2.1 The graph of log CD vs log Re

Some experimental values of CD for spheres in fluid flows at various Reynolds numbers, Re, are:

In[7]:=

  relist = {.05875, .1585, .4786, 3.020, 7.015, 15.49, 57.54,
        144.5, 264.9, 512.9, 1000., 1862., 3162., 
        4764., 8375., .1556 10^5, .2648 10^5,
        .3467 10^5, .5888 10^5, .1000 10^6, .1702 10^6,
        .2317 10^6, .2648 10^6, .2710 10^6, .2851 10^6,
        .3020 10^6, .3388 10^6, .3981 10^6, .5129 10^6,
        .1778 10^7, .2291 10^7, .5012 10^7};
  cdlist = {492.0, 169.8, 58.88, 10.86, 5.623, 3.388,
        1.479, .9204, .7194, .5623, .4786, .4365, .4074,
        .3890, .3981, .4395, .4571, .4775, .4732, .4624,
        .4395, .4046, .3733, .3467, .2472, .1778, .1047,
        .09772, .1000, .1778, .1862, .1862};

Taking the logarithms of these numbers,

In[8]:=

  logrelist = Log[10, relist]
  logcdlist = Log[10, cdlist]

Out[8]=

  {-1.23099, -0.799971, -0.320027, 0.480007, 0.846028, 1.19005, 
   
    1.75997, 2.15987, 2.42308, 2.71003, 3., 3.26998, 3.49996, 
   
    3.67797, 3.92298, 4.19201, 4.42292, 4.53995, 4.76997, 5., 
   
    5.23096, 5.36493, 5.42292, 5.43297, 5.455, 5.48001, 5.52994, 
   
    5.59999, 5.71003, 6.24993, 6.36003, 6.70001}

Out[9]=

  {2.69197, 2.22994, 1.76997, 1.03583, 0.749968, 0.529943, 
   
    0.169968, -0.0360234, -0.14303, -0.250032, -0.320027, 
   
    -0.360016, -0.389979, -0.41005, -0.400008, -0.357041, 
   
    -0.339989, -0.321027, -0.324955, -0.334982, -0.357041, 
   
    -0.392974, -0.427942, -0.460046, -0.606952, -0.750068, 
   
    -0.980053, -1.01002, -1., -0.750068, -0.73002, -0.73002}

Now we plot the graph.

In[10]:=

  regrid[xmin_, xmax_] := Range[Floor[xmin],Floor[xmax], 1];
  cdgrid[xmin_, xmax_] := Range[Floor[xmin],Floor[xmax], 0.2];
  logplot = ListPlot[Table[{logrelist[[i]], logcdlist[[i]]},
            {i,32}],
            PlotJoined -> True,
            AxesLabel -> {"log Re", "log CD"},
            AxesOrigin -> {-2., -1.},
            AspectRatio -> Automatic,
            GridLines -> {regrid, Automatic}];
  

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