Chapter 4 Surface tension and gravity

Gravity is characterized by the specific weight of the liquid $\rho g$, where $\rho$ is the liquid density and $g$ is the acceleration due to gravity. The dimensions of specific gravity are $F/L^3$, where $F$ denotes the dimensions of force and $L$ those of length. Since the dimensions of surface tension $\sigma$ are $F/L$, a balance of surface tension and gravity invariably yields the ratio $(\sigma /\rho g)$, which has the dimensions $L^2$. Based on this arises the capillary length defined as ${\mathrm{\ell }}_{\text{c}}={(\sigma /\rho g)}^{1/2}$. For a fluid like water, with $\sigma =72\times {10}^{-3}$ N/m and $\rho g=9800$ N/m³, the capillary length is ${\mathrm{\ell }}_{\text{c}}=2.7$ mm.