IYPT 2010 Austria, I.R. Iran Reporter: S.M. Bousaki 1

IYPT 2010 Austria, I.R. IranIYPT 2010 Austria, I.R. Iran

Problem No.

LIQUID LIGHT GUIDE

Reporter: S.M. Bousaki

8

1

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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Contents• Basic understanding• Hydraulic studies

– Theory– Experiments– Head loss calculation– Comparison

• Optical studies– Theoretical calculation– Experiments– Comparison

• Conclusion

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Basic understanding• Light guide definition

• Refraction and total reflection

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So… the shape of the liq jet is really important 4 us because we can find the angle …

Hydraulic investigationOptical investigation

sin ri

i

n

n


Hydraulic studies• Finding the path using liquid projectile

motion.

That v is the velocity of the liquid particle.

5

2

22

gxy

v


Hydraulic studies• Finding the velocity using Bernoulli

equation & head loss formula

• Darcy–Weisbach equation:

That c in it is the head loss coefficient.

6

20

1

2v gh p cte

2 vv gh

2

2f

vh c

g

v fh h h

2 ( )fv g h h

2 (1 )v gh c

2 ( )v g h h c


Hydraulic studies - Experiments• Setup

– 3 holes – High vessel– Pump

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IYPT 2010 Austria, I.R. Iran8

Hydraulic studies - Experiments

• Finding the liquid path ,use picture analyzing


Hydraulic studies - Experiments

• The liquid paths are parabola

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0 1 2 3 4 5 6 7 8 9

-25

-20

-15

-10

-5

0R² = 0.999968182393469 0 5 10 15 20 25 30 35 40

-30

-25

-20

-15

-10

-5

0R² = 0.999966323231711


Hydraulic studies - Experiments• Finding the head loss

• So the slope between real head and theory head equals to “1+c”

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v v

f

h h

h h h

2

2

(1 )2

1

(1 )2

vc

gc

vc c

g


Hydraulic studies - Experiments• Comparison

– The linear relation between the real head and the hydraulic head shows the mach between theory and experiments.

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1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

f(x) = 0.514233918373807 x − 0.411963456787669R² = 0.989679080787217


Optical studies• Using the jet path to find the first

attachment angle

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2cot

r r

rm

h h c

(1 )tan

2rh c

r

( )2( )r r

xf x

h ch

0 8 ( )r rx r h ch


Optical studies• Comparing with critical angle

• The jet acts as a light guide if

13

22

1tan

1n

2

(1 ) 1

2 1

h c

r n

2 (1 )tan

2

h c

r

2

2

( 1)(1 )

rh

n c


• Semi guidance situation

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Optical Studies

0y

2

4 v

xy

h

0y y

04 vx h y ,0 2 v

xy

h

0v

yy

h tan cot

v

h

y

tan tan 2 2tan tan

2

1

1vh

y n

2( 1) vy n h


Optical Studies

y

l

r

1

2

2tots r

( )tris l y r

21tris s r

21 ( )s r l y r

2 22 1 ( ( ))tots s s r r l y r

2

tot

sGC

s


• Guidance-velocity head graph

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Optical Studies

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.0160

0.2

0.4

0.6

0.8

1

1.2

velocity head(m)

Gui

denc

e


Optical studies - Experiments• Setup

– Wide light source– Black vessel side

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• Measurement– Using a camera to measure the

intensity and the energy.

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Optical studies - Experiments


• Camera calibration– Finding the relation between

RGB and intensity

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25cm 30cm 31cm 40cm 50cm


• Camera calibration

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0 50 100 150 200 250 3000

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

f(x) = 1.51199882141612E-10 x³ − 2.08369675787402E-08 x² + 2.35058504006379E-06 xR² = 0.999388141042526

Series1Polynomial (Series1)


• Analyzing pictures with

MATLAB program

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guid

ance

Velocity head(cm)0 0.2 0.4 0.6 0.8 1 1.2 1.4

0

0.2

0.4

0.6

0.8

1

1.2

Series1


Optical studies – Exp & theory comparison

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

Experiments

Theory

guid

ance

Velocity head(cm)


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:

24

2

2

( 1)(1 )

r

n c

IYPT 2010 Austria, I.R. IranIYPT 2010 Austria, National team of I. R. Iran

Thank you for your attention

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IYPT 2010 Austria, I.R. Iran Reporter: S.M. Bousaki 1