A horizontal 2-in. I. D. pipe carries water with density 62.3 lbm/ft3 . In order to measure the flow rate, the line is to be fitted with a sharp-edged orifice plate, with pressure tappings that are connected to a mercury manometer that reads up to a 15-in. difference in the mercury levels. If the largest flow rate of water is expected to be 560 lbm/min, specify the diameter of the orifice plate (in inches) that would then just register the full 15-in. difference between the mercury levels. Assume that the coefficient of contraction is 0.62. [Note: The density of mercury can be found in Appendix A.9 of the De Nevers textbook.]