Wind blowing through a chink in a wall on Christmas Day
It sounds very Dickensian: it's a cold winter's day and the wind is blowing hard outside, and you
can hear it whistling shrilly through the chinks in the wall of the Cratchit's humble cottage...
Anyway, the point I'm interested in here is: what happens when we try to stop up the chink? On any
day actually...not just Christmas.
Wind, initially at speed v, goes through an orifice (of area
A) and speeds up.
If A is decreased, the wind speeds up even more, keeping the
flow rate vA constant (assuming constant air density).
As A decreases, the air
flow becomes turbulent at some point, but vA still remains constant - since the density is not affected by the laminar to turbulent transition.
When A has
decreased enough, v equals the speed of sound and the flow is choked.
Assume that the flux J = rvA is constant.
But as A decreases, there is an area value Ac
where the speed v equals the sound speed vs.
J/r = vA = (vS)(Ac)
Further decrease in A cause flux J to decrease linearly to zero.
Note that the laminar to turbulent transition occurs in the flat region of the graph (not shown), but
is not visible because the density remains constant and the vA product also remains the same.
So far, so good. This is the standard picture of choked flow. It also accounts for the fact that you can
in fact close up a chink to prevent the wind from blowing inside.
However, one small caveat: have you - outside a lab, and inside a home - ever heard of winds blowing through a chink at the speed of sound?
I haven't.
Alternatively: the conductance of the orifice, which is proportional to its area,
decreases so
much that the flow rate starts to decrease (when A is sufficiently
small)? That is, at home, the wind just decides to bypass the cottage in which poor tiny Tim lives and leaves the poor guy alone.
A belated Merry Christmas!
