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stream submergence, Equation (8) defines the flow across the roadway. Q = C L HW l.S o d r (8) Qo is the overtopping flow rate in ftSjs (mSjs) Cd is the overtopping discharge coefficient L is the length of the roadway crest, ft (m) HWr is the upstrcam depth, measured from the roadway crest to the watcr surface upstream of the weir dra w- down, ft (m) Sf M NT I X, EGM NT X, GM'r x, ElE'll.21 u~~"., ROADWAY VERTICAL CURVE A.MtTHOtl 1- SUBO,VISION INTO SEGMENTS x ,.ELEVATION OF CREST \""\",,,,,,,,,\,;"'~~'\~~,,\\-,,, B.MET\10D 2 - USE OF A SINGLE SEGMENT Figure III-12--Weir crest length determinations for roadway overtopping. The length and elevation of the roadway crest are difficult to dctermine when the crest is defincd by a roadway sag vertical curve. The sag vertical curve can be broken into a series of horizontal segments as shown in figure Ill-12-A. Using equation (8), the flow over each segment is calculated for a given head- water. Then, the incrcmental flows for t- ~ ~ . each segment are added together, result- ing in the total flow across the roadway. Represen ting the sag vertical curve by a single horizontal line (one segment) is often adequate for culvert design. (figure III-12-B) The length of the weir can be taken as the horizontal length of this segment or it can be based on the roadway profile and an acceptable variation above and below the horizontal line. In effect, this method utilizes an average depth of the upstream pool above the roadway crest for the flow calcula tion. J .. " J .J j ~ ... ... ~ j J l J J J ,J 1 ... 1 .. j l It is a simple matter to calculate the flow across the roadway for a given upstream water surface elevation using equation (8). The problem is that the roadway overflow plus the culvert flow must equal the total design flow. A trial and error process is necessary to determine the amount of the total flow passing through the culvert and the amount flowing across the roadway. Performance' curves may also be superimposed for the culvert flow and the road overflow to yield an overall solution as is discussed later in this chapter. ~ ~ ~ . J I 4 ~ 4 ~ 4. Outlet Velocity. Culvert outlet velocities should be calculated to deter- mine the need for erosion protection at the culvert exit. Culverts usually result in outlet velocities which are higher than the natural stream velocities. These outlet velocities may require flow readjustment or energy dissipation to prevent downstream erosion. , . In inlet control, backwater (also call cd dra wdown) calculations may be necessary to determine the outlet vclocity. These calculations begin at the culvert entrance and proceed down- stream to the cxit. The flow velocity is obtained from the flow and the cross-sectional area at the exit, (equa tion (2)) An approximation may be used to avoid backwater calculations in determining the outlet velocity for culverts oper- ating in inlet control. The water surface 40