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e , ~ - , . e / Figure 3 shows the terms of equation 2, the energy line, the hydrau- lic grade line and the headwater depth, HW. T"ne energy line represents the total energy at any point along the culvert barrel. The hydrauli.l) grade line, sometimes called the pressure line, is defined by the eleva- tions to which water would rise in small vertical pipes attached. to the cuI vert wall a.l.ong its length. The energy line and the pressure line are parallel over the length of the barrel except in the immediate vicinity of the inlet where the flow contracts and re-expa.nds. The difference in elevation between these two lines is the velocity head, V2 . 2g The expression for H is derived by equating the total energy up- stream from the culvert entrance to the energy just inside the culvert outlet with consideration of all the major losses in energy. By refer- ri.ng to figure 3 and using the culvert invert at the outlet as a datum, 'v': fl,et: 2 .. Vl di + 2g + LBo ~ d2 -I- Ir,. + He + Hf where dl and d2 : depths of flow as shown in fig. 3 V2 1 2g = velocity head in entrance pool LSo = length of culvert times barrel slope then v2 dl + ~ + LSo - d2 = Hv + He + Hf and 2 V H ~ dl + ~ + LSo - d2 = Hy + He + Hf 2g From the development of this energy equation and figure 3, head H ~s the difference between the elevations of the hydraulic grade line at the outlet and the energy line at the inlet. Since the velocity head in the entrance pool is usually small under ponded conditions, the watar surface or headwater pool elevation can be assumed to equal the elevation of the energy line. Thus headwater elevations and headwater depths, as computed by the methods given in this circular, for outlet control, can be higher than might occur in some installations. Head- water depth is the vertical distance from the culvert invert at the en- trance to the water surface, assuming the water surface (hydraulic grade 2 line) and the energy line to be coincident, dl + Vl in figure 3. 2g 5-7