Question

For a thin film of a glycerin flowing with a velocity of 0.40 m/s at a depth of 3 mm at 20 °C, determine the value of two important dimensionless parameters (a) the Froude number, V/(gh) (b) the Weber number,

Answer 1

From the physical properties of chemical compounds in texts,

We have surface tension, σ =6.3 × 10−2 N/m, density, ρ=1260 kg/m3

given

v = 0.40m/s

h=3mm=0.003m

g=9.81m/s2

a) Froude Number, = v/
`√(gh)`

Fr = 0.4/√(9.81x0.003) = 2.33

b) Weber Number, We = ρv²h/σ

We = 1260 x 0.4²x 0.003/6.3 × 10⁻² = 9.6