Reporter: S.M. Bousaki
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IYPT 2010 Austria, I.R. Iran
The question
• A transparent vessel is filled with
a liquid (e.g. water). A jet flows
out of the vessel. A light source
is placed so that a horizontal
beam enters the liquid jet (see
picture).
• Under what conditions does the
jet operate like a light guide?
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IYPT 2010 Austria, I.R. Iran
Contents
• Basic understanding
• Hydraulic studies
–
–
–
–
Theory
Experiments
Head loss calculation
Comparison
• Optical studies
– Theoretical calculation
– Experiments
– Comparison
• Conclusion
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IYPT 2010 Austria, I.R. Iran
Basic understanding
• Light guide definition
• Refraction and total reflection
nr
sin i 
ni
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IYPT 2010 Austria, I.R. Iran
Hydraulic studies
• Finding the path using liquid projectile
motion.
2
gx
y 2
2v
That v is the velocity of the liquid particle.
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IYPT 2010 Austria, I.R. Iran
Hydraulic studies
• Finding the velocity using Bernoulli
equation & head loss formula
1 2
 v   gh  p0  cte
2
hv  h  h f
v  2 g (h  h f )
v  2 ghv
v  2 g (h  h c)
• Darcy–Weisbach equation:
v  2 gh (1  c)
v2
hf  c
2g
That c in it is the head loss coefficient.
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IYPT 2010 Austria, I.R. Iran
Hydraulic studies - Experiments
• Setup
– 3 holes
– High vessel
– Pump
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IYPT 2010 Austria, I.R. Iran
Hydraulic studies - Experiments
• Finding the liquid
path ,use picture
analyzing
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IYPT 2010 Austria, I.R. Iran
Hydraulic studies - Experiments
• The liquid paths are parabola
0
0
0
5
10
0
10
20
30
-5
-5
-10
-10
-15
-15
-20
-20
-25
9
R² = 0,9999
-25
R² = 0,9999
-30
IYPT 2010 Austria, I.R. Iran
40
Hydraulic studies - Experiments
• Finding the head loss
hv
hv

h
h  hf
v2
(1  c)
2g
2
v
(1  c  c)
2g
 1 c
• So the slope between real head and
theory head equals to “1+c”
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IYPT 2010 Austria, I.R. Iran
Hydraulic studies - Experiments
• Comparison
2
1,8
1,6
1,4
y = 0,5142x - 0,412
R² = 0,9897
1,2
1
0,8
0,6
0,4
0,2
0
0
1
2
3
4
5
– The linear relation between the real head
and the hydraulic head shows the mach
between theory and experiments.
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IYPT 2010 Austria, I.R. Iran
Optical studies
• Using the jet path to find the first
attachment angle
f ( x)  

x0  8r (hr  chr )
m
2r
 cot 
hr  hr c
tan  
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x
2(hr  chr )
hr (1  c)
2r
IYPT 2010 Austria, I.R. Iran
Optical studies
• Comparing with critical angle
1
tan   2
n 1
2
h (1  c)
tan  
2r
2
h (1  c) 1
 2
2r
n 1
• The jet acts as a light guide if
2r
h 2
(n  1)(1  c)
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IYPT 2010 Austria, I.R. Iran
Optical Studies
• Semi guidance situation
y0


x2
y
4hv
x  4hv y0

 y0  
y
hv
tan   tan 

y   y0
, y0  
x
2hv
tan   cot   
tan 2   tan 2 
hv
1
 2
y n 1
y  (n 2  1)hv
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IYPT 2010 Austria, I.R. Iran
h
yv
Optical Studies
stot   r 2
y
stri  l ( y  r )
r
stri  s1   r 2
s1   r 2  l ( y  r )
l
2
1
15
s2  stot  s1   r 2  ( r 2  l ( y  r ))
s2
GC 
stot
IYPT 2010 Austria, I.R. Iran
Optical Studies
• Guidance-velocity head graph
1,2
1
Guidence
0,8
0,6
0,4
0,2
0
0
16
0,002
0,004
0,006
0,008
velocity head(m)
0,01
0,012
0,014
0,016
IYPT 2010 Austria, I.R. Iran
Optical studies - Experiments
• Setup
– Wide light source
– Black vessel side
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IYPT 2010 Austria, I.R. Iran
Optical studies - Experiments
• Measurement
– Using a camera to measure the
intensity and the energy.
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IYPT 2010 Austria, I.R. Iran
Optical studies - Experiments
• Camera calibration
– Finding the relation between
RGB and intensity
25cm
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30cm
31cm
40cm
50cm
IYPT 2010 Austria, I.R. Iran
Optical studies - Experiments
• Camera calibration
0,0018
0,0016
y = 1,511999E-10x3 - 2,083697E-08x2 +
0,0014
2,350585E-06x
R² = 9,980179E-01
0,0012
0,001
Ряд1
Полиномиальная (Ряд1)
0,0008
0,0006
0,0004
0,0002
0
0
20
50
100
150
200
250
300
IYPT 2010 Austria, I.R. Iran
Optical studies - Experiments
• Analyzing pictures with
MATLAB program
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IYPT 2010 Austria, I.R. Iran
Optical studies - Experiments
1,2
guidance
1
0,8
0,6
Ряд1
0,4
0,2
0
0
22
0,2
0,4
0,6
0,8
1
Velocity head(cm)
1,2
1,4
IYPT 2010 Austria, I.R. Iran
Optical studies – Exp & theory comparison
1,2
1
guidance
0,8
Experiments
0,6
Theory
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
Velocity head(cm)
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IYPT 2010 Austria, I.R. Iran
Conclusion
• The liquid path is parabola, as we
calculated.
• Our theory was true about the reason
of the phenomenon.
• Light guide condition is the case
where the hydraulic head would be
more than:
2r
(n 2  1)(1  c)
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IYPT 2010 Austria, I.R. Iran
IYPT 2010 Austria,IYPT
National
2010team
Austria,
of I.I.R.
R. Iran