For a liquid of surface tension rising in a capillary tube of internal radius
PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
For a liquid of surface tension T rising in a capillary tube of internal radius r, an empirical relation is
h=ρrg2Tcosθ,
where h is the height of the liquid column, ρ is the density of the liquid, g is the acceleration due to gravity and θ is the angle of contact.
(i) Show by dimensional checking whether the equation above is dimensionally consistent.
(ii) Comment on whether the numerical factor 2 and the trigonometric term cosθ can be obtained solely from dimensional considerations. Give reasons for your answer.