NikolaySibiryakov - IYPTsolutions.iypt.org/...RU_Hovercraft_Nikolay_Sibiryakov_1441073327.pdf ·...

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Hovercraft Nikolay Sibiryakov 1

Transcript of NikolaySibiryakov - IYPTsolutions.iypt.org/...RU_Hovercraft_Nikolay_Sibiryakov_1441073327.pdf ·...

Hovercraft

Nikolay Sibiryakov

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The problem

A simple model hovercraft can be built using a CD and a balloon filled with air attached via a tube. Exiting air can lift the device making it float over a surface with low friction. Investigate how the relevant parameters influence the time of the 'low-friction' state.

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First observationsFirst observations

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Floating over the table 4

Force balance

mgRF

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The reactive force

p

FR = pS

Sd = 13,8 mmS = 1,5 cm2

FR = 0,15 N

mg = 0,28 N

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Viscous friction

atmp p

atmpp. .visc fricF

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Force balance over the table

mgRF

HFHF

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Floating under the ceiling 9

Bernoulli’s principle

atmpoutvoutv vp

atmp p

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Force balance under the celling

mg

RF

BF BF

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Final force balance

mgmg

RF

RF

BF

BFBF

BFHF HF

HFHF

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Outline of the report

Pressure under the disk

Hovering experiments

Theoretical model

…how the relevant parameters influence the time of the 'low-friction' state…

Hovering time vs. craft’s weight

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Air pressure Air pressure under the diskunder the disk

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Parameters of the hovercraft

balloon + diskm = 28,3 g

R = 6 cmS = 110 cm2

D = 25 cmV = 8 dm3

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Plug-in nozzles

1.9 mm2.6 mm4.3 mm9.0 mm

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Setup for pressure measurement

Side barriers

Relative pressure sensor

Holes3.5 mm diameter

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-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Distance from center (mm)

Rel

ativ

e pr

essu

re (P

a)

1,9 mm2,6 mm4,2 mm9,0 mm13,8 mm

Nozzle diameter

Pressure distribution under the disk

viscous

viscous

Bernoulli

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HoveringHoveringexperimentsexperiments

“…how the relevant parameters influence the time of the 'low-friction' state…”

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1

10

100

1000

0,1 1,0 10,0 100,0 1000,0Nozzle cross-section (mm2)

Tim

e (s

)

Free flowHovering

Time vs. nozzle cross-section 20

Narrow nozzles Narrow nozzles Viscosity dominatesViscosity dominates

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-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Distance from center (mm)

Rel

ativ

e pr

essu

re (P

a)

1,9 mm2,6 mm4,2 mm9,0 mm13,8 mm

Nozzle diameter

1

10

100

1000

0,1 1,0 10,0 100,0 1000,0Nozzle cross-section (mm2)

Tim

e (s

)

Free flowHovering

What do we already know?

Almost free outflow

Pressure drops along the radius

Small nozzle diameter

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Viscous regime: Hele-Shaw cell

( )2

Qv rr

Continuity condition:

Darcy’s law:2

( )12

dpv rdr

3

6( ) lnQ Rp rr

Q

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Narrow nozzle (d = 1.9 mm)

6051 lnp Pa

r mm

3

6( ) lnQ Rp rr

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Hovering time with narrow nozzle

2*p p u

p

p*Flow through the nozzle:

2* 2lnmg RpR a

Flow under the disk:

Velocity in the nozzle:

221 2lnp mg Ru

p R a

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Hovering time with narrow nozzle

1/2

21 2lnV mg RS p p R a

0

We should know it!

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Measurement of relative pressure

Rulers

Relative pressure sensor

Compressor

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0,00,51,01,52,02,53,03,54,04,55,0

0 1 2 3 4 5 6 7 8 9

Volume (dm3)

Rel

ativ

e pr

essu

re (k

Pa)

Pressure vs. volume

1% of atmospheric pressure

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Hovering time with narrow nozzle

For our parameters of the balloon and the disk

0 1 0,02 ln Ra

If R/a = 60, 01,08

+

1/2

0 21 2lnmg Rp R a

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Wide nozzlesWide nozzlesViscosity + BernoulliViscosity + Bernoulli

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-100

-80

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50 60 70

Distance from center (mm)

Rel

ativ

e pr

essu

re (P

a)

1,9 mm2,6 mm4,2 mm9,0 mm13,8 mm

Nozzle diameter

1

10

100

1000

0,1 1,0 10,0 100,0 1000,0Nozzle cross-section (mm2)

Tim

e (s

)

Free flowHovering

What do we already know?

Outflow differs from the free outflow

Pressure under the central area is less than atmospheric

Big nozzle diameters

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Wide gap: Bernoulli’s regime

( )2

Qv rr

Continuity condition:

2

const2vp

Bernoulli’s principle:

2

2 2 2 2

1 1 1( )4

Qp rR r

Relative Pressure is negative

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Combined regime

2

3 2 2 2 2

6 1 1 1( ) ln4

Q R Qp rr R r

Viscous Bernoulli

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Parabolic velocity profile

2

3 2 2 2 2

6 27 1 1( ) ln140

Q R Qp rr R r

viscous Bernoulli with a parabolic profile

Armengoll J., Calbó J., Pujol T., Roura P. (2011) “Bernoulli correction to viscous losses: Radial flow between two parallel discs”.

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Force balance

2 2

3 23 27 ln

70RQR Q Rmg F

a

Both terms are large compared with the weight, so they are approximately

equal to each other

270

9 ln /RQ

R a

Viscous Bernoulli

Outflow from the nozzle under the disk

p

p0

As outflow from the nozzle into the atmosphere

02Q a v 0pv

p0p

Cylindrical entry

Hovering time with wide nozzle

270

9 ln /RQ

R a

02Q a v

2

0

ln /970 2

R aV

a R v

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1

10

100

1000

0,1 1,0 10,0 100,0 1000,0Nozzle cross-section (mm2)

Tim

e (s

)

Free flowHovering

Theory-experiment comparison

+

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Hovering timeHovering timevs.vs.

weightweight

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The hovering time

0

21 2lnmg Rp R a

2

0

ln /970 2

R aV

a R v

The hovering time almost does not depend on the weight of the vessel until this weight is not

very large.

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Experiment 41

0

2

4

6

8

10

12

0,0 0,5 1,0 1,5

Weight (N)

Tim

e (s

)

Time vs. weight (nozzle 13.8 mm)

+

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SummarySummary

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Conclusions 44

References

• Jackson J.D., Symmons G.R. (1965) “An investigation of a laminar flow between two parallel disks”. Appl. Sci. Res. 15, 59–75.

• Armengoll J., Calbó J., Pujol T., Roura P. (2011) “Bernoulli correction to viscous losses: Radial flow between two parallel discs”. Am. J. Phys. 76, 730–737.

• Izarra Ch., Izarra G. (2014) “Stokes equation in a toy CD hovercraft”. Eur. J. Phys. 32, 89–99.

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