Question

--fluid mechanics--

The diameter of the soap bubbles (d) formed by a bubble toy is thought to be a function of surface tension between the soap-water solution (σs), the pressure difference between inside the bubble and the environment (ΔP), the diameter of the circular wire frame (D), the dynamic viscosity (μ) and the density (ρ) of the soap-water solution.

a) How many dimensionless parameters arise from this configuration?

b) Is there an evident dimensionless parameter which can be found without any calculation? If yes, which parameter?

c) If two of the repeating variables are given as surface tension (σs ) and density (ρ), find the rest of the repeating variable or variables.

d) Find the dimensionless parameters (Pi numbers)

e) The model experiments the D=3 cm diameter wire frame submerged into soap-water solution whose surface tension (σs) is 0,025 N/m, is blown with an effective pressure of 20 mm water-column. Find the effective pressure that needs to be applied if the D=30 cm wire frame prototype will work at 30°C (σs = 0,02 N/m)

Answer 1