Water Resources and Environmental engineering models and applications
Hydrology and hydraulics
Water resources questions combine rainfall-runoff, open-channel flow, pipe hydraulics, and treatment. For small urban catchments, the rational method gives Q = CiA, with Q in cfs when i is in inches per hour and A is in acres; the 1.008 conversion is usually taken as 1.0. Use the time of concentration to select rainfall intensity, and remember that C varies with land use and return period. A frequent trap is using a 24-hour rainfall depth as an intensity.
Open channel and pipes
Manning's equation, Q = (1.486/n) A R^(2/3) S^(1/2), is in US customary units. Hydraulic radius R = A/P, not depth. For circular pipes, partial-flow conditions can produce higher velocity than full flow, so do not assume full-pipe capacity is maximum. Energy and hydraulic grade lines help track head loss; minor losses use K V²/2g.
Worked example
A 10-acre catchment has C = 0.5 and a 25-year intensity of 2.0 in/hr. Q = 0.5 × 2.0 × 10 = 10 cfs. If the intensity were given as 2.0 inches in 24 hours, the result would be wrong by orders of magnitude. Keep rainfall intensity and depth distinct.
Treatment
For water treatment, know coagulation, flocculation, sedimentation, filtration, and disinfection, plus CT concepts. For wastewater, understand BOD, suspended solids, nitrification, and solids retention time. A trap is confusing influent and effluent concentrations when computing removal efficiency. Efficiency = (in − out)/in × 100.
Flow models, reservoirs and hydraulic structures
Continuity is a balance over a defined control volume. For steady incompressible flow, discharge equals velocity times flow area. An unsteady reservoir requires storage change as well as inflow and outflow. The storage balance is not a complete routing model until the relevant level-storage and discharge relationships are specified. A return period describes a model probability framework rather than a guarantee of evenly spaced floods.
Separate pressure head, velocity head and elevation head before writing an energy equation. Pump head adds mechanical energy to the fluid; losses dissipate it. Darcy friction factors and Fanning friction factors differ by a factor of four and must not be mixed. Open-channel critical flow depends on geometry and the Froude criterion, while normal depth depends on slope and resistance. A hydraulic jump dissipates energy even though a suitable momentum balance can relate its conjugate depths.
A dam or retaining hydraulic structure requires more than a resisting-to-driving moment ratio. Uplift, seepage, foundation defects, deformation compatibility, loading scenarios and construction details can control. Scour may alter the supporting ground and expose a previously buried element. Turbine or pump efficiency requires a compatible input-output boundary. A classroom head, power or flow calculation does not verify flood capacity, foundation adequacy or life-safety performance; those remain project-specific engineering responsibilities.