# Weber Number

on . Posted in Dimensionless Numbers

Weber number, abbreviated as We, a dimensionless number, is used in fluid mechanics, often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces.  It is a measure of the relative importance of the fluid's inertia compared the its surrface tension.  The reason this number is important is it can be used to help analyze thin film flows and how droplets and bubbles are formed.

## Weber number formula

$$\large{ We = \frac{ \rho \; v^2 \; l_c }{ \sigma } }$$

### Weber Number - Solve for We

$$\large{ We = \frac{ \rho \; v^2 \; l_c }{ \sigma } }$$

 density, ρ velocity, v characteristic length, lc surface tension, σ

### Weber Number - Solve for ρ

$$\large{ \rho = \frac{ We \; \sigma }{ v^2 \; l_c } }$$

 Weber Number, We velocity, v characteristic length, lc surface tension, σ

### Weber Number - Solve for v

$$\large{ v = \sqrt{ \frac{ We \; \sigma }{ \rho \; l_c } } }$$

 Weber Number, We density, ρ characteristic length, lc surface tension, σ

### Weber Number - Solve for lc

$$\large{ l_c = \frac{ We \; \sigma }{ \rho \; v^2 } }$$

 Weber Number - We density, ρ velocity, v surface tension, σ

### Weber Number - Solve for σ

$$\large{ \sigma = \frac{ \rho \; v^2 \; l_c }{ We } }$$

 Weber Number, We density, ρ velocity, v characteristic length, lc

Symbol English Metric
$$\large{ We }$$ = Weber number $$\large{ dimensionless }$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ v }$$ = velocity of fluid  $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ l_c }$$ = characteristic length $$\large{ ft }$$ $$\large{ m }$$
$$\large{ \sigma }$$  (Greek symbol sigma) = surface tension $$\large{\frac{lbf}{ft}}$$   $$\large{\frac{N}{m}}$$ Tags: Flow Equations