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Show da, dx where: ( 4) fi-( l- e) F{ ^ P- r7dx K ( 5) < 2T72 a = I- Fa2jT1- T>/+ F, 2S 2^ 0 ( 7) ( 8) K1-^ '* 2^ - F2 Vs y T2 + ( F2 - 1) S0 T,= T = x2 2a1( E1 + W1)+ B( 2E1 + I1 + S1) gPia, B 2a2( E2 + W2)+ B( I2 + Z+ 2E2) ( 9) ( 10) ( 11) gP2a2B B = Culvert width D = Culvert depth E = Entrance losses expressed as a force per square foot I = Interfacial losses expressed as a force per square foot W = Wall losses expressed as a force per square foot x = distance in the horizontal direction With the submerged flow equations incorporated in the model, the additional flow regimes shown in figure 4 could now be analyzed. In previous studies submerged flow was approximated by assuming that the culverts had no top. It was believed that lower layer flows would not be significantly influenced by submergence and that upper layer flows would be inaccurate but small with respect to breach flows that would begin when submergence occurred. The model with the new subroutines indicated that when free- surface flows are calculated for an unconfined culvert that lower layer flows will be higher than would be predicted for submerged flows, but sometimes close enough to be within the accuracy of the method. 366 |