GIVEN An open, cylindrical paint can having a diameter D is filled to a depth h with paint having a specific weight \(\gamma\). The vertical deflection, \(\delta\), of the center of the bottom is a function of D, h, d, \(\gamma\), and E, where d is the thickness of the bottom and E is the modulus of elasticity of the bottom material.
FIND Determine the functional relationship between the vertical deflection, \(\delta\), and the independent variables using dimensional analysis.