On the Influence of the Surface-Tension on the Efflux of a Liquid in Jet Form

Abstract

Influence of Surface Tension on the Efflux of a Liquid Jet.—Christiansen suggested that surface tension exerts a pressure acting against the pressure causing the flow, so that the Torricelli equation becomes: $v^2=2\mathrm{}{\pi }^2{\kappa }^4{r}^{4}g(h-h_0)$. If then $\kappa$, the coefficient of effective contraction, is constant, $v^2$ should be a linear function of $h$, intercepting the $h=0\mathrm{}$ axis at $h_0$. Experiments with mercury and water, in which the speed of efflux was determined down to low values of $h$, confirm this theory. With cylindrical holes, straight lines were obtained, but with conical holes the relation is curvilinear because of the decrease of the contraction with the speed; yet both types of curve gave the same value of $h_0$. With water, holes through paraffin paper were used. When the speed decreased to a critical value for each jet, pulsations began to appear but these did not affect the speed of efflux. Photographs are given of various jets. As a qualitative confirmation of the theory, ether vapor, which is known to decrease the surface tension of water, was found to decrease $h_0$ by 18 per cent.