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Tabela A9.1 � Relações Isentrópicas ( 1.4 ) TABELA A9.1 Relações Isentrópicas

Ma /0T T /0p p /0 */A A Ma /0T T /0p p /0 */A A 0.80 1.128E+0 1.524E+0 1.351E+0 1.038E+0 0.02 1.000E+0 1.000E+0 1.000E+0 2.894E+1 0.82 1.134E+0 1.555E+0 1.371E+0 1.030E+0 0.04 1.000E+0 1.001E+0 1.001E+0 1.448E+1 0.84 1.141E+0 1.587E+0 1.391E+0 1.024E+0 0.06 1.001E+0 1.003E+0 1.002E+0 9.666E+0 0.86 1.148E+0 1.621E+0 1.412E+0 1.018E+0 0.08 1.001E+0 1.004E+0 1.003E+0 7.262E+0 0.88 1.155E+0 1.655E+0 1.433E+0 1.013E+0 0.1 1.002E+0 1.007E+0 1.005E+0 5.822E+0 0.90 1.162E+0 1.691E+0 1.456E+0 1.009E+0 0.12 1.003E+0 1.010E+0 1.007E+0 4.864E+0 0.92 1.169E+0 1.729E+0 1.478E+0 1.006E+0 0.14 1.004E+0 1.014E+0 1.010E+0 4.182E+0 0.94 1.177E+0 1.767E+0 1.502E+0 1.003E+0 0.16 1.005E+0 1.018E+0 1.013E+0 3.673E+0 0.96 1.184E+0 1.808E+0 1.526E+0 1.001E+0 0.18 1.006E+0 1.023E+0 1.016E+0 3.278E+0 0.98 1.192E+0 1.850E+0 1.552E+0 1.000E+0 0.2 1.008E+0 1.028E+0 1.020E+0 2.964E+0 1.00 1.200E+0 1.893E+0 1.577E+0 1.000E+0 0.22 1.010E+0 1.034E+0 1.024E+0 2.708E+0 1.02 1.208E+0 1.938E+0 1.604E+0 1.000E+0 0.24 1.012E+0 1.041E+0 1.029E+0 2.496E+0 1.04 1.216E+0 1.985E+0 1.632E+0 1.001E+0 0.26 1.014E+0 1.048E+0 1.034E+0 2.317E+0 1.06 1.225E+0 2.033E+0 1.660E+0 1.003E+0 0.28 1.016E+0 1.056E+0 1.040E+0 2.166E+0 1.08 1.233E+0 2.083E+0 1.689E+0 1.005E+0 0.30 1.018E+0 1.064E+0 1.046E+0 2.035E+0 1.10 1.242E+0 2.135E+0 1.719E+0 1.008E+0 0.32 1.020E+0 1.074E+0 1.052E+0 1.922E+0 1.12 1.251E+0 2.189E+0 1.750E+0 1.011E+0 0.34 1.023E+0 1.083E+0 1.059E+0 1.823E+0 1.14 1.260E+0 2.245E+0 1.782E+0 1.015E+0 0.36 1.026E+0 1.094E+0 1.066E+0 1.736E+0 1.16 1.269E+0 2.303E+0 1.814E+0 1.020E+0 0.38 1.029E+0 1.105E+0 1.074E+0 1.659E+0 1.18 1.278E+0 2.363E+0 1.848E+0 1.025E+0 0.40 1.032E+0 1.117E+0 1.082E+0 1.590E+0 1.20 1.288E+0 2.425E+0 1.883E+0 1.030E+0 0.42 1.035E+0 1.129E+0 1.091E+0 1.529E+0 1.22 1.298E+0 2.489E+0 1.918E+0 1.037E+0 0.44 1.039E+0 1.142E+0 1.100E+0 1.474E+0 1.24 1.308E+0 2.556E+0 1.955E+0 1.043E+0 0.46 1.042E+0 1.156E+0 1.109E+0 1.425E+0 1.26 1.318E+0 2.625E+0 1.992E+0 1.050E+0 0.48 1.046E+0 1.171E+0 1.119E+0 1.380E+0 1.28 1.328E+0 2.697E+0 2.031E+0 1.058E+0 0.50 1.050E+0 1.186E+0 1.130E+0 1.340E+0 1.30 1.338E+0 2.771E+0 2.071E+0 1.066E+0 0.52 1.054E+0 1.202E+0 1.141E+0 1.303E+0 1.32 1.348E+0 2.847E+0 2.112E+0 1.075E+0 0.54 1.058E+0 1.219E+0 1.152E+0 1.270E+0 1.34 1.359E+0 2.927E+0 2.153E+0 1.084E+0 0.56 1.063E+0 1.237E+0 1.164E+0 1.240E+0 1.36 1.370E+0 3.009E+0 2.197E+0 1.094E+0 0.58 1.067E+0 1.256E+0 1.177E+0 1.213E+0 1.38 1.381E+0 3.094E+0 2.241E+0 1.104E+0 0.60 1.072E+0 1.276E+0 1.190E+0 1.188E+0 1.40 1.392E+0 3.182E+0 2.286E+0 1.115E+0 0.62 1.077E+0 1.296E+0 1.203E+0 1.166E+0 1.42 1.403E+0 3.273E+0 2.333E+0 1.126E+0 0.64 1.082E+0 1.317E+0 1.218E+0 1.145E+0 1.44 1.415E+0 3.368E+0 2.381E+0 1.138E+0 0.66 1.087E+0 1.340E+0 1.232E+0 1.127E+0 1.46 1.426E+0 3.465E+0 2.430E+0 1.150E+0 0.68 1.092E+0 1.363E+0 1.247E+0 1.110E+0 1.48 1.438E+0 3.566E+0 2.480E+0 1.163E+0 0.70 1.098E+0 1.387E+0 1.263E+0 1.094E+0 1.50 1.450E+0 3.671E+0 2.532E+0 1.176E+0 0.72 1.104E+0 1.412E+0 1.280E+0 1.081E+0 1.52 1.462E+0 3.779E+0 2.585E+0 1.190E+0 0.74 1.110E+0 1.439E+0 1.297E+0 1.068E+0 1.54 1.474E+0 3.891E+0 2.639E+0 1.204E+0 0.76 1.116E+0 1.466E+0 1.314E+0 1.057E+0 1.56 1.487E+0 4.007E+0 2.695E+0 1.219E+0 0.78 1.122E+0 1.495E+0 1.333E+0 1.047E+0 1.58 1.499E+0 4.127E+0 2.752E+0 1.234E+0

2 Mecânica dos Fluidos

TABELA A9.1 Relações Isentrópicas (cont.)

Ma /0T T /0p p /0 */A A Ma /0T T /0p p /0 */A A 1.60 1.512E+0 4.250E+0 2.811E+0 1.250E+0 3.50 3.450E+0 7.627E+1 2.211E+1 6.790E+0 1.62 1.525E+0 4.378E+0 2.871E+0 1.267E+0 3.55 3.520E+0 8.187E+1 2.325E+1 7.113E+0 1.64 1.538E+0 4.511E+0 2.933E+0 1.284E+0 3.60 3.592E+0 8.784E+1 2.445E+1 7.450E+0 1.66 1.551E+0 4.648E+0 2.996E+0 1.301E+0 3.65 3.664E+0 9.420E+1 2.571E+1 7.802E+0 1.68 1.564E+0 4.790E+0 3.061E+0 1.319E+0 3.70 3.738E+0 1.010E+2 2.701E+1 8.169E+0 1.70 1.578E+0 4.936E+0 3.128E+0 1.338E+0 3.75 3.812E+0 1.082E+2 2.838E+1 8.552E+0 1.72 1.592E+0 5.087E+0 3.196E+0 1.357E+0 3.80 3.888E+0 1.159E+2 2.981E+1 8.951E+0 1.74 1.606E+0 5.244E+0 3.266E+0 1.376E+0 3.85 3.964E+0 1.241E+2 3.129E+1 9.366E+0 1.76 1.620E+0 5.406E+0 3.338E+0 1.397E+0 3.90 4.042E+0 1.328E+2 3.285E+1 9.799E+0 1.78 1.634E+0 5.573E+0 3.411E+0 1.418E+0 3.95 4.120E+0 1.420E+2 3.446E+1 1.025E+1 1.80 1.648E+0 5.746E+0 3.487E+0 1.439E+0 4.00 4.200E+0 1.518E+2 3.615E+1 1.072E+1 1.82 1.662E+0 5.924E+0 3.564E+0 1.461E+0 4.05 4.280E+0 1.623E+2 3.791E+1 1.121E+1 1.84 1.677E+0 6.109E+0 3.643E+0 1.484E+0 4.10 4.362E+0 1.733E+2 3.974E+1 1.171E+1 1.86 1.692E+0 6.300E+0 3.723E+0 1.507E+0 4.15 4.444E+0 1.851E+2 4.164E+1 1.224E+1 1.88 1.707E+0 6.497E+0 3.806E+0 1.531E+0 4.20 4.528E+0 1.975E+2 4.363E+1 1.279E+1 1.90 1.722E+0 6.701E+0 3.891E+0 1.555E+0 4.25 4.612E+0 2.108E+2 4.569E+1 1.336E+1 1.92 1.737E+0 6.911E+0 3.978E+0 1.580E+0 4.30 4.698E+0 2.247E+2 4.784E+1 1.395E+1 1.94 1.753E+0 7.128E+0 4.067E+0 1.606E+0 4.35 4.784E+0 2.396E+2 5.007E+1 1.457E+1 1.96 1.768E+0 7.353E+0 4.158E+0 1.633E+0 4.40 4.872E+0 2.553E+2 5.239E+1 1.521E+1 1.98 1.784E+0 7.585E+0 4.251E+0 1.660E+0 4.45 4.960E+0 2.719E+2 5.480E+1 1.587E+1 2.00 1.800E+0 7.824E+0 4.347E+0 1.688E+0 4.50 5.050E+0 2.894E+2 5.731E+1 1.656E+1 2.05 1.841E+0 8.458E+0 4.596E+0 1.760E+0 4.55 5.140E+0 3.080E+2 5.991E+1 1.728E+1 2.10 1.882E+0 9.145E+0 4.859E+0 1.837E+0 4.60 5.232E+0 3.276E+2 6.261E+1 1.802E+1 2.15 1.925E+0 9.888E+0 5.138E+0 1.919E+0 4.65 5.324E+0 3.483E+2 6.542E+1 1.879E+1 2.20 1.968E+0 1.069E+1 5.433E+0 2.005E+0 4.70 5.418E+0 3.702E+2 6.833E+1 1.958E+1 2.25 2.013E+0 1.156E+1 5.746E+0 2.096E+0 4.75 5.512E+0 3.933E+2 7.135E+1 2.041E+1 2.30 2.058E+0 1.250E+1 6.076E+0 2.193E+0 4.80 5.608E+0 4.177E+2 7.448E+1 2.126E+1 2.35 2.105E+0 1.352E+1 6.425E+0 2.295E+0 4.85 5.704E+0 4.434E+2 7.772E+1 2.215E+1 2.40 2.152E+0 1.462E+1 6.794E+0 2.403E+0 4.90 5.802E+0 4.705E+2 8.109E+1 2.307E+1 2.45 2.201E+0 1.581E+1 7.183E+0 2.517E+0 4.95 5.900E+0 4.990E+2 8.457E+1 2.402E+1 2.50 2.250E+0 1.709E+1 7.594E+0 2.637E+0 5.00 6.000E+0 5.291E+2 8.818E+1 2.500E+1 2.55 2.301E+0 1.847E+1 8.027E+0 2.763E+0 5.10 6.202E+0 5.941E+2 9.579E+1 2.707E+1 2.60 2.352E+0 1.995E+1 8.484E+0 2.896E+0 5.20 6.408E+0 6.661E+2 1.039E+2 2.928E+1 2.65 2.405E+0 2.156E+1 8.965E+0 3.036E+0 5.30 6.618E+0 7.457E+2 1.127E+2 3.165E+1 2.70 2.458E+0 2.328E+1 9.472E+0 3.183E+0 5.40 6.832E+0 8.335E+2 1.220E+2 3.417E+1 2.75 2.513E+0 2.514E+1 1.001E+1 3.338E+0 5.50 7.050E+0 9.304E+2 1.320E+2 3.687E+1 2.80 2.568E+0 2.714E+1 1.057E+1 3.500E+0 5.60 7.272E+0 1.037E+3 1.426E+2 3.974E+1 2.85 2.625E+0 2.929E+1 1.116E+1 3.671E+0 5.70 7.498E+0 1.154E+3 1.539E+2 4.280E+1 2.90 2.682E+0 3.159E+1 1.178E+1 3.850E+0 5.80 7.728E+0 1.283E+3 1.660E+2 4.605E+1 2.95 2.741E+0 3.407E+1 1.243E+1 4.038E+0 5.90 7.962E+0 1.424E+3 1.789E+2 4.951E+1 3.00 2.800E+0 3.673E+1 1.312E+1 4.235E+0 6.00 8.200E+0 1.579E+3 1.925E+2 5.318E+1 3.05 2.861E+0 3.959E+1 1.384E+1 4.441E+0 6.10 8.442E+0 1.748E+3 2.071E+2 5.708E+1 3.10 2.922E+0 4.265E+1 1.459E+1 4.657E+0 6.20 8.688E+0 1.933E+3 2.225E+2 6.121E+1 3.15 2.985E+0 4.593E+1 1.539E+1 4.884E+0 6.30 8.938E+0 2.135E+3 2.388E+2 6.559E+1 3.20 3.048E+0 4.944E+1 1.622E+1 5.121E+0 6.40 9.192E+0 2.355E+3 2.562E+2 7.023E+1 3.25 3.113E+0 5.320E+1 1.709E+1 5.369E+0 6.50 9.450E+0 2.594E+3 2.745E+2 7.513E+1 3.30 3.178E+0 5.722E+1 1.800E+1 5.629E+0 6.60 9.712E+0 2.855E+3 2.939E+2 8.032E+1 3.35 3.245E+0 6.152E+1 1.896E+1 5.900E+0 6.70 9.978E+0 3.138E+3 3.145E+2 8.580E+1 3.40 3.312E+0 6.612E+1 1.996E+1 6.184E+0 6.80 1.025E+1 3.445E+3 3.362E+2 9.159E+1 3.45 3.380E+0 7.103E+1 2.101E+1 6.480E+0 6.90 1.052E+1 3.779E+3 3.591E+2 9.770E+1

Anexo A9: Tabelas e Expressões do Capítulo 10 3

TABELA A9.1 Relações Isentrópicas (cont.)

Ma /0T T /0p p /0 */A A Ma /0T T /0p p /0 */A A 7.00 1.080E+1 4.140E+3 3.833E+2 1.041E+2 20.00 8.100E+1 4.783E+6 5.905E+4 1.538E+4 7.10 1.108E+1 4.531E+3 4.088E+2 1.109E+2 21.00 8.920E+1 6.703E+6 7.515E+4 1.956E+4 7.20 1.137E+1 4.953E+3 4.357E+2 1.181E+2 22.00 9.780E+1 9.251E+6 9.459E+4 2.461E+4 7.30 1.166E+1 5.410E+3 4.640E+2 1.256E+2 23.00 1.068E+2 1.259E+7 1.179E+5 3.065E+4 7.40 1.195E+1 5.903E+3 4.939E+2 1.335E+2 24.00 1.162E+2 1.691E+7 1.456E+5 3.783E+4 7.50 1.225E+1 6.434E+3 5.252E+2 1.418E+2 25.00 1.260E+2 2.245E+7 1.782E+5 4.630E+4 7.60 1.255E+1 7.006E+3 5.582E+2 1.506E+2 26.00 1.362E+2 2.949E+7 2.165E+5 5.624E+4 7.70 1.286E+1 7.623E+3 5.928E+2 1.598E+2 27.00 1.468E+2 3.833E+7 2.611E+5 6.781E+4 7.80 1.317E+1 8.286E+3 6.292E+2 1.694E+2 28.00 1.578E+2 4.936E+7 3.128E+5 8.121E+4 7.90 1.348E+1 8.998E+3 6.674E+2 1.795E+2 29.00 1.692E+2 6.301E+7 3.724E+5 9.666E+4 8.00 1.380E+1 9.763E+3 7.075E+2 1.901E+2 30.00 1.810E+2 7.978E+7 4.408E+5 1.144E+5 8.10 1.412E+1 1.058E+4 7.494E+2 2.012E+2 31.00 1.932E+2 1.002E+8 5.188E+5 1.346E+5 8.20 1.445E+1 1.146E+4 7.934E+2 2.128E+2 32.00 2.058E+2 1.250E+8 6.076E+5 1.576E+5 8.30 1.478E+1 1.241E+4 8.395E+2 2.250E+2 33.00 2.188E+2 1.549E+8 7.081E+5 1.837E+5 8.40 1.511E+1 1.342E+4 8.878E+2 2.378E+2 34.00 2.322E+2 1.908E+8 8.216E+5 2.131E+5 8.50 1.545E+1 1.450E+4 9.383E+2 2.511E+2 35.00 2.460E+2 2.335E+8 9.492E+5 2.461E+5 8.60 1.579E+1 1.565E+4 9.910E+2 2.650E+2 36.00 2.602E+2 2.842E+8 1.092E+6 2.832E+5 8.70 1.614E+1 1.688E+4 1.046E+3 2.796E+2 37.00 2.748E+2 3.440E+8 1.252E+6 3.246E+5 8.80 1.649E+1 1.820E+4 1.104E+3 2.948E+2 38.00 2.898E+2 4.143E+8 1.430E+6 3.707E+5 8.90 1.684E+1 1.961E+4 1.164E+3 3.106E+2 39.00 3.052E+2 4.966E+8 1.627E+6 4.218E+5 9.00 1.720E+1 2.110E+4 1.227E+3 3.272E+2 40.00 3.210E+2 5.926E+8 1.846E+6 4.785E+5 9.10 1.756E+1 2.270E+4 1.293E+3 3.445E+2 41.00 3.372E+2 7.041E+8 2.088E+6 5.412E+5 9.20 1.793E+1 2.440E+4 1.361E+3 3.625E+2 42.00 3.538E+2 8.330E+8 2.354E+6 6.102E+5 9.30 1.830E+1 2.621E+4 1.432E+3 3.812E+2 43.00 3.708E+2 9.817E+8 2.648E+6 6.861E+5 9.40 1.867E+1 2.813E+4 1.507E+3 4.008E+2 44.00 3.882E+2 1.153E+9 2.969E+6 7.694E+5 9.50 1.905E+1 3.017E+4 1.584E+3 4.211E+2 45.00 4.060E+2 1.348E+9 3.321E+6 8.606E+5 9.60 1.943E+1 3.235E+4 1.665E+3 4.423E+2 46.00 4.242E+2 1.572E+9 3.706E+6 9.603E+5 9.70 1.982E+1 3.465E+4 1.748E+3 4.644E+2 47.00 4.428E+2 1.827E+9 4.126E+6 1.069E+6 9.80 2.021E+1 3.710E+4 1.836E+3 4.873E+2 48.00 4.618E+2 2.116E+9 4.583E+6 1.187E+6 9.90 2.060E+1 3.969E+4 1.927E+3 5.112E+2 49.00 4.812E+2 2.444E+9 5.079E+6 1.316E+6 50.00 5.010E+2 2.815E+9 5.618E+6 1.455E+6

10.00 2.100E+1 4.244E+4 2.021E+3 5.359E+2 11.00 2.520E+1 8.033E+4 3.188E+3 8.419E+2 12.00 2.980E+1 1.445E+5 4.848E+3 1.276E+3 13.00 3.480E+1 2.486E+5 7.144E+3 1.876E+3 14.00 4.020E+1 4.119E+5 1.025E+4 2.685E+3 15.00 4.600E+1 6.602E+5 1.435E+4 3.755E+3 16.00 5.220E+1 1.028E+6 1.969E+4 5.145E+3 17.00 5.880E+1 1.559E+6 2.651E+4 6.921E+3 18.00 6.580E+1 2.311E+6 3.512E+4 9.159E+3 19.00 7.320E+1 3.356E+6 4.584E+4 1.195E+4

4 Mecânica dos Fluidos

Tabela A9.2 � Choque Normal ( 1.4 ) TABELA A9.2 Choque Normal

Ma /2 1p p /2 1 /2 1T T /02 01p p 2Ma * */2 1A A 1.00 1.000E+0 1.000E+0 1.000E+0 1.000E+0 1.000E+0 1.000E+0 1.02 1.047E+0 1.033E+0 1.013E+0 1.000E+0 9.805E-1 1.000E+0 1.04 1.095E+0 1.067E+0 1.026E+0 9.999E-1 9.620E-1 1.000E+0 1.06 1.144E+0 1.101E+0 1.039E+0 9.998E-1 9.444E-1 1.000E+0 1.08 1.194E+0 1.135E+0 1.052E+0 9.994E-1 9.277E-1 1.001E+0 1.10 1.245E+0 1.169E+0 1.065E+0 9.989E-1 9.118E-1 1.001E+0 1.12 1.297E+0 1.203E+0 1.078E+0 9.982E-1 8.966E-1 1.002E+0 1.14 1.350E+0 1.238E+0 1.090E+0 9.973E-1 8.820E-1 1.003E+0 1.16 1.403E+0 1.272E+0 1.103E+0 9.961E-1 8.682E-1 1.004E+0 1.18 1.458E+0 1.307E+0 1.115E+0 9.946E-1 8.549E-1 1.005E+0 1.20 1.513E+0 1.342E+0 1.128E+0 9.928E-1 8.422E-1 1.007E+0 1.22 1.570E+0 1.376E+0 1.141E+0 9.907E-1 8.300E-1 1.009E+0 1.24 1.627E+0 1.411E+0 1.153E+0 9.884E-1 8.183E-1 1.012E+0 1.26 1.686E+0 1.446E+0 1.166E+0 9.857E-1 8.071E-1 1.015E+0 1.28 1.745E+0 1.481E+0 1.178E+0 9.827E-1 7.963E-1 1.018E+0 1.30 1.805E+0 1.516E+0 1.191E+0 9.794E-1 7.860E-1 1.021E+0 1.32 1.866E+0 1.551E+0 1.204E+0 9.758E-1 7.760E-1 1.025E+0 1.34 1.928E+0 1.585E+0 1.216E+0 9.718E-1 7.664E-1 1.029E+0 1.36 1.991E+0 1.620E+0 1.229E+0 9.676E-1 7.572E-1 1.034E+0 1.38 2.055E+0 1.655E+0 1.242E+0 9.630E-1 7.483E-1 1.038E+0 1.40 2.120E+0 1.690E+0 1.255E+0 9.582E-1 7.397E-1 1.044E+0 1.42 2.186E+0 1.724E+0 1.268E+0 9.531E-1 7.314E-1 1.049E+0 1.44 2.253E+0 1.759E+0 1.281E+0 9.476E-1 7.235E-1 1.055E+0 1.46 2.320E+0 1.793E+0 1.294E+0 9.420E-1 7.157E-1 1.062E+0 1.48 2.389E+0 1.828E+0 1.307E+0 9.360E-1 7.083E-1 1.068E+0 1.50 2.458E+0 1.862E+0 1.320E+0 9.298E-1 7.011E-1 1.076E+0 1.52 2.529E+0 1.896E+0 1.334E+0 9.233E-1 6.941E-1 1.083E+0 1.54 2.600E+0 1.930E+0 1.347E+0 9.166E-1 6.874E-1 1.091E+0 1.56 2.673E+0 1.964E+0 1.361E+0 9.097E-1 6.809E-1 1.099E+0 1.58 2.746E+0 1.998E+0 1.374E+0 9.026E-1 6.746E-1 1.108E+0 1.60 2.820E+0 2.032E+0 1.388E+0 8.952E-1 6.684E-1 1.117E+0 1.62 2.895E+0 2.065E+0 1.402E+0 8.877E-1 6.625E-1 1.127E+0 1.64 2.971E+0 2.099E+0 1.416E+0 8.799E-1 6.568E-1 1.136E+0 1.66 3.048E+0 2.132E+0 1.430E+0 8.720E-1 6.512E-1 1.147E+0 1.68 3.126E+0 2.165E+0 1.444E+0 8.639E-1 6.458E-1 1.157E+0 1.70 3.205E+0 2.198E+0 1.458E+0 8.557E-1 6.405E-1 1.169E+0 1.72 3.285E+0 2.230E+0 1.473E+0 8.474E-1 6.355E-1 1.180E+0 1.74 3.366E+0 2.263E+0 1.487E+0 8.389E-1 6.305E-1 1.192E+0 1.76 3.447E+0 2.295E+0 1.502E+0 8.302E-1 6.257E-1 1.204E+0 1.78 3.530E+0 2.327E+0 1.517E+0 8.215E-1 6.210E-1 1.217E+0

Anexo A9: Tabelas e Expressões do Capítulo 10 5

TABELA A9.2 Choque Normal (cont.)

Ma /2 1p p /2 1 /2 1T T /02 01p p 2Ma * */2 1A A 1.80 3.613E+0 2.359E+0 1.532E+0 8.127E-1 6.165E-1 1.230E+0 1.82 3.698E+0 2.391E+0 1.547E+0 8.038E-1 6.121E-1 1.244E+0 1.84 3.783E+0 2.422E+0 1.562E+0 7.948E-1 6.078E-1 1.258E+0 1.86 3.870E+0 2.454E+0 1.577E+0 7.857E-1 6.036E-1 1.273E+0 1.88 3.957E+0 2.485E+0 1.592E+0 7.765E-1 5.996E-1 1.288E+0 1.90 4.045E+0 2.516E+0 1.608E+0 7.674E-1 5.956E-1 1.303E+0 1.92 4.134E+0 2.546E+0 1.624E+0 7.581E-1 5.918E-1 1.319E+0 1.94 4.224E+0 2.577E+0 1.639E+0 7.488E-1 5.880E-1 1.335E+0 1.96 4.315E+0 2.607E+0 1.655E+0 7.395E-1 5.844E-1 1.352E+0 1.98 4.407E+0 2.637E+0 1.671E+0 7.302E-1 5.808E-1 1.369E+0

2.00 4.500E+0 2.667E+0 1.688E+0 7.209E-1 5.774E-1 1.387E+0 2.02 4.594E+0 2.696E+0 1.704E+0 7.115E-1 5.740E-1 1.405E+0 2.04 4.689E+0 2.725E+0 1.720E+0 7.022E-1 5.707E-1 1.424E+0 2.06 4.784E+0 2.755E+0 1.737E+0 6.928E-1 5.675E-1 1.443E+0 2.08 4.881E+0 2.783E+0 1.754E+0 6.835E-1 5.643E-1 1.463E+0 2.10 4.978E+0 2.812E+0 1.770E+0 6.742E-1 5.613E-1 1.483E+0 2.12 5.077E+0 2.840E+0 1.787E+0 6.649E-1 5.583E-1 1.504E+0 2.14 5.176E+0 2.868E+0 1.805E+0 6.557E-1 5.554E-1 1.525E+0 2.16 5.277E+0 2.896E+0 1.822E+0 6.464E-1 5.525E-1 1.547E+0 2.18 5.378E+0 2.924E+0 1.839E+0 6.373E-1 5.498E-1 1.569E+0

2.20 5.480E+0 2.951E+0 1.857E+0 6.281E-1 5.471E-1 1.592E+0 2.22 5.583E+0 2.978E+0 1.875E+0 6.191E-1 5.444E-1 1.615E+0 2.24 5.687E+0 3.005E+0 1.892E+0 6.100E-1 5.418E-1 1.639E+0 2.26 5.792E+0 3.032E+0 1.910E+0 6.011E-1 5.393E-1 1.664E+0 2.28 5.898E+0 3.058E+0 1.929E+0 5.921E-1 5.368E-1 1.689E+0 2.30 6.005E+0 3.085E+0 1.947E+0 5.833E-1 5.344E-1 1.714E+0 2.32 6.113E+0 3.110E+0 1.965E+0 5.745E-1 5.321E-1 1.741E+0 2.34 6.222E+0 3.136E+0 1.984E+0 5.658E-1 5.297E-1 1.767E+0 2.36 6.331E+0 3.162E+0 2.002E+0 5.572E-1 5.275E-1 1.795E+0 2.38 6.442E+0 3.187E+0 2.021E+0 5.486E-1 5.253E-1 1.823E+0

2.40 6.553E+0 3.212E+0 2.040E+0 5.401E-1 5.231E-1 1.851E+0 2.42 6.666E+0 3.237E+0 2.059E+0 5.317E-1 5.210E-1 1.881E+0 2.44 6.779E+0 3.261E+0 2.079E+0 5.234E-1 5.189E-1 1.910E+0 2.46 6.894E+0 3.285E+0 2.098E+0 5.152E-1 5.169E-1 1.941E+0 2.48 7.009E+0 3.310E+0 2.118E+0 5.071E-1 5.149E-1 1.972E+0 2.50 7.125E+0 3.333E+0 2.138E+0 4.990E-1 5.130E-1 2.004E+0 2.52 7.242E+0 3.357E+0 2.157E+0 4.911E-1 5.111E-1 2.036E+0 2.54 7.360E+0 3.380E+0 2.177E+0 4.832E-1 5.092E-1 2.070E+0 2.56 7.479E+0 3.403E+0 2.198E+0 4.754E-1 5.074E-1 2.103E+0 2.58 7.599E+0 3.426E+0 2.218E+0 4.677E-1 5.056E-1 2.138E+0

2.60 7.720E+0 3.449E+0 2.238E+0 4.601E-1 5.039E-1 2.173E+0 2.62 7.842E+0 3.471E+0 2.259E+0 4.526E-1 5.022E-1 2.209E+0 2.64 7.965E+0 3.494E+0 2.280E+0 4.452E-1 5.005E-1 2.246E+0 2.66 8.088E+0 3.516E+0 2.301E+0 4.379E-1 4.988E-1 2.284E+0 2.68 8.213E+0 3.537E+0 2.322E+0 4.307E-1 4.972E-1 2.322E+0 2.70 8.338E+0 3.559E+0 2.343E+0 4.236E-1 4.956E-1 2.361E+0 2.72 8.465E+0 3.580E+0 2.364E+0 4.166E-1 4.941E-1 2.401E+0 2.74 8.592E+0 3.601E+0 2.386E+0 4.097E-1 4.926E-1 2.441E+0 2.76 8.721E+0 3.622E+0 2.407E+0 4.028E-1 4.911E-1 2.482E+0 2.78 8.850E+0 3.643E+0 2.429E+0 3.961E-1 4.896E-1 2.525E+0

6 Mecânica dos Fluidos

TABELA A9.2 Choque Normal (cont.)

Ma /2 1p p /2 1 /2 1T T /02 01p p 2Ma * */2 1A A 2.80 8.980E+0 3.664E+0 2.451E+0 3.895E-1 4.882E-1 2.568E+0 2.82 9.111E+0 3.684E+0 2.473E+0 3.829E-1 4.868E-1 2.611E+0 2.84 9.243E+0 3.704E+0 2.496E+0 3.765E-1 4.854E-1 2.656E+0 2.86 9.376E+0 3.724E+0 2.518E+0 3.701E-1 4.840E-1 2.702E+0 2.88 9.510E+0 3.743E+0 2.540E+0 3.639E-1 4.827E-1 2.748E+0 2.90 9.645E+0 3.763E+0 2.563E+0 3.577E-1 4.814E-1 2.795E+0 2.92 9.781E+0 3.782E+0 2.586E+0 3.517E-1 4.801E-1 2.844E+0 2.94 9.918E+0 3.801E+0 2.609E+0 3.457E-1 4.788E-1 2.893E+0 2.96 1.006E+1 3.820E+0 2.632E+0 3.398E-1 4.776E-1 2.943E+0 2.98 1.019E+1 3.839E+0 2.656E+0 3.340E-1 4.764E-1 2.994E+0

3.00 1.033E+1 3.857E+0 2.679E+0 3.283E-1 4.752E-1 3.046E+0 3.05 1.069E+1 3.902E+0 2.738E+0 3.145E-1 4.723E-1 3.180E+0 3.10 1.105E+1 3.947E+0 2.799E+0 3.012E-1 4.695E-1 3.320E+0 3.15 1.141E+1 3.990E+0 2.860E+0 2.885E-1 4.669E-1 3.467E+0 3.20 1.178E+1 4.031E+0 2.922E+0 2.762E-1 4.643E-1 3.620E+0 3.25 1.216E+1 4.072E+0 2.985E+0 2.645E-1 4.619E-1 3.781E+0 3.30 1.254E+1 4.112E+0 3.049E+0 2.533E-1 4.596E-1 3.948E+0 3.35 1.293E+1 4.151E+0 3.114E+0 2.425E-1 4.573E-1 4.123E+0 3.40 1.332E+1 4.188E+0 3.180E+0 2.322E-1 4.552E-1 4.306E+0 3.45 1.372E+1 4.225E+0 3.247E+0 2.224E-1 4.531E-1 4.497E+0

3.50 1.413E+1 4.261E+0 3.315E+0 2.129E-1 4.512E-1 4.696E+0 3.55 1.454E+1 4.296E+0 3.384E+0 2.039E-1 4.492E-1 4.904E+0 3.60 1.495E+1 4.330E+0 3.454E+0 1.953E-1 4.474E-1 5.120E+0 3.65 1.538E+1 4.363E+0 3.525E+0 1.871E-1 4.456E-1 5.346E+0 3.70 1.581E+1 4.395E+0 3.596E+0 1.792E-1 4.439E-1 5.581E+0 3.75 1.624E+1 4.426E+0 3.669E+0 1.717E-1 4.423E-1 5.825E+0 3.80 1.668E+1 4.457E+0 3.743E+0 1.645E-1 4.407E-1 6.080E+0 3.85 1.713E+1 4.487E+0 3.817E+0 1.576E-1 4.392E-1 6.345E+0 3.90 1.758E+1 4.516E+0 3.893E+0 1.510E-1 4.377E-1 6.621E+0 3.95 1.804E+1 4.544E+0 3.969E+0 1.448E-1 4.363E-1 6.908E+0

4.00 1.850E+1 4.571E+0 4.047E+0 1.388E-1 4.350E-1 7.207E+0 4.05 1.897E+1 4.598E+0 4.125E+0 1.330E-1 4.336E-1 7.517E+0 4.10 1.945E+1 4.624E+0 4.205E+0 1.276E-1 4.324E-1 7.840E+0 4.15 1.993E+1 4.650E+0 4.285E+0 1.223E-1 4.311E-1 8.175E+0 4.20 2.041E+1 4.675E+0 4.367E+0 1.173E-1 4.299E-1 8.523E+0 4.25 2.091E+1 4.699E+0 4.449E+0 1.126E-1 4.288E-1 8.884E+0 4.30 2.141E+1 4.723E+0 4.532E+0 1.080E-1 4.277E-1 9.259E+0 4.35 2.191E+1 4.746E+0 4.616E+0 1.036E-1 4.266E-1 9.648E+0 4.40 2.242E+1 4.768E+0 4.702E+0 9.948E-2 4.255E-1 1.005E+1 4.45 2.294E+1 4.790E+0 4.788E+0 9.550E-2 4.245E-1 1.047E+1

4.50 2.346E+1 4.812E+0 4.875E+0 9.170E-2 4.236E-1 1.091E+1 4.55 2.399E+1 4.833E+0 4.963E+0 8.806E-2 4.226E-1 1.136E+1 4.60 2.452E+1 4.853E+0 5.052E+0 8.459E-2 4.217E-1 1.182E+1 4.65 2.506E+1 4.873E+0 5.142E+0 8.126E-2 4.208E-1 1.231E+1 4.70 2.561E+1 4.893E+0 5.233E+0 7.809E-2 4.199E-1 1.281E+1 4.75 2.616E+1 4.912E+0 5.325E+0 7.505E-2 4.191E-1 1.333E+1 4.80 2.671E+1 4.930E+0 5.418E+0 7.214E-2 4.183E-1 1.386E+1 4.85 2.728E+1 4.948E+0 5.512E+0 6.936E-2 4.175E-1 1.442E+1 4.90 2.784E+1 4.966E+0 5.607E+0 6.670E-2 4.167E-1 1.499E+1 4.95 2.842E+1 4.983E+0 5.703E+0 6.415E-2 4.160E-1 1.559E+1

Anexo A9: Tabelas e Expressões do Capítulo 10 7

TABELA A9.2 Choque Normal (cont.)

Ma /2 1p p /2 1 /2 1T T /02 01p p 2Ma * */2 1A A 5.00 2.900E+1 5.000E+0 5.800E+0 6.172E-2 4.152E-1 1.620E+1 5.05 2.959E+1 5.016E+0 5.898E+0 5.938E-2 4.145E-1 1.684E+1 5.10 3.018E+1 5.033E+0 5.997E+0 5.715E-2 4.138E-1 1.750E+1 5.15 3.078E+1 5.048E+0 6.096E+0 5.501E-2 4.132E-1 1.818E+1 5.20 3.138E+1 5.064E+0 6.197E+0 5.297E-2 4.125E-1 1.888E+1 5.25 3.199E+1 5.079E+0 6.299E+0 5.100E-2 4.119E-1 1.961E+1 5.30 3.260E+1 5.093E+0 6.401E+0 4.913E-2 4.113E-1 2.036E+1 5.35 3.323E+1 5.108E+0 6.505E+0 4.733E-2 4.107E-1 2.113E+1 5.40 3.385E+1 5.122E+0 6.610E+0 4.560E-2 4.101E-1 2.193E+1 5.45 3.449E+1 5.136E+0 6.715E+0 4.395E-2 4.095E-1 2.275E+1

5.50 3.512E+1 5.149E+0 6.822E+0 4.236E-2 4.090E-1 2.361E+1 5.55 3.577E+1 5.162E+0 6.929E+0 4.084E-2 4.084E-1 2.449E+1 5.60 3.642E+1 5.175E+0 7.038E+0 3.938E-2 4.079E-1 2.539E+1 5.65 3.708E+1 5.187E+0 7.147E+0 3.798E-2 4.074E-1 2.633E+1 5.70 3.774E+1 5.200E+0 7.258E+0 3.664E-2 4.069E-1 2.729E+1 5.75 3.841E+1 5.212E+0 7.369E+0 3.536E-2 4.064E-1 2.828E+1 5.80 3.908E+1 5.224E+0 7.481E+0 3.412E-2 4.059E-1 2.931E+1 5.85 3.976E+1 5.235E+0 7.595E+0 3.293E-2 4.055E-1 3.036E+1 5.90 4.044E+1 5.246E+0 7.709E+0 3.179E-2 4.050E-1 3.145E+1 5.95 4.114E+1 5.257E+0 7.824E+0 3.070E-2 4.046E-1 3.257E+1

6.00 4.183E+1 5.268E+0 7.941E+0 2.965E-2 4.042E-1 3.373E+1 6.10 4.324E+1 5.289E+0 8.176E+0 2.767E-2 4.033E-1 3.614E+1 6.20 4.468E+1 5.309E+0 8.415E+0 2.584E-2 4.025E-1 3.869E+1 6.30 4.614E+1 5.329E+0 8.658E+0 2.416E-2 4.018E-1 4.140E+1 6.40 4.762E+1 5.347E+0 8.905E+0 2.259E-2 4.011E-1 4.426E+1 6.50 4.912E+1 5.365E+0 9.156E+0 2.115E-2 4.004E-1 4.729E+1 6.60 5.065E+1 5.382E+0 9.411E+0 1.981E-2 3.997E-1 5.048E+1 6.70 5.220E+1 5.399E+0 9.670E+0 1.857E-2 3.991E-1 5.386E+1 6.80 5.378E+1 5.415E+0 9.933E+0 1.741E-2 3.985E-1 5.742E+1 6.90 5.538E+1 5.430E+0 1.020E+1 1.634E-2 3.979E-1 6.118E+1

7.00 5.700E+1 5.444E+0 1.047E+1 1.535E-2 3.974E-1 6.514E+1 7.10 5.864E+1 5.459E+0 1.074E+1 1.443E-2 3.968E-1 6.931E+1 7.20 6.031E+1 5.472E+0 1.102E+1 1.357E-2 3.963E-1 7.370E+1 7.30 6.200E+1 5.485E+0 1.130E+1 1.277E-2 3.958E-1 7.832E+1 7.40 6.372E+1 5.498E+0 1.159E+1 1.202E-2 3.954E-1 8.317E+1 7.50 6.546E+1 5.510E+0 1.188E+1 1.133E-2 3.949E-1 8.827E+1 7.60 6.722E+1 5.522E+0 1.217E+1 1.068E-2 3.945E-1 9.363E+1 7.70 6.900E+1 5.533E+0 1.247E+1 1.008E-2 3.941E-1 9.925E+1 7.80 7.081E+1 5.544E+0 1.277E+1 9.510E-3 3.937E-1 1.052E+2 7.90 7.264E+1 5.555E+0 1.308E+1 8.982E-3 3.933E-1 1.113E+2

8.00 7.450E+1 5.565E+0 1.339E+1 8.488E-3 3.929E-1 1.178E+2 8.10 7.638E+1 5.575E+0 1.370E+1 8.025E-3 3.925E-1 1.246E+2 8.20 7.828E+1 5.585E+0 1.402E+1 7.592E-3 3.922E-1 1.317E+2 8.30 8.020E+1 5.594E+0 1.434E+1 7.187E-3 3.918E-1 1.391E+2 8.40 8.215E+1 5.603E+0 1.466E+1 6.806E-3 3.915E-1 1.469E+2 8.50 8.412E+1 5.612E+0 1.499E+1 6.449E-3 3.912E-1 1.551E+2 8.60 8.612E+1 5.620E+0 1.532E+1 6.114E-3 3.909E-1 1.636E+2 8.70 8.814E+1 5.628E+0 1.566E+1 5.799E-3 3.906E-1 1.724E+2 8.80 9.018E+1 5.636E+0 1.600E+1 5.504E-3 3.903E-1 1.817E+2 8.90 9.224E+1 5.644E+0 1.634E+1 5.226E-3 3.901E-1 1.914E+2

8 Mecânica dos Fluidos

TABELA A9.2 Choque Normal (cont.)

Ma /2 1p p /2 1 /2 1T T /02 01p p 2Ma * */2 1A A 9.00 9.433E+1 5.651E+0 1.669E+1 4.964E-3 3.898E-1 2.015E+2 9.10 9.644E+1 5.658E+0 1.704E+1 4.718E-3 3.895E-1 2.120E+2 9.20 9.858E+1 5.665E+0 1.740E+1 4.486E-3 3.893E-1 2.229E+2 9.30 1.007E+2 5.672E+0 1.776E+1 4.267E-3 3.891E-1 2.344E+2 9.40 1.029E+2 5.679E+0 1.812E+1 4.061E-3 3.888E-1 2.463E+2 9.50 1.051E+2 5.685E+0 1.849E+1 3.866E-3 3.886E-1 2.586E+2 9.60 1.074E+2 5.691E+0 1.886E+1 3.683E-3 3.884E-1 2.715E+2 9.70 1.096E+2 5.697E+0 1.924E+1 3.510E-3 3.882E-1 2.849E+2 9.80 1.119E+2 5.703E+0 1.962E+1 3.346E-3 3.880E-1 2.989E+2 9.90 1.142E+2 5.709E+0 2.000E+1 3.191E-3 3.878E-1 3.134E+2 10.00 1.165E+2 5.714E+0 2.039E+1 3.045E-3 3.876E-1 3.284E+2 10.10 1.188E+2 5.720E+0 2.078E+1 2.906E-3 3.874E-1 3.441E+2 10.20 1.212E+2 5.725E+0 2.117E+1 2.775E-3 3.872E-1 3.603E+2 10.30 1.236E+2 5.730E+0 2.157E+1 2.651E-3 3.870E-1 3.772E+2 10.40 1.260E+2 5.735E+0 2.197E+1 2.534E-3 3.869E-1 3.947E+2 10.50 1.285E+2 5.740E+0 2.238E+1 2.422E-3 3.867E-1 4.129E+2 10.60 1.309E+2 5.744E+0 2.279E+1 2.317E-3 3.865E-1 4.317E+2 10.70 1.334E+2 5.749E+0 2.321E+1 2.216E-3 3.864E-1 4.512E+2 10.80 1.359E+2 5.753E+0 2.362E+1 2.121E-3 3.862E-1 4.714E+2 10.90 1.384E+2 5.758E+0 2.405E+1 2.031E-3 3.861E-1 4.924E+2 11.00 1.410E+2 5.762E+0 2.447E+1 1.945E-3 3.859E-1 5.141E+2 12.00 1.678E+2 5.799E+0 2.894E+1 1.287E-3 3.847E-1 7.772E+2 13.00 1.970E+2 5.828E+0 3.380E+1 8.771E-4 3.837E-1 1.140E+3 14.00 2.285E+2 5.851E+0 3.905E+1 6.138E-4 3.829E-1 1.629E+3 15.00 2.623E+2 5.870E+0 4.469E+1 4.395E-4 3.823E-1 2.275E+3 16.00 2.985E+2 5.885E+0 5.072E+1 3.212E-4 3.817E-1 3.113E+3 17.00 3.370E+2 5.898E+0 5.714E+1 2.390E-4 3.813E-1 4.184E+3 18.00 3.778E+2 5.909E+0 6.394E+1 1.807E-4 3.810E-1 5.533E+3 19.00 4.210E+2 5.918E+0 7.114E+1 1.386E-4 3.806E-1 7.212E+3 20.00 4.665E+2 5.926E+0 7.872E+1 1.078E-4 3.804E-1 9.279E+3 21.00 5.143E+2 5.933E+0 8.669E+1 8.478E-5 3.802E-1 1.180E+4 22.00 5.645E+2 5.939E+0 9.506E+1 6.741E-5 3.800E-1 1.483E+4 23.00 6.170E+2 5.944E+0 1.038E+2 5.414E-5 3.798E-1 1.847E+4 24.00 6.718E+2 5.948E+0 1.129E+2 4.388E-5 3.796E-1 2.279E+4 25.00 7.290E+2 5.952E+0 1.225E+2 3.586E-5 3.795E-1 2.789E+4 26.00 7.885E+2 5.956E+0 1.324E+2 2.953E-5 3.794E-1 3.386E+4 27.00 8.503E+2 5.959E+0 1.427E+2 2.450E-5 3.793E-1 4.082E+4 28.00 9.145E+2 5.962E+0 1.534E+2 2.046E-5 3.792E-1 4.888E+4 29.00 9.810E+2 5.965E+0 1.645E+2 1.719E-5 3.791E-1 5.816E+4 30.00 1.050E+3 5.967E+0 1.759E+2 1.453E-5 3.790E-1 6.882E+4 31.00 1.121E+3 5.969E+0 1.878E+2 1.235E-5 3.790E-1 8.098E+4 32.00 1.195E+3 5.971E+0 2.001E+2 1.055E-5 3.789E-1 9.481E+4 33.00 1.270E+3 5.973E+0 2.127E+2 9.053E-6 3.789E-1 1.105E+5 34.00 1.349E+3 5.974E+0 2.257E+2 7.804E-6 3.788E-1 1.281E+5 35.00 1.429E+3 5.976E+0 2.391E+2 6.757E-6 3.788E-1 1.480E+5 36.00 1.512E+3 5.977E+0 2.529E+2 5.874E-6 3.787E-1 1.702E+5 37.00 1.597E+3 5.978E+0 2.671E+2 5.125E-6 3.787E-1 1.951E+5 38.00 1.685E+3 5.979E+0 2.817E+2 4.488E-6 3.786E-1 2.228E+5 39.00 1.774E+3 5.980E+0 2.967E+2 3.944E-6 3.786E-1 2.535E+5

Anexo A9: Tabelas e Expressões do Capítulo 10 9

TABELA A9.2 Choque Normal (cont.)

Ma /2 1p p /2 1 /2 1T T /02 01p p 2Ma * */2 1A A 40.00 1.867E+3 5.981E+0 3.121E+2 3.477E-6 3.786E-1 2.876E+5 41.00 1.961E+3 5.982E+0 3.278E+2 3.075E-6 3.785E-1 3.252E+5 42.00 2.058E+3 5.983E+0 3.439E+2 2.727E-6 3.785E-1 3.667E+5 43.00 2.157E+3 5.984E+0 3.605E+2 2.425E-6 3.785E-1 4.123E+5 44.00 2.259E+3 5.985E+0 3.774E+2 2.163E-6 3.785E-1 4.623E+5 45.00 2.362E+3 5.985E+0 3.947E+2 1.934E-6 3.784E-1 5.171E+5 46.00 2.469E+3 5.986E+0 4.124E+2 1.733E-6 3.784E-1 5.770E+5 47.00 2.577E+3 5.986E+0 4.305E+2 1.557E-6 3.784E-1 6.422E+5 48.00 2.688E+3 5.987E+0 4.489E+2 1.402E-6 3.784E-1 7.133E+5 49.00 2.801E+3 5.988E+0 4.678E+2 1.265E-6 3.784E-1 7.905E+5 50.00 2.917E+3 5.988E+0 4.871E+2 1.144E-6 3.784E-1 8.743E+5

10 Mecânica dos Fluidos

Tabela A9.3 � Ângulo de Prandtl-Meyer ( 1.4 ) TABELA A9.3 Ângulo de Prandtl-Meyer

Ma Ma Ma 1.00 0.000E+0 9.000E+1 1.80 2.073E+1 3.375E+1 2.60 4.141E+1 2.262E+1 1.02 1.257E-1 7.864E+1 1.82 2.130E+1 3.333E+1 2.62 4.186E+1 2.244E+1 1.04 3.510E-1 7.406E+1 1.84 2.188E+1 3.292E+1 2.64 4.231E+1 2.226E+1 1.06 6.367E-1 7.063E+1 1.86 2.245E+1 3.252E+1 2.66 4.275E+1 2.208E+1 1.08 9.680E-1 6.781E+1 1.88 2.302E+1 3.213E+1 2.68 4.319E+1 2.191E+1 1.10 1.336E+0 6.538E+1 1.90 2.359E+1 3.176E+1 2.70 4.362E+1 2.174E+1 1.12 1.735E+0 6.323E+1 1.92 2.415E+1 3.139E+1 2.72 4.405E+1 2.157E+1 1.14 2.160E+0 6.131E+1 1.94 2.471E+1 3.103E+1 2.74 4.448E+1 2.141E+1 1.16 2.607E+0 5.955E+1 1.96 2.527E+1 3.068E+1 2.76 4.491E+1 2.124E+1 1.18 3.074E+0 5.794E+1 1.98 2.583E+1 3.033E+1 2.78 4.533E+1 2.108E+1 1.20 3.558E+0 5.644E+1 2.00 2.638E+1 3.000E+1 2.80 4.575E+1 2.092E+1 1.22 4.057E+0 5.505E+1 2.02 2.693E+1 2.967E+1 2.82 4.616E+1 2.077E+1 1.24 4.569E+0 5.375E+1 2.04 2.748E+1 2.935E+1 2.84 4.657E+1 2.062E+1 1.26 5.093E+0 5.253E+1 2.06 2.802E+1 2.904E+1 2.86 4.698E+1 2.047E+1 1.28 5.627E+0 5.138E+1 2.08 2.856E+1 2.874E+1 2.88 4.739E+1 2.032E+1 1.30 6.170E+0 5.028E+1 2.10 2.910E+1 2.844E+1 2.90 4.779E+1 2.017E+1 1.32 6.721E+0 4.925E+1 2.12 2.963E+1 2.814E+1 2.92 4.819E+1 2.003E+1 1.34 7.279E+0 4.827E+1 2.14 3.016E+1 2.786E+1 2.94 4.859E+1 1.989E+1 1.36 7.844E+0 4.733E+1 2.16 3.069E+1 2.758E+1 2.96 4.898E+1 1.975E+1 1.38 8.413E+0 4.644E+1 2.18 3.121E+1 2.730E+1 2.98 4.937E+1 1.961E+1 1.40 8.987E+0 4.558E+1 2.20 3.173E+1 2.704E+1 3.00 4.976E+1 1.947E+1 1.42 9.565E+0 4.477E+1 2.22 3.225E+1 2.677E+1 3.05 5.071E+1 1.914E+1 1.44 1.015E+1 4.398E+1 2.24 3.276E+1 2.651E+1 3.10 5.165E+1 1.882E+1 1.46 1.073E+1 4.323E+1 2.26 3.327E+1 2.626E+1 3.15 5.257E+1 1.851E+1 1.48 1.132E+1 4.251E+1 2.28 3.378E+1 2.601E+1 3.20 5.347E+1 1.821E+1 1.50 1.191E+1 4.181E+1 2.30 3.428E+1 2.577E+1 3.25 5.435E+1 1.792E+1 1.52 1.249E+1 4.114E+1 2.32 3.478E+1 2.553E+1 3.30 5.522E+1 1.764E+1 1.54 1.309E+1 4.049E+1 2.34 3.528E+1 2.530E+1 3.35 5.607E+1 1.737E+1 1.56 1.368E+1 3.987E+1 2.36 3.577E+1 2.507E+1 3.40 5.691E+1 1.710E+1 1.58 1.427E+1 3.927E+1 2.38 3.626E+1 2.485E+1 3.45 5.773E+1 1.685E+1 1.60 1.486E+1 3.868E+1 2.40 3.675E+1 2.462E+1 3.50 5.853E+1 1.660E+1 1.62 1.545E+1 3.812E+1 2.42 3.723E+1 2.441E+1 3.55 5.932E+1 1.636E+1 1.64 1.604E+1 3.757E+1 2.44 3.771E+1 2.419E+1 3.60 6.009E+1 1.613E+1 1.66 1.663E+1 3.704E+1 2.46 3.818E+1 2.399E+1 3.65 6.085E+1 1.590E+1 1.68 1.722E+1 3.653E+1 2.48 3.866E+1 2.378E+1 3.70 6.160E+1 1.568E+1 1.70 1.781E+1 3.603E+1 2.50 3.912E+1 2.358E+1 3.75 6.233E+1 1.547E+1 1.72 1.840E+1 3.555E+1 2.52 3.959E+1 2.338E+1 3.80 6.304E+1 1.526E+1 1.74 1.898E+1 3.508E+1 2.54 4.005E+1 2.318E+1 3.85 6.375E+1 1.505E+1 1.76 1.956E+1 3.462E+1 2.56 4.051E+1 2.299E+1 3.90 6.444E+1 1.486E+1 1.78 2.015E+1 3.418E+1 2.58 4.096E+1 2.281E+1 3.95 6.512E+1 1.466E+1

Anexo A9: Tabelas e Expressões do Capítulo 10 11

TABELA A9.3 Ângulo de Prandtl-Meyer (cont.)

Ma Ma Ma 4.00 6.578E+1 1.448E+1 6.00 8.496E+1 9.594E+0 10.00 1.023E+2 5.739E+0 4.05 6.644E+1 1.429E+1 6.10 8.563E+1 9.435E+0 10.10 1.026E+2 5.682E+0 4.10 6.708E+1 1.412E+1 6.20 8.629E+1 9.282E+0 10.20 1.028E+2 5.626E+0 4.15 6.771E+1 1.394E+1 6.30 8.694E+1 9.133E+0 10.30 1.031E+2 5.571E+0 4.20 6.833E+1 1.377E+1 6.40 8.756E+1 8.989E+0 10.40 1.034E+2 5.518E+0 4.25 6.894E+1 1.361E+1 6.50 8.817E+1 8.850E+0 10.50 1.036E+2 5.465E+0 4.30 6.954E+1 1.345E+1 6.60 8.876E+1 8.715E+0 10.60 1.039E+2 5.413E+0 4.35 7.013E+1 1.329E+1 6.70 8.933E+1 8.584E+0 10.70 1.041E+2 5.363E+0 4.40 7.071E+1 1.314E+1 6.80 8.990E+1 8.457E+0 10.80 1.043E+2 5.313E+0 4.45 7.127E+1 1.299E+1 6.90 9.044E+1 8.333E+0 10.90 1.046E+2 5.264E+0 4.50 7.183E+1 1.284E+1 7.00 9.097E+1 8.213E+0 11.00 1.048E+2 5.216E+0 4.55 7.238E+1 1.270E+1 7.10 9.149E+1 8.097E+0 12.00 1.069E+2 4.780E+0 4.60 7.292E+1 1.256E+1 7.20 9.200E+1 7.984E+0 13.00 1.087E+2 4.412E+0 4.65 7.345E+1 1.242E+1 7.30 9.249E+1 7.874E+0 14.00 1.102E+2 4.096E+0 4.70 7.397E+1 1.228E+1 7.40 9.297E+1 7.766E+0 15.00 1.115E+2 3.823E+0 4.75 7.448E+1 1.215E+1 7.50 9.344E+1 7.662E+0 16.00 1.127E+2 3.583E+0 4.80 7.499E+1 1.202E+1 7.60 9.390E+1 7.561E+0 17.00 1.137E+2 3.372E+0 4.85 7.548E+1 1.190E+1 7.70 9.434E+1 7.462E+0 18.00 1.146E+2 3.185E+0 4.90 7.597E+1 1.178E+1 7.80 9.478E+1 7.366E+0 19.00 1.155E+2 3.017E+0 4.95 7.645E+1 1.166E+1 7.90 9.521E+1 7.272E+0 5.00 7.692E+1 1.154E+1 8.00 9.562E+1 7.181E+0 20.00 1.162E+2 2.866E+0 5.05 7.738E+1 1.142E+1 8.10 9.603E+1 7.092E+0 21.00 1.169E+2 2.729E+0 5.10 7.784E+1 1.131E+1 8.20 9.643E+1 7.005E+0 22.00 1.175E+2 2.605E+0 5.15 7.829E+1 1.120E+1 8.30 9.682E+1 6.920E+0 23.00 1.180E+2 2.492E+0 5.20 7.873E+1 1.109E+1 8.40 9.720E+1 6.837E+0 24.00 1.186E+2 2.388E+0 5.25 7.917E+1 1.098E+1 8.50 9.757E+1 6.756E+0 25.00 1.190E+2 2.292E+0 5.30 7.960E+1 1.088E+1 8.60 9.794E+1 6.677E+0 26.00 1.195E+2 2.204E+0 5.35 8.002E+1 1.077E+1 8.70 9.829E+1 6.600E+0 27.00 1.199E+2 2.123E+0 5.40 8.043E+1 1.067E+1 8.80 9.864E+1 6.525E+0 28.00 1.202E+2 2.047E+0 5.45 8.084E+1 1.057E+1 8.90 9.898E+1 6.451E+0 29.00 1.206E+2 1.976E+0 5.50 8.124E+1 1.048E+1 9.00 9.932E+1 6.379E+0 30.00 1.209E+2 1.910E+0 5.55 8.164E+1 1.038E+1 9.10 9.965E+1 6.309E+0 31.00 1.212E+2 1.849E+0 5.60 8.203E+1 1.029E+1 9.20 9.997E+1 6.240E+0 32.00 1.215E+2 1.791E+0 5.65 8.242E+1 1.019E+1 9.30 1.003E+2 6.173E+0 33.00 1.218E+2 1.737E+0 5.70 8.280E+1 1.010E+1 9.40 1.006E+2 6.107E+0 34.00 1.220E+2 1.685E+0 5.75 8.317E+1 1.002E+1 9.50 1.009E+2 6.042E+0 35.00 1.223E+2 1.637E+0 5.80 8.354E+1 9.928E+0 9.60 1.012E+2 5.979E+0 36.00 1.225E+2 1.592E+0 5.85 8.390E+1 9.842E+0 9.70 1.015E+2 5.917E+0 37.00 1.227E+2 1.549E+0 5.90 8.426E+1 9.758E+0 9.80 1.018E+2 5.857E+0 38.00 1.229E+2 1.508E+0 5.95 8.461E+1 9.675E+0 9.90 1.020E+2 5.797E+0 39.00 1.231E+2 1.469E+0

12 Mecânica dos Fluidos

Tabela A9.4 � Escoamento com Atrito ( 1.4 ) TABELA A9.4 Escoamento com Atrito

Ma */T T */p p */ */A A * /f L d 0.02 1.200E+0 5.477E+1 4.565E+1 2.894E+1 1.778E+3 0.04 1.200E+0 2.738E+1 2.283E+1 1.448E+1 4.404E+2 0.06 1.199E+0 1.825E+1 1.522E+1 9.666E+0 1.930E+2 0.08 1.198E+0 1.368E+1 1.142E+1 7.262E+0 1.067E+2 0.10 1.198E+0 1.094E+1 9.138E+0 5.822E+0 6.692E+1 0.12 1.197E+0 9.116E+0 7.618E+0 4.864E+0 4.541E+1 0.14 1.195E+0 7.809E+0 6.533E+0 4.182E+0 3.251E+1 0.16 1.194E+0 6.829E+0 5.720E+0 3.673E+0 2.420E+1 0.18 1.192E+0 6.066E+0 5.088E+0 3.278E+0 1.854E+1 0.20 1.190E+0 5.455E+0 4.583E+0 2.964E+0 1.453E+1 0.22 1.188E+0 4.955E+0 4.169E+0 2.708E+0 1.160E+1 0.24 1.186E+0 4.538E+0 3.825E+0 2.496E+0 9.386E+0 0.26 1.184E+0 4.185E+0 3.535E+0 2.317E+0 7.688E+0 0.28 1.181E+0 3.882E+0 3.286E+0 2.166E+0 6.357E+0 0.30 1.179E+0 3.619E+0 3.070E+0 2.035E+0 5.299E+0 0.32 1.176E+0 3.389E+0 2.882E+0 1.922E+0 4.447E+0 0.34 1.173E+0 3.185E+0 2.716E+0 1.823E+0 3.752E+0 0.36 1.170E+0 3.004E+0 2.568E+0 1.736E+0 3.180E+0 0.38 1.166E+0 2.842E+0 2.437E+0 1.659E+0 2.705E+0 0.40 1.163E+0 2.696E+0 2.318E+0 1.590E+0 2.308E+0 0.42 1.159E+0 2.563E+0 2.212E+0 1.529E+0 1.974E+0 0.44 1.155E+0 2.443E+0 2.114E+0 1.474E+0 1.692E+0 0.46 1.151E+0 2.333E+0 2.026E+0 1.425E+0 1.451E+0 0.48 1.147E+0 2.231E+0 1.945E+0 1.380E+0 1.245E+0 0.50 1.143E+0 2.138E+0 1.871E+0 1.340E+0 1.069E+0 0.52 1.138E+0 2.052E+0 1.802E+0 1.303E+0 9.174E-1 0.54 1.134E+0 1.972E+0 1.739E+0 1.270E+0 7.866E-1 0.56 1.129E+0 1.898E+0 1.680E+0 1.240E+0 6.736E-1 0.58 1.124E+0 1.828E+0 1.626E+0 1.213E+0 5.757E-1 0.60 1.119E+0 1.763E+0 1.575E+0 1.188E+0 4.908E-1 0.62 1.114E+0 1.703E+0 1.528E+0 1.166E+0 4.172E-1 0.64 1.109E+0 1.646E+0 1.484E+0 1.145E+0 3.533E-1 0.66 1.104E+0 1.592E+0 1.442E+0 1.127E+0 2.979E-1 0.68 1.098E+0 1.541E+0 1.403E+0 1.110E+0 2.498E-1 0.70 1.093E+0 1.493E+0 1.367E+0 1.094E+0 2.081E-1 0.72 1.087E+0 1.448E+0 1.332E+0 1.081E+0 1.721E-1 0.74 1.082E+0 1.405E+0 1.299E+0 1.068E+0 1.411E-1 0.76 1.076E+0 1.365E+0 1.269E+0 1.057E+0 1.145E-1 0.78 1.070E+0 1.326E+0 1.240E+0 1.047E+0 9.167E-2 0.80 1.064E+0 1.289E+0 1.212E+0 1.038E+0 7.229E-2 0.82 1.058E+0 1.254E+0 1.186E+0 1.030E+0 5.593E-2 0.84 1.052E+0 1.221E+0 1.161E+0 1.024E+0 4.226E-2 0.86 1.045E+0 1.189E+0 1.137E+0 1.018E+0 3.097E-2 0.88 1.039E+0 1.158E+0 1.115E+0 1.013E+0 2.179E-2 0.90 1.033E+0 1.129E+0 1.093E+0 1.009E+0 1.451E-2 0.92 1.026E+0 1.101E+0 1.073E+0 1.006E+0 8.913E-3 0.94 1.020E+0 1.074E+0 1.053E+0 1.003E+0 4.815E-3 0.96 1.013E+0 1.049E+0 1.035E+0 1.001E+0 2.057E-3 0.98 1.007E+0 1.024E+0 1.017E+0 1.000E+0 4.947E-4

Anexo A9: Tabelas e Expressões do Capítulo 10 13

TABELA A9.4 Escoamento com Atrito (cont.)

Ma */T T */p p */ */A A * /f L d 1.00 1.000E+0 1.000E+0 1.000E+0 1.000E+0 0.000E+0 1.02 9.933E-1 9.771E-1 9.837E-1 1.000E+0 4.587E-4 1.04 9.866E-1 9.551E-1 9.681E-1 1.001E+0 1.769E-3 1.06 9.798E-1 9.338E-1 9.531E-1 1.003E+0 3.838E-3 1.08 9.730E-1 9.133E-1 9.387E-1 1.005E+0 6.585E-3 1.10 9.662E-1 8.936E-1 9.249E-1 1.008E+0 9.935E-3 1.12 9.593E-1 8.745E-1 9.116E-1 1.011E+0 1.382E-2 1.14 9.524E-1 8.561E-1 8.988E-1 1.015E+0 1.819E-2 1.16 9.455E-1 8.383E-1 8.865E-1 1.020E+0 2.298E-2 1.18 9.386E-1 8.210E-1 8.747E-1 1.025E+0 2.814E-2 1.20 9.317E-1 8.044E-1 8.633E-1 1.030E+0 3.364E-2 1.22 9.247E-1 7.882E-1 8.524E-1 1.037E+0 3.943E-2 1.24 9.178E-1 7.726E-1 8.418E-1 1.043E+0 4.547E-2 1.26 9.108E-1 7.574E-1 8.316E-1 1.050E+0 5.174E-2 1.28 9.038E-1 7.427E-1 8.218E-1 1.058E+0 5.820E-2 1.30 8.969E-1 7.285E-1 8.123E-1 1.066E+0 6.483E-2 1.32 8.899E-1 7.147E-1 8.031E-1 1.075E+0 7.161E-2 1.34 8.829E-1 7.012E-1 7.942E-1 1.084E+0 7.850E-2 1.36 8.760E-1 6.882E-1 7.856E-1 1.094E+0 8.550E-2 1.38 8.690E-1 6.755E-1 7.773E-1 1.104E+0 9.259E-2 1.40 8.621E-1 6.632E-1 7.693E-1 1.115E+0 9.974E-2 1.42 8.551E-1 6.512E-1 7.615E-1 1.126E+0 1.069E-1 1.44 8.482E-1 6.396E-1 7.540E-1 1.138E+0 1.142E-1 1.46 8.413E-1 6.282E-1 7.467E-1 1.150E+0 1.215E-1 1.48 8.344E-1 6.172E-1 7.397E-1 1.163E+0 1.288E-1 1.50 8.276E-1 6.065E-1 7.328E-1 1.176E+0 1.361E-1 1.52 8.207E-1 5.960E-1 7.262E-1 1.190E+0 1.433E-1 1.54 8.139E-1 5.858E-1 7.198E-1 1.204E+0 1.506E-1 1.56 8.071E-1 5.759E-1 7.135E-1 1.219E+0 1.579E-1 1.58 8.004E-1 5.662E-1 7.074E-1 1.234E+0 1.651E-1 1.60 7.937E-1 5.568E-1 7.016E-1 1.250E+0 1.724E-1 1.62 7.869E-1 5.476E-1 6.958E-1 1.267E+0 1.795E-1 1.64 7.803E-1 5.386E-1 6.903E-1 1.284E+0 1.867E-1 1.66 7.736E-1 5.299E-1 6.849E-1 1.301E+0 1.938E-1 1.68 7.670E-1 5.213E-1 6.796E-1 1.319E+0 2.008E-1 1.70 7.605E-1 5.130E-1 6.745E-1 1.338E+0 2.078E-1 1.72 7.539E-1 5.048E-1 6.696E-1 1.357E+0 2.147E-1 1.74 7.474E-1 4.969E-1 6.648E-1 1.376E+0 2.216E-1 1.76 7.410E-1 4.891E-1 6.601E-1 1.397E+0 2.284E-1 1.78 7.345E-1 4.815E-1 6.555E-1 1.418E+0 2.352E-1 1.80 7.282E-1 4.741E-1 6.511E-1 1.439E+0 2.419E-1 1.82 7.218E-1 4.668E-1 6.467E-1 1.461E+0 2.485E-1 1.84 7.155E-1 4.597E-1 6.425E-1 1.484E+0 2.551E-1 1.86 7.093E-1 4.528E-1 6.384E-1 1.507E+0 2.616E-1 1.88 7.030E-1 4.460E-1 6.344E-1 1.531E+0 2.680E-1 1.90 6.969E-1 4.394E-1 6.305E-1 1.555E+0 2.743E-1 1.92 6.907E-1 4.329E-1 6.267E-1 1.580E+0 2.806E-1 1.94 6.847E-1 4.265E-1 6.230E-1 1.606E+0 2.868E-1 1.96 6.786E-1 4.203E-1 6.193E-1 1.633E+0 2.929E-1 1.98 6.726E-1 4.142E-1 6.158E-1 1.660E+0 2.990E-1

14 Mecânica dos Fluidos

TABELA A9.4 Escoamento com Atrito (cont.)

Ma */T T */p p */ */A A * /f L d 2.00 6.667E-1 4.082E-1 6.124E-1 1.688E+0 3.050E-1 2.05 6.520E-1 3.939E-1 6.041E-1 1.760E+0 3.197E-1 2.10 6.376E-1 3.802E-1 5.963E-1 1.837E+0 3.339E-1 2.15 6.235E-1 3.673E-1 5.890E-1 1.919E+0 3.476E-1 2.20 6.098E-1 3.549E-1 5.821E-1 2.005E+0 3.609E-1 2.25 5.963E-1 3.432E-1 5.756E-1 2.096E+0 3.738E-1 2.30 5.831E-1 3.320E-1 5.694E-1 2.193E+0 3.862E-1 2.35 5.702E-1 3.213E-1 5.635E-1 2.295E+0 3.983E-1 2.40 5.576E-1 3.111E-1 5.580E-1 2.403E+0 4.099E-1 2.45 5.453E-1 3.014E-1 5.527E-1 2.517E+0 4.211E-1 2.50 5.333E-1 2.921E-1 5.477E-1 2.637E+0 4.320E-1 2.55 5.216E-1 2.832E-1 5.430E-1 2.763E+0 4.425E-1 2.60 5.102E-1 2.747E-1 5.385E-1 2.896E+0 4.526E-1 2.65 4.991E-1 2.666E-1 5.342E-1 3.036E+0 4.624E-1 2.70 4.882E-1 2.588E-1 5.301E-1 3.183E+0 4.718E-1 2.75 4.776E-1 2.513E-1 5.262E-1 3.338E+0 4.809E-1 2.80 4.673E-1 2.441E-1 5.225E-1 3.500E+0 4.898E-1 2.85 4.572E-1 2.373E-1 5.189E-1 3.671E+0 4.983E-1 2.90 4.474E-1 2.307E-1 5.155E-1 3.850E+0 5.065E-1 2.95 4.379E-1 2.243E-1 5.123E-1 4.038E+0 5.145E-1 3.00 4.286E-1 2.182E-1 5.092E-1 4.235E+0 5.222E-1 3.05 4.195E-1 2.124E-1 5.062E-1 4.441E+0 5.296E-1 3.10 4.107E-1 2.067E-1 5.034E-1 4.657E+0 5.368E-1 3.15 4.021E-1 2.013E-1 5.007E-1 4.884E+0 5.437E-1 3.20 3.937E-1 1.961E-1 4.980E-1 5.121E+0 5.504E-1 3.25 3.855E-1 1.911E-1 4.955E-1 5.369E+0 5.569E-1 3.30 3.776E-1 1.862E-1 4.931E-1 5.629E+0 5.632E-1 3.35 3.699E-1 1.815E-1 4.908E-1 5.900E+0 5.693E-1 3.40 3.623E-1 1.770E-1 4.886E-1 6.184E+0 5.752E-1 3.45 3.550E-1 1.727E-1 4.865E-1 6.480E+0 5.809E-1 3.50 3.478E-1 1.685E-1 4.845E-1 6.790E+0 5.864E-1 3.55 3.409E-1 1.645E-1 4.825E-1 7.113E+0 5.918E-1 3.60 3.341E-1 1.606E-1 4.806E-1 7.450E+0 5.970E-1 3.65 3.275E-1 1.568E-1 4.788E-1 7.802E+0 6.020E-1 3.70 3.210E-1 1.531E-1 4.770E-1 8.169E+0 6.068E-1 3.75 3.148E-1 1.496E-1 4.753E-1 8.552E+0 6.115E-1 3.80 3.086E-1 1.462E-1 4.737E-1 8.951E+0 6.161E-1 3.85 3.027E-1 1.429E-1 4.721E-1 9.366E+0 6.206E-1 3.90 2.969E-1 1.397E-1 4.706E-1 9.799E+0 6.248E-1 3.95 2.912E-1 1.366E-1 4.691E-1 1.025E+1 6.290E-1 4.00 2.857E-1 1.336E-1 4.677E-1 1.072E+1 6.331E-1 4.05 2.803E-1 1.307E-1 4.663E-1 1.121E+1 6.370E-1 4.10 2.751E-1 1.279E-1 4.650E-1 1.171E+1 6.408E-1 4.15 2.700E-1 1.252E-1 4.637E-1 1.224E+1 6.445E-1 4.20 2.650E-1 1.226E-1 4.625E-1 1.279E+1 6.481E-1 4.25 2.602E-1 1.200E-1 4.613E-1 1.336E+1 6.516E-1 4.30 2.554E-1 1.175E-1 4.601E-1 1.395E+1 6.550E-1 4.35 2.508E-1 1.151E-1 4.590E-1 1.457E+1 6.583E-1 4.40 2.463E-1 1.128E-1 4.579E-1 1.521E+1 6.615E-1 4.45 2.419E-1 1.105E-1 4.569E-1 1.587E+1 6.646E-1

Anexo A9: Tabelas e Expressões do Capítulo 10 15

TABELA A9.4 Escoamento com Atrito (cont.)

Ma */T T */p p */ */A A * /f L d 4.50 2.376E-1 1.083E-1 4.559E-1 1.656E+1 6.676E-1 4.55 2.334E-1 1.062E-1 4.549E-1 1.728E+1 6.706E-1 4.60 2.294E-1 1.041E-1 4.539E-1 1.802E+1 6.734E-1 4.65 2.254E-1 1.021E-1 4.530E-1 1.879E+1 6.762E-1 4.70 2.215E-1 1.001E-1 4.521E-1 1.958E+1 6.790E-1 4.75 2.177E-1 9.823E-2 4.512E-1 2.041E+1 6.816E-1 4.80 2.140E-1 9.637E-2 4.504E-1 2.126E+1 6.842E-1 4.85 2.104E-1 9.457E-2 4.495E-1 2.215E+1 6.867E-1 4.90 2.068E-1 9.281E-2 4.487E-1 2.307E+1 6.891E-1 4.95 2.034E-1 9.110E-2 4.480E-1 2.402E+1 6.915E-1 5.00 2.000E-1 8.944E-2 4.472E-1 2.500E+1 6.938E-1 5.10 1.935E-1 8.625E-2 4.458E-1 2.707E+1 6.983E-1 5.20 1.873E-1 8.322E-2 4.444E-1 2.928E+1 7.025E-1 5.30 1.813E-1 8.034E-2 4.431E-1 3.165E+1 7.065E-1 5.40 1.756E-1 7.761E-2 4.419E-1 3.417E+1 7.104E-1 5.50 1.702E-1 7.501E-2 4.407E-1 3.687E+1 7.140E-1 5.60 1.650E-1 7.254E-2 4.396E-1 3.974E+1 7.175E-1 5.70 1.600E-1 7.018E-2 4.385E-1 4.280E+1 7.208E-1 5.80 1.553E-1 6.794E-2 4.375E-1 4.605E+1 7.240E-1 5.90 1.507E-1 6.580E-2 4.366E-1 4.951E+1 7.270E-1 6.00 1.463E-1 6.376E-2 4.357E-1 5.318E+1 7.299E-1 6.10 1.421E-1 6.181E-2 4.348E-1 5.708E+1 7.326E-1 6.20 1.381E-1 5.994E-2 4.340E-1 6.121E+1 7.353E-1 6.30 1.343E-1 5.816E-2 4.332E-1 6.559E+1 7.378E-1 6.40 1.305E-1 5.646E-2 4.324E-1 7.023E+1 7.402E-1 6.50 1.270E-1 5.482E-2 4.317E-1 7.513E+1 7.425E-1 6.60 1.236E-1 5.326E-2 4.310E-1 8.032E+1 7.448E-1 6.70 1.203E-1 5.176E-2 4.304E-1 8.580E+1 7.469E-1 6.80 1.171E-1 5.032E-2 4.298E-1 9.159E+1 7.489E-1 6.90 1.140E-1 4.894E-2 4.292E-1 9.770E+1 7.509E-1 7.00 1.111E-1 4.762E-2 4.286E-1 1.041E+2 7.528E-1 7.10 1.083E-1 4.635E-2 4.280E-1 1.109E+2 7.546E-1 7.20 1.056E-1 4.512E-2 4.275E-1 1.181E+2 7.564E-1 7.30 1.029E-1 4.395E-2 4.270E-1 1.256E+2 7.580E-1 7.40 1.004E-1 4.282E-2 4.265E-1 1.335E+2 7.597E-1 7.50 9.796E-2 4.173E-2 4.260E-1 1.418E+2 7.612E-1 7.60 9.560E-2 4.068E-2 4.256E-1 1.506E+2 7.627E-1 7.70 9.333E-2 3.967E-2 4.251E-1 1.598E+2 7.642E-1 7.80 9.113E-2 3.870E-2 4.247E-1 1.694E+2 7.656E-1 7.90 8.901E-2 3.776E-2 4.243E-1 1.795E+2 7.669E-1 8.00 8.696E-2 3.686E-2 4.239E-1 1.901E+2 7.682E-1 8.10 8.497E-2 3.599E-2 4.235E-1 2.012E+2 7.694E-1 8.20 8.306E-2 3.515E-2 4.232E-1 2.128E+2 7.707E-1 8.30 8.120E-2 3.433E-2 4.228E-1 2.250E+2 7.718E-1 8.40 7.941E-2 3.355E-2 4.225E-1 2.378E+2 7.729E-1 8.50 7.767E-2 3.279E-2 4.221E-1 2.511E+2 7.740E-1 8.60 7.599E-2 3.205E-2 4.218E-1 2.650E+2 7.751E-1 8.70 7.436E-2 3.134E-2 4.215E-1 2.796E+2 7.761E-1 8.80 7.278E-2 3.066E-2 4.212E-1 2.948E+2 7.771E-1 8.90 7.125E-2 2.999E-2 4.209E-1 3.106E+2 7.781E-1

16 Mecânica dos Fluidos

TABELA A9.4 Escoamento com Atrito (cont.)

Ma */T T */p p */ */A A * /f L d 9.00 6.977E-2 2.935E-2 4.207E-1 3.272E+2 7.790E-1 9.10 6.833E-2 2.873E-2 4.204E-1 3.445E+2 7.799E-1 9.20 6.693E-2 2.812E-2 4.201E-1 3.625E+2 7.808E-1 9.30 6.558E-2 2.754E-2 4.199E-1 3.812E+2 7.816E-1 9.40 6.427E-2 2.697E-2 4.196E-1 4.008E+2 7.824E-1 9.50 6.299E-2 2.642E-2 4.194E-1 4.211E+2 7.832E-1 9.60 6.175E-2 2.589E-2 4.192E-1 4.423E+2 7.840E-1 9.70 6.055E-2 2.537E-2 4.190E-1 4.644E+2 7.847E-1 9.80 5.938E-2 2.487E-2 4.187E-1 4.873E+2 7.854E-1 9.90 5.825E-2 2.438E-2 4.185E-1 5.112E+2 7.861E-1 10.00 5.714E-2 2.390E-2 4.183E-1 5.359E+2 7.868E-1 11.00 4.762E-2 1.984E-2 4.166E-1 8.419E+2 7.927E-1 12.00 4.027E-2 1.672E-2 4.153E-1 1.276E+3 7.972E-1 13.00 3.448E-2 1.428E-2 4.142E-1 1.876E+3 8.007E-1 14.00 2.985E-2 1.234E-2 4.134E-1 2.685E+3 8.036E-1 15.00 2.609E-2 1.077E-2 4.128E-1 3.755E+3 8.058E-1 16.00 2.299E-2 9.476E-3 4.122E-1 5.145E+3 8.077E-1 17.00 2.041E-2 8.403E-3 4.118E-1 6.921E+3 8.093E-1 18.00 1.824E-2 7.502E-3 4.114E-1 9.159E+3 8.106E-1 19.00 1.639E-2 6.739E-3 4.111E-1 1.195E+4 8.117E-1 20.00 1.481E-2 6.086E-3 4.108E-1 1.538E+4 8.126E-1 21.00 1.345E-2 5.523E-3 4.106E-1 1.956E+4 8.135E-1 22.00 1.227E-2 5.035E-3 4.104E-1 2.461E+4 8.142E-1 23.00 1.124E-2 4.609E-3 4.102E-1 3.065E+4 8.148E-1 24.00 1.033E-2 4.234E-3 4.100E-1 3.783E+4 8.153E-1 25.00 9.524E-3 3.904E-3 4.099E-1 4.630E+4 8.158E-1 26.00 8.811E-3 3.610E-3 4.098E-1 5.624E+4 8.162E-1 27.00 8.174E-3 3.349E-3 4.096E-1 6.781E+4 8.166E-1 28.00 7.605E-3 3.114E-3 4.095E-1 8.121E+4 8.170E-1 29.00 7.092E-3 2.904E-3 4.095E-1 9.666E+4 8.173E-1 30.00 6.630E-3 2.714E-3 4.094E-1 1.144E+5 8.176E-1 31.00 6.211E-3 2.542E-3 4.093E-1 1.346E+5 8.178E-1 32.00 5.831E-3 2.386E-3 4.092E-1 1.576E+5 8.180E-1 33.00 5.484E-3 2.244E-3 4.092E-1 1.837E+5 8.182E-1 34.00 5.168E-3 2.114E-3 4.091E-1 2.131E+5 8.184E-1 35.00 4.878E-3 1.996E-3 4.091E-1 2.461E+5 8.186E-1 36.00 4.612E-3 1.886E-3 4.090E-1 2.832E+5 8.188E-1 37.00 4.367E-3 1.786E-3 4.090E-1 3.246E+5 8.189E-1 38.00 4.141E-3 1.693E-3 4.090E-1 3.707E+5 8.190E-1 39.00 3.932E-3 1.608E-3 4.089E-1 4.218E+5 8.192E-1 40.00 3.738E-3 1.529E-3 4.089E-1 4.785E+5 8.193E-1 41.00 3.559E-3 1.455E-3 4.089E-1 5.412E+5 8.194E-1 42.00 3.392E-3 1.387E-3 4.088E-1 6.102E+5 8.195E-1 43.00 3.236E-3 1.323E-3 4.088E-1 6.861E+5 8.196E-1 44.00 3.091E-3 1.264E-3 4.088E-1 7.694E+5 8.197E-1 45.00 2.956E-3 1.208E-3 4.088E-1 8.606E+5 8.197E-1 46.00 2.829E-3 1.156E-3 4.087E-1 9.603E+5 8.198E-1 47.00 2.710E-3 1.108E-3 4.087E-1 1.069E+6 8.199E-1 48.00 2.599E-3 1.062E-3 4.087E-1 1.187E+6 8.200E-1 49.00 2.494E-3 1.019E-3 4.087E-1 1.316E+6 8.200E-1 50.00 2.395E-3 9.788E-4 4.087E-1 1.455E+6 8.201E-1

Anexo A9: Tabelas e Expressões do Capítulo 10 17

Tabela A9.5 � Escoamento com Transferência de Calor ( 1.4 ) TABELA A9.5 Escoamento com Transferência de Calor

Ma */p p */T T */ */0 0p p */0 0T T 0.02 2.399E+0 2.301E-3 1.042E+3 1.268E+0 1.918E-3 0.04 2.395E+0 9.175E-3 2.610E+2 1.266E+0 7.648E-3 0.06 2.388E+0 2.053E-2 1.163E+2 1.265E+0 1.712E-2 0.08 2.379E+0 3.621E-2 6.569E+1 1.262E+0 3.022E-2 0.10 2.367E+0 5.602E-2 4.225E+1 1.259E+0 4.678E-2 0.12 2.353E+0 7.970E-2 2.952E+1 1.255E+0 6.661E-2 0.14 2.336E+0 1.069E-1 2.184E+1 1.251E+0 8.947E-2 0.16 2.317E+0 1.374E-1 1.686E+1 1.246E+0 1.151E-1 0.18 2.296E+0 1.708E-1 1.344E+1 1.241E+0 1.432E-1 0.20 2.273E+0 2.066E-1 1.100E+1 1.235E+0 1.736E-1 0.22 2.248E+0 2.445E-1 9.192E+0 1.228E+0 2.057E-1 0.24 2.221E+0 2.841E-1 7.817E+0 1.221E+0 2.395E-1 0.26 2.193E+0 3.250E-1 6.747E+0 1.214E+0 2.745E-1 0.28 2.163E+0 3.667E-1 5.898E+0 1.206E+0 3.104E-1 0.30 2.131E+0 4.089E-1 5.213E+0 1.199E+0 3.469E-1 0.32 2.099E+0 4.512E-1 4.652E+0 1.190E+0 3.837E-1 0.34 2.066E+0 4.933E-1 4.188E+0 1.182E+0 4.206E-1 0.36 2.031E+0 5.348E-1 3.798E+0 1.174E+0 4.572E-1 0.38 1.996E+0 5.755E-1 3.469E+0 1.165E+0 4.935E-1 0.40 1.961E+0 6.151E-1 3.188E+0 1.157E+0 5.290E-1 0.42 1.925E+0 6.535E-1 2.945E+0 1.148E+0 5.638E-1 0.44 1.888E+0 6.903E-1 2.736E+0 1.139E+0 5.975E-1 0.46 1.852E+0 7.254E-1 2.552E+0 1.131E+0 6.301E-1 0.48 1.815E+0 7.587E-1 2.392E+0 1.122E+0 6.614E-1 0.50 1.778E+0 7.901E-1 2.250E+0 1.114E+0 6.914E-1 0.52 1.741E+0 8.196E-1 2.124E+0 1.106E+0 7.199E-1 0.54 1.704E+0 8.469E-1 2.012E+0 1.098E+0 7.470E-1 0.56 1.668E+0 8.723E-1 1.912E+0 1.090E+0 7.725E-1 0.58 1.632E+0 8.955E-1 1.822E+0 1.083E+0 7.965E-1 0.60 1.596E+0 9.167E-1 1.741E+0 1.075E+0 8.189E-1 0.62 1.560E+0 9.358E-1 1.667E+0 1.068E+0 8.398E-1 0.64 1.525E+0 9.530E-1 1.601E+0 1.061E+0 8.592E-1 0.66 1.491E+0 9.682E-1 1.540E+0 1.055E+0 8.771E-1 0.68 1.457E+0 9.814E-1 1.484E+0 1.049E+0 8.935E-1 0.70 1.423E+0 9.929E-1 1.434E+0 1.043E+0 9.085E-1 0.72 1.391E+0 1.003E+0 1.387E+0 1.038E+0 9.221E-1 0.74 1.359E+0 1.011E+0 1.344E+0 1.033E+0 9.344E-1 0.76 1.327E+0 1.017E+0 1.305E+0 1.028E+0 9.455E-1 0.78 1.296E+0 1.022E+0 1.268E+0 1.023E+0 9.553E-1 0.80 1.266E+0 1.025E+0 1.234E+0 1.019E+0 9.639E-1 0.82 1.236E+0 1.028E+0 1.203E+0 1.016E+0 9.715E-1 0.84 1.207E+0 1.029E+0 1.174E+0 1.012E+0 9.781E-1 0.86 1.179E+0 1.028E+0 1.147E+0 1.010E+0 9.836E-1 0.88 1.152E+0 1.027E+0 1.121E+0 1.007E+0 9.883E-1 0.90 1.125E+0 1.025E+0 1.098E+0 1.005E+0 9.921E-1 0.92 1.098E+0 1.021E+0 1.076E+0 1.003E+0 9.951E-1 0.94 1.073E+0 1.017E+0 1.055E+0 1.002E+0 9.973E-1 0.96 1.048E+0 1.012E+0 1.035E+0 1.001E+0 9.988E-1 0.98 1.024E+0 1.006E+0 1.017E+0 1.000E+0 9.997E-1

18 Mecânica dos Fluidos

TABELA A9.5 Escoamento com Transferência de Calor (cont.)

Ma */p p */T T */ */0 0p p */0 0T T 1.00 1.000E+0 1.000E+0 1.000E+0 1.000E+0 1.000E+0 1.02 9.770E-1 9.930E-1 9.838E-1 1.000E+0 9.997E-1 1.04 9.546E-1 9.855E-1 9.686E-1 1.001E+0 9.989E-1 1.06 9.327E-1 9.776E-1 9.542E-1 1.002E+0 9.977E-1 1.08 9.115E-1 9.691E-1 9.406E-1 1.003E+0 9.960E-1 1.10 8.909E-1 9.603E-1 9.277E-1 1.005E+0 9.939E-1 1.12 8.708E-1 9.512E-1 9.155E-1 1.007E+0 9.915E-1 1.14 8.512E-1 9.417E-1 9.039E-1 1.010E+0 9.887E-1 1.16 8.322E-1 9.320E-1 8.930E-1 1.012E+0 9.856E-1 1.18 8.137E-1 9.220E-1 8.826E-1 1.016E+0 9.823E-1 1.20 7.958E-1 9.118E-1 8.727E-1 1.019E+0 9.787E-1 1.22 7.783E-1 9.015E-1 8.633E-1 1.023E+0 9.749E-1 1.24 7.613E-1 8.911E-1 8.543E-1 1.028E+0 9.709E-1 1.26 7.447E-1 8.805E-1 8.458E-1 1.033E+0 9.668E-1 1.28 7.287E-1 8.699E-1 8.376E-1 1.038E+0 9.624E-1 1.30 7.130E-1 8.592E-1 8.299E-1 1.044E+0 9.580E-1 1.32 6.978E-1 8.484E-1 8.225E-1 1.050E+0 9.534E-1 1.34 6.830E-1 8.377E-1 8.154E-1 1.056E+0 9.487E-1 1.36 6.686E-1 8.269E-1 8.086E-1 1.063E+0 9.440E-1 1.38 6.546E-1 8.161E-1 8.021E-1 1.070E+0 9.391E-1 1.40 6.410E-1 8.054E-1 7.959E-1 1.078E+0 9.343E-1 1.42 6.278E-1 7.947E-1 7.900E-1 1.086E+0 9.293E-1 1.44 6.149E-1 7.840E-1 7.843E-1 1.094E+0 9.243E-1 1.46 6.024E-1 7.735E-1 7.788E-1 1.103E+0 9.193E-1 1.48 5.902E-1 7.629E-1 7.736E-1 1.112E+0 9.143E-1 1.50 5.783E-1 7.525E-1 7.685E-1 1.122E+0 9.093E-1 1.52 5.668E-1 7.422E-1 7.637E-1 1.132E+0 9.042E-1 1.54 5.555E-1 7.319E-1 7.590E-1 1.142E+0 8.992E-1 1.56 5.446E-1 7.217E-1 7.545E-1 1.153E+0 8.942E-1 1.58 5.339E-1 7.117E-1 7.502E-1 1.164E+0 8.892E-1 1.60 5.236E-1 7.017E-1 7.461E-1 1.176E+0 8.842E-1 1.62 5.135E-1 6.919E-1 7.421E-1 1.188E+0 8.792E-1 1.64 5.036E-1 6.822E-1 7.383E-1 1.200E+0 8.743E-1 1.66 4.940E-1 6.726E-1 7.345E-1 1.213E+0 8.694E-1 1.68 4.847E-1 6.631E-1 7.310E-1 1.226E+0 8.645E-1 1.70 4.756E-1 6.538E-1 7.275E-1 1.240E+0 8.597E-1 1.72 4.668E-1 6.445E-1 7.242E-1 1.254E+0 8.549E-1 1.74 4.581E-1 6.355E-1 7.210E-1 1.269E+0 8.502E-1 1.76 4.497E-1 6.265E-1 7.178E-1 1.284E+0 8.455E-1 1.78 4.415E-1 6.176E-1 7.148E-1 1.300E+0 8.409E-1 1.80 4.335E-1 6.089E-1 7.119E-1 1.316E+0 8.363E-1 1.82 4.257E-1 6.004E-1 7.091E-1 1.332E+0 8.317E-1 1.84 4.181E-1 5.919E-1 7.064E-1 1.349E+0 8.273E-1 1.86 4.107E-1 5.836E-1 7.038E-1 1.367E+0 8.228E-1 1.88 4.035E-1 5.754E-1 7.012E-1 1.385E+0 8.185E-1 1.90 3.964E-1 5.673E-1 6.988E-1 1.403E+0 8.141E-1 1.92 3.895E-1 5.594E-1 6.964E-1 1.422E+0 8.099E-1 1.94 3.828E-1 5.516E-1 6.940E-1 1.442E+0 8.057E-1 1.96 3.763E-1 5.439E-1 6.918E-1 1.462E+0 8.015E-1 1.98 3.699E-1 5.364E-1 6.896E-1 1.482E+0 7.974E-1

Anexo A9: Tabelas e Expressões do Capítulo 10 19

TABELA A9.5 Escoamento com Transferência de Calor (cont.)

Ma */p p */T T */ */0 0p p */0 0T T 2.00 3.636E-1 5.289E-1 6.875E-1 1.503E+0 7.934E-1 2.05 3.487E-1 5.109E-1 6.825E-1 1.558E+0 7.835E-1 2.10 3.345E-1 4.936E-1 6.778E-1 1.616E+0 7.741E-1 2.15 3.212E-1 4.770E-1 6.735E-1 1.678E+0 7.649E-1 2.20 3.086E-1 4.611E-1 6.694E-1 1.743E+0 7.561E-1 2.25 2.968E-1 4.458E-1 6.656E-1 1.813E+0 7.477E-1 2.30 2.855E-1 4.312E-1 6.621E-1 1.886E+0 7.395E-1 2.35 2.749E-1 4.172E-1 6.588E-1 1.963E+0 7.317E-1 2.40 2.648E-1 4.038E-1 6.557E-1 2.045E+0 7.242E-1 2.45 2.552E-1 3.910E-1 6.527E-1 2.131E+0 7.170E-1 2.50 2.462E-1 3.787E-1 6.500E-1 2.222E+0 7.101E-1 2.55 2.375E-1 3.669E-1 6.474E-1 2.317E+0 7.034E-1 2.60 2.294E-1 3.556E-1 6.450E-1 2.418E+0 6.970E-1 2.65 2.216E-1 3.448E-1 6.427E-1 2.523E+0 6.908E-1 2.70 2.142E-1 3.344E-1 6.405E-1 2.634E+0 6.849E-1 2.75 2.071E-1 3.244E-1 6.384E-1 2.751E+0 6.793E-1 2.80 2.004E-1 3.149E-1 6.365E-1 2.873E+0 6.738E-1 2.85 1.940E-1 3.057E-1 6.346E-1 3.001E+0 6.685E-1 2.90 1.879E-1 2.969E-1 6.329E-1 3.136E+0 6.635E-1 2.95 1.820E-1 2.884E-1 6.312E-1 3.277E+0 6.586E-1 3.00 1.765E-1 2.803E-1 6.296E-1 3.424E+0 6.540E-1 3.05 1.711E-1 2.725E-1 6.281E-1 3.579E+0 6.495E-1 3.10 1.660E-1 2.650E-1 6.267E-1 3.741E+0 6.452E-1 3.15 1.612E-1 2.577E-1 6.253E-1 3.910E+0 6.410E-1 3.20 1.565E-1 2.508E-1 6.240E-1 4.087E+0 6.370E-1 3.25 1.520E-1 2.441E-1 6.228E-1 4.272E+0 6.331E-1 3.30 1.477E-1 2.377E-1 6.216E-1 4.465E+0 6.294E-1 3.35 1.436E-1 2.315E-1 6.205E-1 4.667E+0 6.258E-1 3.40 1.397E-1 2.255E-1 6.194E-1 4.878E+0 6.224E-1 3.45 1.359E-1 2.197E-1 6.183E-1 5.098E+0 6.190E-1 3.50 1.322E-1 2.142E-1 6.173E-1 5.328E+0 6.158E-1 3.55 1.287E-1 2.088E-1 6.164E-1 5.568E+0 6.127E-1 3.60 1.254E-1 2.037E-1 6.155E-1 5.817E+0 6.097E-1 3.65 1.221E-1 1.987E-1 6.146E-1 6.078E+0 6.068E-1 3.70 1.190E-1 1.939E-1 6.138E-1 6.349E+0 6.040E-1 3.75 1.160E-1 1.893E-1 6.130E-1 6.631E+0 6.013E-1 3.80 1.131E-1 1.848E-1 6.122E-1 6.926E+0 5.987E-1 3.85 1.103E-1 1.805E-1 6.114E-1 7.232E+0 5.962E-1 3.90 1.077E-1 1.763E-1 6.107E-1 7.551E+0 5.937E-1 3.95 1.051E-1 1.722E-1 6.100E-1 7.882E+0 5.914E-1 4.00 1.026E-1 1.683E-1 6.094E-1 8.227E+0 5.891E-1 4.05 1.002E-1 1.645E-1 6.087E-1 8.585E+0 5.869E-1 4.10 9.782E-2 1.609E-1 6.081E-1 8.958E+0 5.847E-1 4.15 9.557E-2 1.573E-1 6.075E-1 9.345E+0 5.827E-1 4.20 9.340E-2 1.539E-1 6.070E-1 9.747E+0 5.807E-1 4.25 9.130E-2 1.506E-1 6.064E-1 1.016E+1 5.787E-1 4.30 8.927E-2 1.473E-1 6.059E-1 1.060E+1 5.768E-1 4.35 8.730E-2 1.442E-1 6.054E-1 1.105E+1 5.750E-1 4.40 8.540E-2 1.412E-1 6.049E-1 1.152E+1 5.732E-1 4.45 8.356E-2 1.383E-1 6.044E-1 1.200E+1 5.715E-1

20 Mecânica dos Fluidos

TABELA A9.5 Escoamento com Transferência de Calor (cont.)

Ma */p p */T T */ */0 0p p */0 0T T 4.50 8.177E-2 1.354E-1 6.039E-1 1.250E+1 5.698E-1 4.55 8.004E-2 1.326E-1 6.035E-1 1.302E+1 5.682E-1 4.60 7.837E-2 1.300E-1 6.030E-1 1.356E+1 5.666E-1 4.65 7.675E-2 1.274E-1 6.026E-1 1.412E+1 5.651E-1 4.70 7.517E-2 1.248E-1 6.022E-1 1.470E+1 5.636E-1 4.75 7.365E-2 1.224E-1 6.018E-1 1.530E+1 5.622E-1 4.80 7.217E-2 1.200E-1 6.014E-1 1.592E+1 5.608E-1 4.85 7.073E-2 1.177E-1 6.010E-1 1.657E+1 5.594E-1 4.90 6.934E-2 1.154E-1 6.007E-1 1.723E+1 5.581E-1 4.95 6.798E-2 1.132E-1 6.003E-1 1.792E+1 5.568E-1 5.00 6.667E-2 1.111E-1 6.000E-1 1.863E+1 5.556E-1 5.10 6.415E-2 1.070E-1 5.994E-1 2.013E+1 5.532E-1 5.20 6.177E-2 1.032E-1 5.987E-1 2.173E+1 5.509E-1 5.30 5.951E-2 9.950E-2 5.982E-1 2.344E+1 5.487E-1 5.40 5.738E-2 9.602E-2 5.976E-1 2.527E+1 5.467E-1 5.50 5.536E-2 9.272E-2 5.971E-1 2.721E+1 5.447E-1 5.60 5.345E-2 8.958E-2 5.966E-1 2.928E+1 5.429E-1 5.70 5.163E-2 8.660E-2 5.962E-1 3.148E+1 5.411E-1 5.80 4.990E-2 8.376E-2 5.957E-1 3.382E+1 5.394E-1 5.90 4.826E-2 8.106E-2 5.953E-1 3.631E+1 5.378E-1 6.00 4.669E-2 7.849E-2 5.949E-1 3.895E+1 5.363E-1 6.10 4.520E-2 7.603E-2 5.945E-1 4.174E+1 5.349E-1 6.20 4.378E-2 7.369E-2 5.942E-1 4.471E+1 5.335E-1 6.30 4.243E-2 7.145E-2 5.938E-1 4.785E+1 5.322E-1 6.40 4.114E-2 6.931E-2 5.935E-1 5.117E+1 5.309E-1 6.50 3.990E-2 6.726E-2 5.932E-1 5.468E+1 5.297E-1 6.60 3.872E-2 6.531E-2 5.929E-1 5.840E+1 5.285E-1 6.70 3.759E-2 6.343E-2 5.926E-1 6.232E+1 5.274E-1 6.80 3.651E-2 6.164E-2 5.923E-1 6.645E+1 5.264E-1 6.90 3.547E-2 5.991E-2 5.921E-1 7.082E+1 5.254E-1 7.00 3.448E-2 5.826E-2 5.918E-1 7.541E+1 5.244E-1 7.10 3.353E-2 5.668E-2 5.916E-1 8.026E+1 5.234E-1 7.20 3.262E-2 5.516E-2 5.914E-1 8.536E+1 5.225E-1 7.30 3.174E-2 5.370E-2 5.912E-1 9.072E+1 5.217E-1 7.40 3.090E-2 5.229E-2 5.909E-1 9.636E+1 5.208E-1 7.50 3.009E-2 5.094E-2 5.907E-1 1.023E+2 5.200E-1 7.60 2.932E-2 4.964E-2 5.905E-1 1.085E+2 5.193E-1 7.70 2.857E-2 4.839E-2 5.904E-1 1.150E+2 5.185E-1 7.80 2.785E-2 4.719E-2 5.902E-1 1.219E+2 5.178E-1 7.90 2.716E-2 4.603E-2 5.900E-1 1.291E+2 5.171E-1 8.00 2.649E-2 4.491E-2 5.898E-1 1.366E+2 5.165E-1 8.10 2.585E-2 4.383E-2 5.897E-1 1.445E+2 5.158E-1 8.20 2.523E-2 4.279E-2 5.895E-1 1.528E+2 5.152E-1 8.30 2.463E-2 4.179E-2 5.894E-1 1.614E+2 5.146E-1 8.40 2.405E-2 4.082E-2 5.892E-1 1.705E+2 5.140E-1 8.50 2.349E-2 3.988E-2 5.891E-1 1.799E+2 5.135E-1 8.60 2.296E-2 3.898E-2 5.890E-1 1.898E+2 5.130E-1 8.70 2.244E-2 3.810E-2 5.888E-1 2.001E+2 5.124E-1 8.80 2.193E-2 3.726E-2 5.887E-1 2.109E+2 5.119E-1 8.90 2.145E-2 3.644E-2 5.886E-1 2.222E+2 5.114E-1

Anexo A9: Tabelas e Expressões do Capítulo 10 21

TABELA A9.5 Escoamento com Transferência de Calor (cont.)

Ma */p p */T T */ */0 0p p */0 0T T 9.00 2.098E-2 3.565E-2 5.885E-1 2.339E+2 5.110E-1 9.10 2.052E-2 3.488E-2 5.884E-1 2.461E+2 5.105E-1 9.20 2.008E-2 3.414E-2 5.883E-1 2.589E+2 5.101E-1 9.30 1.966E-2 3.342E-2 5.882E-1 2.722E+2 5.097E-1 9.40 1.925E-2 3.273E-2 5.880E-1 2.860E+2 5.092E-1 9.50 1.885E-2 3.205E-2 5.880E-1 3.004E+2 5.088E-1 9.60 1.846E-2 3.140E-2 5.879E-1 3.154E+2 5.085E-1 9.70 1.808E-2 3.076E-2 5.878E-1 3.310E+2 5.081E-1 9.80 1.772E-2 3.015E-2 5.877E-1 3.472E+2 5.077E-1 9.90 1.736E-2 2.955E-2 5.876E-1 3.641E+2 5.074E-1 10.00 1.702E-2 2.897E-2 5.875E-1 3.816E+2 5.070E-1 11.00 1.408E-2 2.400E-2 5.868E-1 5.977E+2 5.041E-1 12.00 1.185E-2 2.021E-2 5.862E-1 9.041E+2 5.018E-1 13.00 1.010E-2 1.724E-2 5.858E-1 1.327E+3 5.001E-1 14.00 8.715E-3 1.489E-2 5.855E-1 1.896E+3 4.986E-1 15.00 7.595E-3 1.298E-2 5.852E-1 2.649E+3 4.975E-1 16.00 6.678E-3 1.142E-2 5.850E-1 3.625E+3 4.966E-1 17.00 5.917E-3 1.012E-2 5.848E-1 4.873E+3 4.958E-1 18.00 5.279E-3 9.030E-3 5.846E-1 6.445E+3 4.952E-1 19.00 4.739E-3 8.109E-3 5.845E-1 8.402E+3 4.946E-1 20.00 4.278E-3 7.321E-3 5.844E-1 1.081E+4 4.942E-1 21.00 3.881E-3 6.642E-3 5.843E-1 1.374E+4 4.937E-1 22.00 3.537E-3 6.054E-3 5.842E-1 1.728E+4 4.934E-1 23.00 3.236E-3 5.540E-3 5.841E-1 2.152E+4 4.931E-1 24.00 2.973E-3 5.089E-3 5.841E-1 2.656E+4 4.928E-1 25.00 2.740E-3 4.691E-3 5.840E-1 3.250E+4 4.926E-1 26.00 2.533E-3 4.338E-3 5.839E-1 3.946E+4 4.924E-1 27.00 2.349E-3 4.023E-3 5.839E-1 4.757E+4 4.922E-1 28.00 2.185E-3 3.742E-3 5.839E-1 5.697E+4 4.920E-1 29.00 2.037E-3 3.488E-3 5.838E-1 6.779E+4 4.919E-1 30.00 1.903E-3 3.260E-3 5.838E-1 8.021E+4 4.917E-1 31.00 1.783E-3 3.053E-3 5.838E-1 9.439E+4 4.916E-1 32.00 1.673E-3 2.866E-3 5.837E-1 1.105E+5 4.915E-1 33.00 1.573E-3 2.695E-3 5.837E-1 1.288E+5 4.914E-1 34.00 1.482E-3 2.539E-3 5.837E-1 1.494E+5 4.913E-1 35.00 1.399E-3 2.396E-3 5.837E-1 1.725E+5 4.912E-1 36.00 1.322E-3 2.265E-3 5.837E-1 1.985E+5 4.911E-1 37.00 1.252E-3 2.144E-3 5.836E-1 2.274E+5 4.911E-1 38.00 1.187E-3 2.033E-3 5.836E-1 2.597E+5 4.910E-1 39.00 1.127E-3 1.930E-3 5.836E-1 2.956E+5 4.909E-1 40.00 1.071E-3 1.835E-3 5.836E-1 3.353E+5 4.909E-1 41.00 1.019E-3 1.747E-3 5.836E-1 3.791E+5 4.908E-1 42.00 9.714E-4 1.665E-3 5.836E-1 4.275E+5 4.908E-1 43.00 9.268E-4 1.588E-3 5.836E-1 4.807E+5 4.907E-1 44.00 8.852E-4 1.517E-3 5.835E-1 5.390E+5 4.907E-1 45.00 8.463E-4 1.450E-3 5.835E-1 6.029E+5 4.907E-1 46.00 8.099E-4 1.388E-3 5.835E-1 6.726E+5 4.906E-1 47.00 7.758E-4 1.330E-3 5.835E-1 7.488E+5 4.906E-1 48.00 7.438E-4 1.275E-3 5.835E-1 8.316E+5 4.906E-1 49.00 7.138E-4 1.223E-3 5.835E-1 9.217E+5 4.905E-1 50.00 6.855E-4 1.175E-3 5.835E-1 1.019E+6 4.905E-1

22 Mecânica dos Fluidos

Dedução da expressão (10.60)

Usando (10.59), tem-se:

2 12 1 2 1

2 1 2 1

2 2 1 1 2 1

2 1

2 2 12 2 1

2

1 2 11

p p 1 1 1h h p p1 1 2

p p p p p p1 11 2 1 2

2 p 1 p pp p p2 11 2

p p p1 2

1 2 12 p 1 p p2 1

2 2 1

1 2 1

2 1 2 2 22

1 1 11 1

22 1 2

11 1

2 p 1 p p2 p 1 p p

1 p p p p1 p 1 1p 1 1p 2 p p 2 2p 2 p

p1 11 p p p1 11 1 1 2 2 p2 p 2 p

12

2

1

p 2 1p 2

2 12

12

2

2 1

2 21

1 1

p1 1p

p p1 1p p

Dedução da expressão (10.61) Recordando (10.49-10.51), fazendo D 0 e notando que h pode ser expresso em

termos de p e de , por recurso a (10.59), vem:

1 1 2 2V V (1)

2 21 2 2 2 1 1p p V V (2)

2 21 1 2 2

1 1h V h V2 2

(3)

ph1

(4)

De (1) e (2): 2

2 1 2 1 11 2 1 1 2 1 1 2

1 1

p p Vp p V V V V

V (5)

Anexo A9: Tabelas e Expressões do Capítulo 10 23

De (3), (4) e (5): 22

2 2 21 2 1 2 1 11 2 2 1 1

1 2 1 1

p p p p V2 h h V V 2 V1 V

(6)

Por seu turno, a relação 2 2/p pode ser expressa por recurso a (1) e a (5):

2 22 2 1 2 2 1 2 2 2 1 1

2 22 1 2 1 1 1 1

p p p V p p p p VV V

(7)

Retomando agora (6): 2 2

2 21 1 2 2 2 1 11 12 2

1 1 1

2 2 41 2 1 1

p p p p p V2 V1 V

p p V 2 2 41 2 1 1 1 12 p p V V

2 2 21 1 1 1 2 2 2 1 1

2 2 21 2 1 2 1 2 1 1

2 p V p p p p V

1 p p 2 p p 2 p p V

21 2 1 12 p p V 1 22 p p 2

2

2 21 2 1 2

2 p

p p 2 p p 21 2 1 12 p p V

2 2 21 2 1 2 1 2 1 1p p 2 p p 2 p p V

2 21 2 1 2 1 2p p p p p p

21 2p p 2

1 1 1 22 V p p2 2

2 2 1 1 2 1 1

1 1 1 1 1

22 1 1

1 1

p p 2 V p 2 V1 1 1 1p p p p p

p 2 V1 1p 1 p

24 Mecânica dos Fluidos

Dedução da expressão (10.79) Relações trigonométricas necessárias:

2 2

2 2

tg tg tg / 1 tg tg

sen cos 1cos sen cos 2

Partindo de (10.78): 2 2

12 2

1

2 21

2 21

2 21

2 21

2 21

21

1 Ma sentg tgtg tgtg 1 Ma sen 2

1 tg tgtg tg

1 Ma sen 21 tg tgtg 1 Ma sen

1 Ma sen tg 2tgtg tg1 tg tg 1 Ma sen

1 tg tg 1 Ma sen tg 2tgtg tg

1 Ma 2sen

2 22 2 2 21 1

2 21

2 22 2 2 21 1

2 2 22 2 21 1 1

2 2 2 21

2 21

1 Ma sen tg 2tg 1 Ma sen tg tg 2tg tg1 Ma sen

1 Ma sen tg 2tg 1 Ma sen tg tg 2tg tg1 Ma sen 1 Ma sen 1 Ma sen

1 Ma sen tg tg 2tg tgtg1 Ma sen 1 Ma 2 2

1

2 21

2 21

2 22 2 2 21 1

2 21

2 22 21 1

2 21

sen

1 Ma sen tg 2tgtg

1 Ma sen

1 Ma sen 1 Ma sen tg 2tgtg

1 Ma sen

1 Ma sen tg 1 Ma sen tg 2tg1 Ma sen

Anexo A9: Tabelas e Expressões do Capítulo 10 25

2 22 21 1

2 22 2 2 21 1

2 21

1 Ma sen tg 1 Ma sen tg 2tgtg

1 Ma sen 1 Ma sen tg 2tg

Ma sen tg 12 22 2 2 2

1 1

1 2tg

1 Ma sen 1 Ma sen tg 2tg

2 21

22 2 2

1 12

2 21

22 2

1 2

2 Ma sen cotg 2cotgsen1 Ma 1 Ma sen 2tg

2cotg Ma sen 1

1 senMa 1 sen 2

tg

2 21

2 2 22

1 2

2cotg Ma sen 1

1 sen 1 sen tgMa 2

tg

Desenvolvendo o conteúdo do parêntesis recto da expressão anterior, vem: 2 2 2 2

22 2

2 2 2 2 2 2

2 2 2 2

1 sen 1 sen tg sen1 1 sentg tg

1 cos 1 sen cos cos sen sen

cos sen cos sen cos 2

Deste modo, tem-se, finalmente: 2 2

1

21

2cotg Ma sen 1tg

Ma cos 2 2 (10.79)