Drainage calculations and engineering

The design of hydraulic structures from small culverts to large dams requires engineers to calculate the amount of water that will flow through the channel along which the structure is built. The rate of flow through a stream channel, or discharge, is measured using units of cubic feet per second for engineering

projects in the United States, and in units of cubic meters per second in other countries.

In many cases, knowledge of the maximum rate of flow that is likely to occur in a channel is required. For example, an engineer may wish to ensure that a bridge will be built high enough to allow passage of the largest flood likely to occur during the useful life of the bridge. If the maximum discharge is known or can be estimated, then it is a simple matter to calculate the height to which water will rise in a given channel. This is can be accomplished using Manning's equation, which relates discharge to the channel cross-sectional area and perimeter, the channel slope, and channel roughness.

The relationship between precipitation and the discharge of nearby streams is controlled by many factors. These include rainfall intensity and duration, drainage basin area, topography , soil and bedrock type, land use, vegetative ground cover, and the amount of precipitation in the days or weeks before a storm. Because it is difficult to incorporate this degree of complexity into mathematical models reflecting the physics of precipitation and stream discharges, let alone forecast the weather , probabilistic approaches based on the historical frequency of peak discharges are commonly used in engineering calculations. For drainage basins in which a long record of maximum annual discharges is available, discharges can be ranked from largest to smallest. Standard formulae are then used to estimate the probability that a given discharge will be exceeded over a specified period of time. A 100-year flood, for example, is one with a discharge that is inferred to occur on average once every 100 years. The term "on average" is an important qualifier because it means that a 100-year flood may occur more or less often than once every 100 years.

The probability that a discharge of given magnitude will occur over a specified time period is estimated using a binomial probability distribution. The binomial distribution can be used to show that there is a 37% chance that no 100-year flood will occur during any given 100-year period. Similarly, there is an 18% probability that two 100-year floods will occur during any given 100-year period. This logic can be extended to determine with a specified level of certainty the largest discharge that is likely to occur during the useful life of a hydraulic structure. An engineer designing a flood conveyance channel large enough to handle the discharge with a 90% like-lihood of not being exceeded during the 50 year useful life of the channel would not use the discharge of the 50-year flood, but rather the discharge of the 475-year flood.

In some cases, particularly in small or remote drainage basins, flood discharge records may not be available and other methods must be used. One of the simplest techniques is the rational method, which relates peak stream discharge to the product of drainage basin area, rainfall intensity, and a coefficient representing the type of land use or ground cover in the drainage basin. In the United States, the rational method uses units of inches per hour for rainfall intensity and acres for drainage basin area. Values for the coefficient are tabulated in engineering reference books, and range from 0.05 for grassy areas with sandy soil to 0.95 for paved areas. The values can be averaged in cases where there are several different land uses within a drainage basin.

More sophisticated techniques can be used when the change in discharge as a function of time, as opposed to simply the peak discharge, is an important factor in design.

See also Drainage basins and drainage patterns; Hydrologic cycle; Stream valleys, channels, and floodplains