7 PDF - Kern E. Kenyon, Vena contracta and surface tension


Volume 23: Pages 579-583, 2010

Vena contracta and surface tension

Kern E. Kenyon 1

14632 North Lane, Del Mar, California 92014-4134, USA

The observed narrowing of a horizontal fluid jet after exiting a small round hole in the side of a large container, called the vena contracta, and the accompanying speeding up of the flow are discussed in relation to the action of surface tension between air and the fluid for hole radii of the order of 1 cm or less. Bernoulli’s law for steady frictionless flow in the jet incorporating surface tension is conjectured to be p=const−1/2ρq2+T/R along a streamline, in cylindrical polar coordinates, where ρ, q, T, and R, are, respectively, the fluid density, speed, surface tension coefficient, and the radius of curvature of the stream in cross-sections normal to the flow, and p is the total pressure. Together the last two terms in the equation are the balance between the static and dynamic pressures in the jet, and this balance is qualitatively consistent with the observations of the narrowing and speeding up of the jet.

Keywords: Vena Contracta, Surface Tension

Received: February 27, 2010; Accepted: August 17, 2010; Published Online: September 9, 2010