Recap: Principles of Physical Similarity & Dimensional Analysis | Fluid Mechanics for Mechanical Engineering PDF Download

Recap
In this course you have learnt the following

• Physical similarities are always sought between the problems of same physics. The complete physical similarity requires geometric similarity, kinematic similarity and dynamic similarity to exist simultaneously
   
• In geometric similarity, the ratios of the corresponding geometrical dimensions between, the systems remain the same. In kinematic similarity, the ratios of corresponding motions and in dynamic similarity, the ratios of corresponding forces between the systems remain the same
   
• For prediction of the performance characteristics of actual systems in practice from the results of model scale experiments in laboratories, complete physical similarity has to be achieved between the prototype and the model.
   
• Dimensional homogeneity of physical quantities implies that the number of dimensionless independent variables are smaller as compared to the number of their dimensional counterparts to describe a physical phenomenon. The dimensionless variables represent the criteria of similarity. Buckingham’s π theorem states that if a physical problem is described by m dimensional variables which can be expressed by n fundamental dimensions, then the number of independent dimensionless variables defining the problem will be m-n. These dimensionless variables are known as π terms. The independent π terms of a physical problem are determined either by Buckingham’s π theorem or by Rayleigh’s indicial method.