Hydraulic Design of Highway Culverts - DOT On-Line Publications

Backwater Calculations
From hydraulic tables for elliptical conduits (60):
for Q = 155.744 m³/s, dc = 3.780 m
for Q = 212.378 m³/s, dc = 4.450 m
Since TW > dc, start backwater calculations at TW depth.
Determine normal depths (dn) using hydraulic tables.
for Q = 155.744 m³/s, n = 0.034;
dn = 3.993 m
for Q = 212.378 m³/s, n = 0.034;
dn = 5.090 m
since dn > dc, flow is subcritical
since TW > dn, water surface has an M-1 profile
Plot Area and Hydraulic Radius vs. depth from data obtained from tables.
d/D d A/BD A R/D R
0.65 3.962 0.5537 30.864 0.3642 2.220
0.70 4.267 0.6013 33.518 0.3781 2.305
0.75 4.572 0.6472 36.076 0.3886 2.369
0.80 4.877 0.6908 38.506 0.3950 2.408
0.85 5.182 0.7313 40.764 0.3959 2.413
0.90 5.486 0.7671 42.760 0.3870 2.359
0.95 5.791 0.7953 44.331 0.3649 2.224
1.00 6.096 0.8108 45.195 0.3060 1.865
Complete Water Surface Computations (see attached calculation sheet).
HW = specific head (H) + ke (V²/2g)
Neglecting approach velocity head:
for Q = 155,744 m³/s:
HW = 5.481 + 0.5 (.970) = 5.966 m
ELho = 67.056 + 5.966b = 73.022 m
for Q = 212.378 m³/s:
HWf = 6.90 + (0.5) (1.19) = 7.495 m
ELho = 67.056 + 7.495 = 74.551 m
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