Capillary action in narrow and wide tubes—a unified approach

For the purpose of calculating meniscus volume, an ellipsoidal air–liquid interface has been assumed. A formula for the meniscus volume as a function of the radius ( r ) of a tube and capillary constant ( a 2 ) has been derived without resorting to approximations or introducing any arbitrary variable. The formula holds good for all values of r / a . Earlier there were two distinct sets of formulae: one set of formulae was for smaller values of r / a from 0 up to 3.1 and another set was for wider tubes with r / a beginning from 6 onward. No formula existed for intermediate values of r / a from 3.2 to 5.9. The formula derived by the author is universal in this respect. The values of meniscus volumes derived from the author's formula agree very well with those given by Bashforth and Adams for smaller bore tubes. For wider tubes the values of meniscus volume derived from the author's formula are in general smaller but agree to within 10% of the mean values derived from the Rayleigh and Laplace formulae.