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.

This model is not realistic. We present this just to illustrate that improvement over this simple argument is difficult, tantamount to impossible. But there are similar analog.

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 Faucet Cylinder Reservoir

Experimental Setup Front view Side view

Observation Water stream flows along the cylinder's circumference. Continues up the other side.

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

Typical Result Collide and separateConverge and detach

Water Speed

Impact Angle

Cylinder Diameter

Cylinder Material

Leaving Angle- Impact Angle The dependence on the angle is not strongly correlated. Material: acrylic

Leaving angle- Initial speed No significant relation is found.

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!