Continuum Mechanics and Its Practical Applications at the Level of Scaling Laws

Abstract In this heuristic article, we show the usefulness of arguments at the level of scaling laws through examples taken from classic and practical problems. In the textbooks of elasticity and hydrodynamics, exactly solvable problems are very limited, and even for such problems, derivations of solutions require lengthy calculations. However, if we give up deriving numerical coefficients for the solutions, most of them can be obtained by simple dimensional analysis, i.e., arguments at the level of scaling laws. This is a powerful tool to cope with practical problems. We start our discussion from classic problems and proceed to two examples relevant to biomedical applications: microfluidic devices and elasticity tuning of sheet materials.