Hydrology traces the continuous movement of water through the environment. The hydrologic cycle encompasses evaporation from surface waters, transpiration from vegetation, condensation into clouds, precipitation as rain or snow, infiltration into the soil, surface runoff back to streams and rivers, and storage in groundwater, lakes, and reservoirs. Civil engineers harness this cycle by designing drainage systems, reservoirs, levees, and stormwater controls that capture and convey water safely, while also mitigating floods and droughts.
For small urban watersheds, peak runoff is commonly estimated using the rational method, expressed as Q = CiA, where Q is the peak discharge, C is a dimensionless runoff coefficient reflecting land cover and soil type, i is the rainfall intensity for the chosen storm duration, and A is the drainage area. The duration that produces the largest peak flow is the time of concentration, Tc, defined as the time required for water to travel from the hydraulically most distant point in the watershed to the outlet. Choosing i from an intensity-duration-frequency curve for a duration of Tc and the desired return period completes the calculation.
Larger watersheds require continuous or semi-continuous hydrograph methods. A unit hydrograph is the direct runoff hydrograph produced by one unit of effective rainfall distributed uniformly over the watershed for a specified duration. By scaling and superposition, unit hydrographs predict runoff from complex storms of varying intensity and duration, and they form the basis for flood routing in channels and reservoirs. Statistical analysis of historical flood records yields flood frequency estimates, often using the Log-Pearson Type III or Gumbel distributions, which relate flood magnitude to its probability of exceedance. This probability is summarized by the return period, also called the average recurrence interval, expressed in years; a 100-year flood has a 1 percent chance of being equaled or exceeded in any given year. Although often misunderstood as a guarantee, the return period properly conveys the long-term average frequency rather than a fixed cycle.
For watershed modeling, the Soil Conservation Service curve number, CN, represents the runoff potential of a catchment as a dimensionless value from 0 to 100, computed from soil group, land use, and antecedent moisture condition. Higher CN values indicate greater runoff. Paired with design rainfall depths, the curve number drives event-based runoff estimation in many practical designs. The supporting intensity-duration-frequency relationship is summarized in IDF curves, which graph rainfall intensity against storm duration for several return periods and are used directly to select design rainfall for storm sewers, culverts, bridges, and detention basins.
Hydraulic engineering takes over once flow enters channels, culverts, or storm sewers. Manning's equation, V = (1/n) R^(2/3) S^(1/2), provides the average velocity for uniform open-channel flow, where n is a roughness coefficient reflecting channel surface conditions, R is the hydraulic radius (cross-sectional area divided by wetted perimeter), and S is the energy slope. With V known and the cross-sectional area specified, designers compute discharge capacity and check whether channels and pipes can convey the design flow within available freeboard.