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2.25 Advanced Fluid Mechanics
Solution to Prob 1, Quiz 1, Fall 2003
Ain S.
This device is a very clever, simple design that yields information about exhalation
pressure and volume flow rate with one single measurement. Blowing into the tube for a
few seconds raises the interior pressure
p
and moves the piston outward, which raises
the pressure (because of spring extension) and also the volume flow rate also (the open
slit area increases), until the piston reaches an equilibrium displacement
x
.
Let the pressure inside the tube be
p
, and the inlet velocity be
V
1
=
Q
/
π
R
2
.
Since the
outflow area wx at the slit is very small compared with the inflow area
R
2
, the velocity
V
1
at the mouth (and thus everywhere inside the tube) is negligible compared with the
velocity
V
2
at the slit. Applying Bernoulli’s equation from the tube to a point in the jet from
the slit, just outside the slit, where the pressure is atmospheric (
p
=0), gives
V
2
=
p
ρ
(1)
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 Fall '05
 GarethMcKinley

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