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<br />Moment1lDl theory applied between the two sections results in <br /> <br />fllQpVl + yAiYl - flAQpvA - yAAYA = F <br /> <br />(1) <br /> <br />where: <br /> <br />, <br /> <br />Q <br /> <br />= discharge - ft3/sec <br />2 4 <br />= fluid density - lb sec /ft <br /> <br />p <br /> <br />Vl,VA = mean velocities at Sections:l and A, respective~ - ft/sec <br />fll,flA = momentum coefficients - dimensionless <br />Al,AA - flow areas at Sections 1 and A, respective~ _ ft2 <br />y = unit weight of fluid - lb/ft3 <br /> <br />Yl'YA = vertical distances from water surface to centroids of <br />Sections 1 and A, respective~ - ft <br /> <br />F = force exerted by piers on flow - lb <br /> <br /> <br />Division of Equation (1) by Y and substitution ofQ.Q\ for v results in <br /> <br />t - <br />gA + A1Yl <br />1 <br /> <br />2 <br />_s=. -A'i <br />gAA 'A A <br /> <br />F <br />= - <br />y <br /> <br />(2) <br /> <br />It is ass1lDled in the above equation and subsequent equations that the <br /> <br />moment1lDl coefficients due to a non-uniform distribution of velocity are <br /> <br />equal to 1. It is also assumed that boundary friction forces are <br /> <br />negligible compared with the force exerted on the flow by the piers. <br /> <br />Koch. and Carstanjen proposed that the static and dynamic forces exerted <br /> <br />by the upstream ends of square piers be given as <br /> <br />~l <br />y~lYpl and Y'A <br />1 <br /> <br />rl <br />gAl <br /> <br />, respective~ <br /> <br />'4 <br />