778 f - lb slug lbm c 9 c cv + R c cv c + R r c R c R / ( ) 9 If s, Eq
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