Sticky Water

TaiwanHsieh, Tsung-Lin

Question

When a horizontal cylinder is placed in a vertical stream of water, the stream can follow the cylinder's circumference along the bottom and continue up the other side before it detaches.

Explain this phenomenon and investigate the relevant parameters.

Coanda Effect

The tendency for a fluid jet to be attracted to a nearby surface.

Theoretical explanation is difficult because we have to deal with fluid mechanics, not particle mechanics.

A Simple Argument

From a book “Fluid Dynamics for Physicists” by T. E. Faber, we have a simple argument but not realistic. 2-d flow (the 3rd dimension is infinite) A perfect imcompressible fluid (No viscosity,

no vorticity) No gravity Conservation of energy Conservation of tangential momentum

At the impact point, tangential momentum is conserved, so the backward jet is thinner, less mass.

The two jets move half a circle in equal time and collide again.

The jet detaches because of collision.

Some Subtle Differences

We should consider Adhesive force Cohesive force Gravity Viscosity Vorticity

The cross section of the jet will be subjected to a free surface boundary condition by the air pressure and the cylinder.

Experimental Setup

Water tank

FaucetCylinder

Reservoir

Experimental Setup

Front view Side view

At the impact point

Water spread out in every direction.

There is more momentum (mv) in the forward direction.

Water flow

Spreading Out

The water jet flows down due to gravity.

The velocity will be different at different point.

Wetting

Surface tension

Convergence

The stream converges because: The velocity is greater, Evidently, the cohesion

wins over the wetting.

Surface tension

Wetting

Instability

Convergence results in instability.

Do not necessary flows tangentially.

Detachment

• Fluid instability results in detachment.

Parameters

Initial speed at the point of impact -220 ,200 ,170 ,150 cm/s

Cylinder material- acrylic, steel, wax paper Impact angle- 20~75 deg Cylinder diameter Faucet bore diameter

Definitions

Water Speed

-500

50100150

0 2 4 6

speed

deta

chm

ent a

ngle

Impact Angle

0

50

100

150

0 20 40 60 80

impact angle

deta

chm

ent a

ngle

Cylinder Diameter

-500

50100150200

0 1 2 3 4 5

cylinder diameter

deta

chm

ent a

ngle

Cylinder Material

-50

0

50

100

acrylic paper steel

deta

chm

ent a

ngle

17cm

20cm

Higher velocity, larger is the spread. Water spreads wider on acrylic cylinder.

Side Width- Initial Speed

Maximum width

Summary

The “sticky water” effect is real. The leaving angle have large error due to

instability of the stream. No significant relation is found.

Stream spreads out when the speed is higher, and wider on acrylic cylinder.

Reference

Fluid Dynamics for Physicists by T. E. Faber Flying Circus of Physics by …

Teapot effect Halliday…

Thank you!