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24 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Sticky Water

Taiwan

Hsieh, 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

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

Faucet

Cylinder

Reservoir

Experimental Setup

Front view

Side view

At the impact point

every direction.

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

Water flow

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
c
m/s

Cylinder material
-

acrylic, steel, wax paper

Impact angle
-

20
~
75
deg

Cylinder diameter

Faucet bore diameter

Definitions

Water Speed

Impact Angle

Cylinder Diameter

Cylinder Material

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!