Question

For the flow of a thin film of a liquid with a depth h and a free surface, two important dimensionless parameters are the Froudenumber,and Weber number. Determine the value ofthese two parameters for glycerin (at 20 Celsius) flowing with a velocity of 0.5 m/s at a depth of 2mm.

Answer 1

Step-by-step explanation:

You will need this table to solve.

Answer 2

To develop the problem it is necessary to define the concepts presented in the statement, that is to say the two dimensionless parameters of Froude and Weber.

The Froude number is defined as

`F = (V)/(√(gh))`

Where

V = Velocity of liquid

h = Depth of the film

g = Gravitational constant

With our values we have that

V = 0.7m/s

`g = 9.81m/s^2`

h=0.003m

Replacing we have,

`F = (V)/(√(gh))\\F = (0.7)/(√(9.81*0.003))\\F = 4.08`

Therefore the value of Froude number for glycerin is 4.08

El número de Weber esta definido bajo la expresión

`W = (\rho V^2h)/(\sigma)`

Where,

`\rho =`Density

`\sigma =` Surface tension

V = Velocity

h = Depth of the film

For the two values at 20°C it is neccesary search for the properties of glycerin at the tables. I find that at 20°C

`\rho_g = 1261kg/m^3`

`\sigma = 0.0634N/m`

Replacing we have,

`W = (\rho V^2h)/(\sigma)\\W = (1261*0.7^2*0.003)/(0.0634)\\W = 29.23`

Therefore the Weber number is 29.23