BRAZILIAN TEAMBRAZILIAN TEAM

17th IYPT - AUSTRALIA - Brisbane - 24th June to 1st July

14. Fountain14. Fountain

Construct a fountain with 1m ‘head of water’. Optimise the other

parameters of the fountain to gain the maximumjet height by varying the parameters of the tube and by using different water solutions.

By Luíza de Almeida Aoki

I. Applications of the study

Irrigation

Fuel injection

IntroductionIntroduction

I. Bibliographic research

II. Theory and experiment for maximum jet height

III. Determination of the Relevant Parameters

MethodologyMethodology

IV. Maximization of the jet height

I. Tank -> Mariotte siphon

II. Tube -> Wide diameter

III. Nozzle -> Smooth

IV. Jet

a) Thin

b) Thick

General ViewGeneral View

I. Jet escape speed on the nozzle

21 2

1VPP A

From Bernoulli Eq.gYPP 01

Hidrostatics

b) Turbulent flow

From Prandtl one-seventh power law

25.020 Re079.0)(

VL

rPPA

a) Laminar flow

L

PrVSQ

8

4

Poisseuille LawbbgYV 22

2

8

r

LbWhere

Turbulence discussionVd

Re

Mathematical AnalysisMathematical Analysis

II. Jet height dependence

34

3

R

m

0

20 2ghVV

dt

dxRmg

dt

xdm ar6

2

2

Motion:

vRF

6From Stokes Law:

00

0 1ln1

Hg

aV

a

gV

aH

Finally

22

9

Ra ar

20 )1)((

)(a

gateaVgtx

at

Where

Solving:

Other influences on jet height

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1

t(s)

x+

Ho

(m

)

Mathematical AnalysisMathematical Analysis

IV. Viscoelastic solutions (polimers)

I. Density

II. Viscosity

III. Surface tension (temperature)

Water SolutionsWater Solutions

General Schematic

Calibration of the Mariotte Siphon

Detail of the Mariotte Siphon

ExperimentExperiment

Practical measure

Jet escapeNozzle detail

Jet top detail

ExperimentExperiment

Water at temperature (°C) Average jet height (cm)25 8550 8475 81

Solutions Average jet height (cm) at 25°CDetergent solution (about 0.2g/L) 83Detergent solution (about 1g/L) 82

Salt solution (density about 1.2g/cm 3̂) 85Salt solution (density about 1.5g/cm 3̂) 86

Tube diameter (mm) Average jet height (cm) at 25°C0 0

0,6 602 856 78

10 5015 35 0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12 14 16

Nozzle diameter (mm)

Je

t h

eig

ht

(cm

)

I. Theory validity

II. Proposition of the optimal parameters

Experimental DataExperimental Data

Source of ErrorsSource of Errors

Loss of energy

Imprecision on the measure

Air resistance