A large number of studies carried out to data confirms that flow phenomena in gas stirred ladle systems were essentially predominated by the inertial and gravitational forces (e.g. Froude dominated). On the other hand, mixing, from a fundamental stand point, depends on flow and turbulence parameters in the system. Consequently, it is difficult to conceptualize any inter-dependence between mixing times and physical properties of the system (e.g., interfacial tension and viscosity), particularly in the absence of a second buoyant phase [8]. Thus, as a first approximation, assuming flow phenomena to be essentially Froude dominated and furthermore, considering mixing time is influenced by aspect ratio (H/D), the tuyere positions, the flow rate and liquid-gas density ratio, etc. According to Buckingham pi theorem [9], it is necessary to determine the number of dimensionless parameters into which the variables may be combined. The relationship between them can be written as follows:

Equation (5) is also represented in the following dimensionless form:

where K, a, b, c and d are undetermined coefficient and Fr', p_{p}, and W are

dimensionless parameters.

Substituted Eqs. (1) and (6)-(8) into (5), Eq. (5) can be rewritten in a dimensionless form as follow:

where W is dimensionless value about tuyere configuration. It represents the values of each tuyere position.