DIMENSIONAL ANALYSIS PROBLEMS

The rise in a tube h due to capillary action is a function of the diameter of the tube D, angle in radians, surface tension , acceleration due to gravity g, and density .

Show that, ( hD )=function [( σ

D2 ρg ) , θ]

2. In the laminar flow of a viscous fluid through a horizontal capillary tube , the pressure drop is a function of the velocity, diameter, viscosity and length L (distance between the upstream and downstream point in the pipe). Determine the ’s involved and derive that the pressure drop is equal to 32VL/D2.

3. Derive an expression for the discharge Q over a spillway in the form of a function including dimensionless parameters. The discharge Q is dependent on height of the spillway P, head H on the spillway (height of water above the crest of spillway), viscosity of water , density of water , surface tension , and acceleration due to gravity g. Use Q, , and H as the repeating variables.