Solution: water will be used as an analogue of steel.

Base length of model tundish

Width of the tundish

Height of tundish

Volumetric flow rate

Dynamic similarity requires similarity in Reynold’s and Froude number

 

 

 

 is velocity of steel,  kinematic viscosity of steel melt  In the prototype tundish velocity of steel melt is not known. Putting value of up =   in the Reynolds number, we get

 

 

Similarly one can calculate Froude number of the prototype

 

 

 


For the dynamic similarity both Reylold,s and Froude,s number should be same. As  pointed out in lecture 38, both numbers can be made similar for scale factor 1. In the present model scale factor is 0.5, hence either Reyonld’s number similarity can be observed or Froude number similarity.

It is shown (see the references given at the end of this lecture) that in turbulent flow, the transport of the momentum to the neighboring fluid layers occurs via eddies. There is a wide spectrum of eddies of different lengths in a fully developed turbulent flow. Based on the analysis of different lengths of the eddies in molten steel and water system, it is shown that the lengths of the eddies produced at the exit of the submerged shroud for water and steel are of the same order of magnitude, irrespective of the scale of the model and type of fluid. This suggests that within the turbulent flow regime the mechanism of flow of steel melt in the prototype and water in the model  may  not depend significantly on the absolute value of the Reynold,s number as long as flow is turbulent. Therefore Froude number similarity is considered

Following Froude number similarity model submerged ladle shroud diameter can be determined.