Two conditions must be satisfied by an ideal piston ring. (a) It should be truly circular when in the cylinder, and (b) it should exert a uniform pressure all around. Assuming that these conditions are satisfied by specifying the initial shape and the cross-section, show that the initial gap width must be

3pr 4 /EI, if the ring is closed inside the cylinder. p is the uniform pressure per centimetre of circumference. EI is kept constant.