Capillary Action Dimensional Analysis · CAP 2010 #Q12
Physics · fluid-mechanics
Problem
A liquid will rise in a narrow tube (capillary action) if the adhesive forces between the molecules of the liquid and the molecules of the tube are greater than the cohesive forces between the molecules of the liquid. The height of a column of liquid of density ρ drawn up a tube of radius r is given by
h=ρgr2γcosθ
where θ is the contact angle between the surface of the liquid and the tube, g is the acceleration due to gravity, and γ is a constant that depends on a number of parameters. The dimensions of γ are given by
a) ML⁻²; b) MLT⁻²; c) M⁻¹LT⁻²; d) MT⁻²; e) none of the above.