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abutments, for all abutments with angles between 45 and 60 degrees, and for all bridges with openings more than 200 feet wide. The upper curves are for less efficient abutment angles. The middle curve (No.2) should be used for angles that approach 30 degrees. The top curve (No.3) should be used for angles that approach 90 degrees. It the pier is not oriented parallel to the direction of water flow, the input value used for pier width is the projected pier width (see page 15 of the BPR Manual). For some bridges this would completely close off the opening, which is obviously unrealistic. Therefore, the maximum projected pier width used should be'about three times the actual pier width. WSP2 uses equation 30 on page 95 of the BPR Manual for the basic loss relation- ship. This equation states that head loss equals the total backwater loss coefficient times the velocity head within the bridge plus the difference between the exit and approach velocity heads. The head loss is assumed as previously described. WSP2 calculates the loss coefficient and exit and approach velocity heads, uses equation 30 to determine the velocity head within the bridge, and calculates velocity (V) through the bridge from the bridge velocity head. The bridge capacity for the assumed loss is then found from the continuity equation (0 = A V), where A is the area within the bridge below the tailwater elevation. The lengths important to bridge analysis are found in the input as follows: 1. The reach length on the ROAD card is the distance from the road centerline to the exit section. 2. The reach length on the approach sec- tion REACH card is the distance from the approach section to the centerline of the road. Some bridges restrict flow to the extent ,that flow passes through critical in the bridge section. Such bridges are illustrated in figure 4 in the BPR Manual. If flow ap- proaches critical in the bridge section (Froude number is 0.8 to 1.2). WSP2 uses equations 25 and 26 on pages 57 and 58 of the BPR Manual to compare the energy level for flow at the approach section (as- suming the headwater as described previ- ously) with the energy level in the bridge section (assuming critical flow). At the same time, subcriticalflow is computed as described above. If the two specific energies balance be- fore obtaining enough head to cause the required flow under subcritical conditions, the solution is assumed to be critical. Flow always is assumed to be critical if the Froude number is more than 1.2, in which case the energy levels are computed as above without regard to the subcritical flow calculations. The headwater is taken as the , elevation at which the specific energies of the two sections balance. If the headwater elevation is subcritical at the bridge en- trance, the headwater elevation is set equal to the critical elevation. Culvert loss analysis In one,road restriction WSP2 can analyze losses through as many as five culvert openings of different shapes or elevations or an unlimited number of culvert openings with the same configuration.. Only rectangu- lar, circular, and standard metal-pipe arch shapes can be analyzed. The capability to analyze open channel flow in multiple cul- verts with different configurations has caused the solution to be a double trial- and-error procedure. The problem is to find the amount of flow that will go through each culvert for the head loss increment or headwater elevation assumed in step 2 of the section Road Restriction Analysis. WSP2 solves the prob- lem as follows: Step 1.-Assume a discharge. Step 2.-Compute an open channel flow profile from the tailwater point through the culvert with the assumed discharge. Solve for open channel flow by the direct step method using the reach length found for a change in depth of 0.2 foot. If this e,x- tends the profile past the upstream end of the culvert, WSP2 interpolates the water surface at the entrance and adds an en- 6