Dr Faustus of Modern Physics - Department of Speech, Music and ...

Chapter 26
D’Alembert’s Paradox
How wonderful that we have met with a paradox. Now we have some
hope of making progress. (Nils Bohr)
Science cannot solve the ultimate mystery of Nature, because in the
last analysis we ourselves are part of the mystery we are trying to
solve. (Max Planck)
In Essai d’une nouvelle théorie de la résistance des fluides published in
1752, d’Alembert formulated his famous Paradox on page 34: “Je fais voir
que si on suivit une telle hypothese pour déterminer la résistance d’un Fluide,
cette résistance se trouveroit nulle, ce qui est contraire à toute experience”.
More precisely, d’Alembert showed by mathematical arguments that the
drag, or resistance to motion, of a body moving through an ideal fluid with
zero (or very small) viscosity, should be zero (or very small). d’Alembert
stated that this conclusion is against all experience for motion through e.g.
air or water, which are fluids with very small viscosity, for which the drag is
not small at all. More precisely there was no net force from the fluid acting
on the moving body, in particular no lift force on a wing contradicting the
undeniable flight of birds.
The Paradox remained unsolved, despite many efforts to come up with
an explanation for the striking difference between mathematical prediction
and physical observation, until 1904 when Ludwig Prandtl in the short note
Motion of fluids with very little viscosity read before the Third International
Congress of Mathematicians at Heidelberg in 1904, presented his by now
accepted solution to the Paradox. This saved Fluid Dynamics as a mathematical
science for the rest of the century, as expressed in Prandtls own
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