Hydraulics and Hydrology
Hydraulics
Manning's equation, Q = (1.486/n) A R^(2/3) S^(1/2) in US customary units (coefficient 1.0 in SI), is the workhorse for gravity pipe and open-channel problems. The hydraulic radius is R = A/P, and for a circular pipe flowing full R = D/4, not D. The energy equation tracks pressure, velocity, and elevation head; friction loss follows Darcy-Weisbach, h_f = f (L/D)(V²/2g), with minor losses from fittings. Open-channel flow adds specific energy, critical depth, and the Froude number; subcritical and supercritical flow behave differently at controls, and a hydraulic jump converts one to the other.
Hydrology
The rational method Q = C i A gives peak flow when i is rainfall intensity in in/hr for a duration equal to time of concentration and A is in acres (about 1.008 converts to cfs). The SCS curve-number method estimates runoff depth: S = 1000/CN − 10 inches and Q = (P − 0.2S)²/(P + 0.8S). Unit hydrographs scale runoff linearly with excess rainfall, and reservoir or channel routing (Muskingum) attenuates peaks.
Traps
Watch unit systems in Manning's equation, use R = D/4 for full pipes, and remember that the rational method's duration is set by Tc, not by the return period. Curve numbers shift with antecedent moisture; do not treat CN as a fixed physical constant. Time of concentration is a travel-time concept, not a storage volume.
Worked example
A 24-in concrete pipe (n = 0.013) flows full at S = 0.005. D = 2 ft, so A = 3.14 ft² and R = 0.5 ft. Q = (1.486/0.013)(3.14)(0.5)^(2/3)(0.005)^(1/2) ≈ 16 cfs.