a) What is the Reynolds number
for a golf ball driven off the tee? (search the web for estimates
of the velocity).
"A golf ball leaves
the tee with a speed of about 70 m/s"
http://math.ucr.edu/home/baez/physics/General/golf.html
"A golf ball has a diameter of 4.27 cm"
http://www.unc.edu/~rowlett/math111/SpaceshipEarth.PDF (These are not
the best sources, but I'm only interested in an approximation, so they
are good enough).
We can use the density and viscosity of air from the first problem to
estimate the Reynolds number.
density of air = 1173.6 g/m3
viscosity of air 0.00018 kg/ms
estimate of Re is therefore 8700.
b)What is the Re for a baseball pitch?
Poking around the web and vaguely
remembering, I'll use 60-90 mph as a pitch.
"Diameter of a regulation baseball: 2.90 in (7.36
cm)."
http://www.wisconsinproject.org/pubs/articles/2001/bomb%20facts.htm
estimate of Re is therefore 13,0000-19,000.
c) In terms
of the shape of the log C
d versus Re curve, explain why golf
balls are dimpled. Should baseballs be dimpled too?
Golf balls fly in the flat portion of non-laminar flow. In this
flat portion the boundary layer (the flow layer closest to the surface
of the ball) is laminar. At Re between 105 and 106
the laminar boundary layer becomes turbulent and the drag drops (the
drag is lower with the turbulent boundary layer because the turbulent
boundary layer separates at the top and bottom of the ball while the
laminar boundary layer clings to the ball surface and detatches from
the ball on the back side). Golf balls are dimpled to make this
transition to turbulent boundary layer occur at a lower Re.
Baseballs also fly in this same region of laminar boundary
layers. The issue with baseballs, however, is not how far they go
but rather the control that the pitcher has. The shape of a
baseball, including the precise construction of its seams, is now
closely monitored. The tricks that good pitchers can play with
baseballs has more to do with spinning effects than drag, and so
dimples are not really an issue.