Transcript Chaos… of a dripping faucet

CHAOS…
OF A
DRIPPING
FAUCET
Dan Allan
and
Adam Bublitz
CHAOS


Dripping faucet is nonlinear
dynamic system
Drop influences initial conditions of
faucet


Affects next drop
Therefore, increasing flow rate
causes bifurcations

Leads to chaos
OUR SET-UP



Water bucket acts
as reservoir
Flow to dropper on
stand
Through HeNe laser


Blocks beam aimed
at detector
LabView writes
data
RECONSTRUCTION, PHASE 1

Previous lab disrepair

Hoses leaked…very close to our
electronics

Bought new hoses and fixtures

Rearranged

Computers and water are now as far
apart as possible

Cleaned the equipment

Assembled a new set-up
MISSING DATA

Problem with our LabView
program


Changing clock speed of
waveform minimizes data
“drops”


Dropped seconds of data
randomly
Default Clock Rate
700 Clock Rate
Dove into the LabView code for
experiment
Cannot eliminate completely or
resolution suffers
100 Clock Rate
RECONSTRUCTION, PHASE 2

Consequence of trying to fix missed data


rewrote the LabView vi
Old Code
count each smallest increment of time (1/1000 sec)
the laser was blocked
 only write to file after certain number of samples
 not commented and hard to understand


New Code
commented
 much shorter
 writes differences of time (only important data)

Old Code
New Code
Computer
lag results in missed
drops
DATA ANALYSIS:
Sources
of Error
 Not every drop passes through the laser beam
 Also had a problem with the drop rate “jumping”
discretely (shown below)


thought to be most probably caused by our changing
pressure in our reservoir
DROPPER A (1.9 mm)
7.51 DROPS/SEC
The “Spectrum” of Drop
Frequency
# Drops
Time(sec)
Logistic Map: Comparing
Successive Drops
Time(sec)
Time(ms)
DROPPER A (1.9 mm)
15.56 DROPS/SEC
The “Spectrum” of Drop
Frequency
# Drops
Time(sec)
Logistic Map: Comparing
Successive Drops
Time(sec)
Time(ms)
DROPPER A (1.9 mm)
21.41 DROPS/SEC
The “Spectrum” of Drop
Frequency
# Drops
Time(sec)
Logistic Map: Comparing
Successive Drops
Time(sec)
Time(ms)
DROPPER B (0.45 mm)
6.21 DROPS/SEC
The “Spectrum” of Drop
Frequency
# Drops
Time(sec)
Logistic Map: Comparing
Successive Drops
Time(sec)
Time(ms)
DROPPER B (0.45 mm)
9.47 DROPS/SEC
The “Spectrum” of Drop
Frequency
# Drops
Time(sec)
Logistic Map: Comparing
Successive Drops
Time(sec)
Time(ms)
DROPPER B (0.45 mm)
11.10 DROPS/SEC
The “Spectrum” of Drop
Frequency
# Drops
Time(sec)
Logistic Map: Comparing
Successive Drops
Time(sec)
Time(ms)
Dropper A (1.9 mm)
Dropper B (0.45 mm)
SUGGESTIONS FOR FUTURE
GROUPS
Take time to understand flow of
our LabView code
 We finally stopped the leaks on
the second bucket


You can now have constant
pressure in your reservoir
Find a way to make the laser,
detector, and dropper stay
aligned
 Now that everything works well,
take many data sets: varying
water flow and dropper diameter
