There are models for fluid flow and from that, you could get reaction forces associated with the no-slip boundary condition.
Assuming you want the total drag, so summing it up in the direction of interest should be possible.
Should be fairly simple to export that data somehow (reaction forces associated with Dirichlet boundary conditions). Right now, the code probably does sends something out.

(Related to this; There has been a longstanding feature-request to export the reaction forces into *.VTU files)

There are two methods for transient flows (i.e. with acceleration), CBS and SUPG/PSPG (which I don't know much about), and one for vicous flow (Stokes' flow).
Perhaps the Stokes' flow is most suitable for these kind of simulations. I just checked a small example, and I see that the reaction forces are in fact *not* printed in the *.out files.
It would be a simple matter to add to the code (the reactions forces can be computed by adding a single line of code, its just a matter of printing them to the file).
The structural problem classes does this already, and it looks like this;

    R E A C T I O N S  O U T P U T:
    _______________________________


    Node        1 iDof  2 reaction -3.0240e-02    [bc-id: 1]
    Node        2 iDof  2 reaction  3.0240e-02    [bc-id: 2]
    Node        3 iDof  2 reaction  1.3440e-02    [bc-id: 2]
    Node        4 iDof  2 reaction -1.3440e-02    [bc-id: 1]
    Node        5 iDof  1 reaction  2.7891e-13    [bc-id: 1]
    Node        5 iDof  2 reaction -1.3440e-02    [bc-id: 1]
    Node        5 iDof  3 reaction  1.3896e-13    [bc-id: 1]
    Node        6 iDof  2 reaction  1.3440e-02    [bc-id: 2]
    Node        7 iDof  2 reaction  1.3440e-02    [bc-id: 2]
    Node        8 iDof  2 reaction -1.3440e-02    [bc-id: 1]
    Node        8 iDof  3 reaction  1.3899e-13    [bc-id: 1]

and from what I gather, you would want to sum up all reaction forces associated with some bc-id. Technically, its all there, but it could be made much more convenient by doing some post-processing within OOFEM.