2.25 ADVANCED FLUID MECHANICS
Fall 2005
QUIZ 1
THURSDAY, October 13, 2005, 7:009:00 P.M.
OPEN QUIZ WHEN TOLD AT 7:00 PM
THERE ARE TWO PROBLEMS
OF EQUAL WEIGHT
Please answer each question in SEPARATE books
You may use FOUR (4) pages of handwritten notes as well as the handout on
Bernoulli equation plus any tables you feel are necessary
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±
²
³
Consider a channel of height 2
R
with rectangular crosssection as shown in the sketch.
A
hinged plank of a length
L < R
and at an angle
θ
is located at the center of the channel.
(You may assume that
L
is small compared to the length perpendicular to the sketch.)
The plank has a mass per unit width,
m
. A constant volume ﬂux per unit width,
Q
, of an
inviscid, incompressible ﬂuid is applied at the inlet of the channel.
a.)
Find all equilibrium values for
θ
(include BOTH stable and unstable equilibria!)
To simplify your calculation, you may assume that we have chosen the mass,
m
, and volume ﬂux,
Q
, such that for
at least one
equilibrium state,
θ
is small.
b.)
Which values of
θ
from part (a) represent stable equilibria? Which are unstable?
Justify your answers.
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 Spring '06
 Prof.CarolLivermore
 Fluid Dynamics, #, 5 cm, 2$, 0.1cm, 0.2 cm

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