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<br />. <br /> <br />rm FLCM THROUGH BRIDGES <br />As previously stated. low flow through bridges refers to flow <br />conditions that exist when water is not in contact with the low chord <br />of the bridge. In the BEe computer program approach the losses due to <br />expansion and contraction of the flow area on the upstream and down- <br />stream sides of the structure are computed separately from the loss <br />through the structure itself. The contraction and expansion losses at <br />the bridge are evaluated in the same way as expansion and contraction <br />losses where bridges are not present; that is. by multiplying a loss <br />coefficient times the absolute difference between the velocity heads <br />within and outside of the bridge constriction. For bridges without <br />piers. skin friction along the sides of the bridge are accounted for <br />with normal backwater COIIIputations using standard step procedures <br />(reference 6). When piers are present. the pier losses can be evaJ.uated <br />by application of momentum principles as proposed by Koch and Carstanjen <br />(reference 1). Application of momentum principles for rectangular- <br />shaped channels is given in reference 3. The general theory. applicable <br />to channels of any shape. is given below. The HEC program is presently <br />programmed for trapezoidal-shaped constrictions in natural channels. <br />Con:l.ider the plan and profile views of flow past bridge piers shown <br />in Figure 1. Section 1 and Section A are located immediately upstream <br />and downstream from the upstream ends of the piers. respectively. It <br />is assumed that the pressure distribution in these sections is hydrostatic. <br /> <br />~ <br /> <br />, <br /> <br />3 <br />