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<br />gradient elevation is above the minimum top of roadway elevation, then a <br />combination of low flow under the bridge and weir flow over the roadway approach <br />exists; if the energy elevation is below the minimum top of road~ay, then low <br />flow controls. <br /> <br />(4) Low flow is further classified as Class A, Band C depending <br />on whether subcritical, critical, or super critical flow occurs between bridge <br />piers. <br /> <br />(a) Class A flow, identified by procedures explained in later <br />paragraph, is solved from Yarnell's energy equation shown on sheet 010-6 of <br />the WES Hydraulic Design Charts: <br /> <br />113 <br /> <br />~ <br /> <br />4 2 <br />2K (K + lOw - O.6)(a + 15a ) V3 /2g <br /> <br />where, <br /> <br />113 <br /> <br />~ <br /> <br />drop in water surface in feet from upstream to downstream sides <br />of the bridge <br /> <br />K <br /> <br />~ <br /> <br />pier shape coefficient (see exhibit 2) <br /> <br />w <br /> <br />~ <br /> <br />ratio of velocity head to depth downstream from the bridge <br /> <br />obstructed area <br />total unobstructed area <br /> <br />a <br /> <br />~ <br /> <br />V3 <br /> <br />= <br /> <br />velocity downstream from the bridge in feet per second <br /> <br />The computed upstream water surface elevation is simply H) plus the downstream <br />water surface elevation. <br /> <br />(b) Class Band C flows are handled by employing the following <br />momentum relations proposed by Koch and Carstanjen in reference (b): <br />~ ~ ~ <br />ml - mpl + g(Al)2 (AI - ApI) ~ m2 + gA2 ~ m3 - (mp) 3 + gA3 <br /> <br />where, <br /> <br />ml, m2, m) <br /> <br />~ <br /> <br />AIyl, A2Y2 and A)Y3' respectively <br /> <br />mpl' mp3 <br /> <br />. <br /> <br />AplYpl and Ap3Yp3' respectively <br /> <br />AI' A) <br /> <br />= <br /> <br />unobstructed (gross) area at upstream and downstream <br />sections, respectively <br /> <br />A2 <br /> <br />= <br /> <br />flow area (gross area - area of piers) at a section within <br />constricted reach <br /> <br />9 <br />