Today, a wind blows by us. The University of
Houston's College of Engineering presents this
series about the machines that make our
civilization run, and the people whose ingenuity
Aerodynamics is all about
flow around airfoils or golf balls or submarines.
It's about gases and liquids parting to move around
solid bodies. But fluids have an odd property that
we didn't really see until the invention of the
airplane drove us to look more closely. It is that
fluids stick to bodies.
That means two kinds of drag affect any body. One's
the pressure that builds up as, say, your moving
car pushes air aside. The other is fluid dragging
on the surface -- the kind of resistance you feel
when you pull a knife out of a cold jar of honey.
That resistance adds to the pressure drag when you
drive down the highway.
If you could get very close to the surface of your
moving car and measure the speed of air next to it,
you'd find it moves at the same speed as the car.
But that speed falls off sharply as you move away
from the surface. Within a fraction of an inch, the
air is practically still once more. That thin
little region where the changing airspeed is
concentrated is called a boundary layer.
The boundary layer became the major focus of
aerodynamics in the early 20th century. The whole
picture of flow around any body is drastically
affected by that tiny region -- something we began
to realize just as the Wright Brothers finished
A key player in that process was the great German
mathematician Felix Klein. A gulf had grown up
between science and engineering, and Klein had a
plan for bridging it. He created a system of
technical institutes. The person he put in charge
of the new Institute for Technical Physics at
Göttingen was the young engineer Ludwig
Prandtl. And Prandtl had caught Klein's eye when he
gave a brilliant paper on the mathematics of the
At Göttingen, Prandtl gave theoretical
aerodynamics its modern form. His work helped
Fokker to shape the airplanes that gave Allied
armies such headaches over the trenches in WW-I.
Prandtl's students were still shaping fluid
mechanics when I was a student. One of them,
Theodore von Karman, worked at Cal Tech. And there
he wrote about Prandtl in his own autobiography.
Prandtl's life, he said, was marked by overtones of
naïveté. When Prandtl was thirty-four,
he decided it was time to marry, so he went to his
old professor to ask his daughter's hand in
marriage. But Prandtl didn't say which daughter.
The canny professor and his wife had a hurried
caucus and prudently decided it should be the older
one. That was fine. The marriage was a long and
Prandtl died in 1953. Three years later, that thin
little layer of fluid was at the center of my own
graduate studies. Now the problem was how to make
boundary layers thick enough on nose cones of
returning rockets to buffer the terrible heat of
re-entry. (That's why nose cones are blunt, not
pointed. It's to keep astronauts from burning up.)
The boundary layer is such a little thing, but like
the fabled horseshoe nail, everything depends upon
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
The boundary layer is treated in almost any book on
fluid flow or heat transfer. I give an entry-level
discussion of it in: J. H. Lienhard IV and J. H. Lienhard V, A Heat Transfer Textbook, 5th ed., Dover Pubs. Inc., Mineola, NY, 2019. You can easily download the entire book, free of charge, at https://ahtt.mit.edu/. See Chapter 7. The classical
treatment is given by another German fluid mechanic,
Schlichting, H., Boundary Layer Theory, (6th
ed, tr. J. Kestin), New York: McGraw-Hill Book Co.,
Lienhard, J. H., Prandtl, Ludwig., Dictionary of
Scientific Biography, Vol. XI, (C.C. Gillespie,
ed.). New York: Charles Scribner's Sons, 1975, pp.