Dynamic similarity requires that the corresponding forces acting at corresponding time and location must bear the same ratio between the model and the prototype. In steelmaking the inertial, viscous and surface tension forces are of relevance. The ratio between inertial and viscous force is called Reynold’s number

(2)

Where u is velocity, L is characteristic linear dimension and  is kinematic viscosity. Reynold’s number characterize the type of flow, that is whether laminar or turbulent.

The ratio between inertia and gravity force is Froude number

 

Modified Froude number   is  more relevant than simple Froude number
                                          

(3)

 is the density of gas and  is density of liquid. Froude number determines the importance of aerodynamics force and gravitational force when gas jet either impinges the bath or submerged into the bath. Froude number similarity is very important to model the chemically active or inert gas injection in steelmaking processes.

Weber number  is the ratio of aerodynamic to surface tension force

(4)

 is surface tension of liquid. The dynamic similarity requires

(5)

(6)

(7)

The similarity in Reynold’s number requires that,

(8)

The subscript m denotes model and p denotes prototype. The similarity in Froude number requires that.

(9)

  
And Weber number requires that,

(10)

Weber number is relevant when droplet formation occurs in the actual system.