Appendix B
Values for Falkner-Skan
flows
This table includes values of the Thwaites variables calculated by the
author for the discussion of Falkner-Skan flows in SECTION 4.6.1.
The table is shown schematically (without values) in FIGURE 4.21.
- K. Coles
Table B.1: Calculated values of Thwaites variables for the
Falkner-Skan flows.
λ
F
(
λ
)
β
(or
n
)
δ
∗
θ
τ
w
θ
μu
∞
θ
2
ν
d
u
∞
d
x
u
∞
ν
d
θ
2
d
x
0.000000
0.000000
–
0.000000
0.000000
-0.015264
-0.055265
-0.005478
-0.000150
0.019955
-0.030000
-0.082563
-0.013505
-0.000803
0.055119
-0.050000
-0.108271
-0.025774
-0.002834
0.119007
(Continued on next page)
617
618
APPENDIX B. VALUES FOR FALKNER-SKAN FLOWS
(Thwaites variables for Falkner-Skan flows, continued)
-0.060000
-0.117924
-0.032016
-0.004423
0.156269
-0.070000
-0.125859
-0.038132
-0.006426
0.196437
-0.080000
-0.132228
-0.043996
-0.008857
0.239128
-0.090000
-0.137114
-0.049490
-0.011725
0.283998
-0.100000
-0.140546
-0.054495
-0.015034
0.330744
-0.110000
-0.142508
-0.058885
-0.018781
0.379043
-0.120000
-0.142935
-0.062524
-0.022962
0.428618
-0.130000
-0.141710
-0.065251
-0.027562
0.479162
-0.140000
-0.138639
-0.066866
-0.032566
0.530367
-0.150000
-0.133425
-0.067102
-0.037939
0.581731
-0.160000
-0.125568
-0.065609
-0.043680
0.633361
-0.170000
-0.114227
-0.061774
-0.049719
0.684365
-0.180000
-0.097692
-0.054494
-0.056008
0.734320
-0.190000
-0.071336
-0.040901
-0.062462
0.782419
-0.195000
-0.048967
-0.028424
-0.065703
0.805282
-0.198800
0.000000
0.000000
-0.068147
0.821764
–
–
–
–
–
-0.198800
0.000000
-0.000402
-0.068100
0.821764
-0.195000
0.055173
0.032077
-0.065900
0.807771
-0.190000
0.085700
0.049410
-0.063156
0.791066
-0.180000
0.128640
0.073029
-0.058022
0.760600
-0.170000
0.162109
0.090731
-0.053244
0.732944
-0.160000
0.190774
0.105350
-0.048777
0.707415
-0.150000
0.216356
0.117959
-0.044577
0.683620
-0.140000
0.239736
0.129114
-0.040608
0.661300
-0.130000
-0.120000
0.281761
0.148285
-0.033237
0.620405
-0.110000
-0.100000
0.319270
0.164440
-0.026522
0.583599
-0.090000
-0.080000
(Continued on next page)
619
(Thwaites variables for Falkner-Skan flows, continued)
-0.070000
-0.060000
-0.050000
0.400323
0.196346
-0.012022
0.505166
-0.030000
-0.015264
0.000000
0.000000
–
–
–
–
–
0.000000
0.469601
0.220526
0.000000
0.441044
0.050000
0.531129
0.239790
0.010198
0.387268
0.100000
0.587036
0.255631
0.018966
0.341344
0.200000
0.686708
0.280342
0.033336
0.266644
0.300000
0.774754
0.298855
0.044633
0.208300
0.400000
0.854421
0.313315
0.053785
0.161355
0.500000
0.927681
0.324944
0.061345
0.122690
0.600000
0.995838
0.334506
0.067700
0.090267
0.800000
1.120269
0.349356
0.077799
0.038899
1.000000
1.232588
0.360343
0.085465
0.000000
1.110000
1.290233
0.365113
0.088977
-0.017797
1.250000
1.360309
0.370629
0.092793
-0.037118
1.428571
1.444784
0.376389
0.096955
-0.058173
1.666600
1.550344
0.382615
0.101512
-0.082110
2.000000
1.687218
0.389382
0.106522
-0.106545
2.500000
1.874028
0.396759
0.112058
-0.134468
3.333000
2.149689
0.404811
0.118203
-0.165487
5.000000
2.615779
0.413702
0.125067
-0.200125
10.000000
3.675234
0.423494
0.132779
-0.238989
infiniti
1.154701
infiniti
0.141498
-0.282995
I
J
J
2
(
1 +
β
+
β
I
J
)
J
2
β
2
J
2
(1
−
β
)