# Discharge (hydrology)

Last updated

In hydrology, discharge is the volumetric flow rate (volume per time, in units of m3/h or ft3/h) of a stream. It equals the product of average flow velocity (with dimension of length per time, in m/h or ft/h) and the cross-sectional area (in m2 or ft2). [1] It includes any suspended solids (e.g. sediment), dissolved chemicals (e.g. CaCO3(aq)), or biologic material (e.g. diatoms) in addition to the water itself. Terms may vary between disciplines. For example, a fluvial hydrologist studying natural river systems may define discharge as streamflow, whereas an engineer operating a reservoir system may equate it with outflow, contrasted with inflow.

## Formulation

A discharge is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass. Thus the water discharge of a tap (faucet) can be measured with a measuring jug and a stopwatch. Here the discharge might be 1 litre per 15 seconds, equivalent to 67 ml/second or 4 litres/minute. This is an average measure. For measuring the discharge of a river we need a different method and the most common is the 'area-velocity' method. The area is the cross sectional area across a river and the average velocity across that section needs to be measured for a unit time, commonly a minute. Measurement of cross sectional area and average velocity, although simple in concept, are frequently non-trivial to determine.

The units that are typically used to express discharge in streams or rivers include m3/s (cubic meters per second), ft3/s (cubic feet per second or cfs) and/or acre-feet per day. [2]

A commonly applied methodology for measuring, and estimating, the discharge of a river is based on a simplified form of the continuity equation. The equation implies that for any incompressible fluid, such as liquid water, the discharge (Q) is equal to the product of the stream's cross-sectional area (A) and its mean velocity (${\displaystyle {\bar {u}}}$), and is written as:

${\displaystyle Q=A\,{\bar {u}}}$

where

• ${\displaystyle Q}$ is the discharge ([L3T−1]; m3/s or ft3/s)
• ${\displaystyle A}$ is the cross-sectional area of the portion of the channel occupied by the flow ([L2]; m2 or ft2)
• ${\displaystyle {\bar {u}}}$ is the average flow velocity ([LT−1]; m/s or ft/s)

For example, the average discharge of the Rhine river in Europe is 2,200 cubic metres per second (78,000 cu ft/s) or 190,000,000 cubic metres (150,000 acre⋅ft) per day.

Because of the difficulties of measurement, a stream gauge is often used at a fixed location on the stream or river.

## Hydrograph

A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel, or conduit carrying flow. The rate of flow is typically expressed in cubic meters or cubic feet per second (cms or cfs).

Hydrographs often relate changes of precipitation to changes in discharge over time. [3] It can also refer to a graph showing the volume of water reaching a particular outfall, or location in a sewerage network. Graphs are commonly used in the design of sewerage, more specifically, the design of surface water sewerage systems and combined sewers.

## Catchment discharge

The catchment of a river above a certain location is determined by the surface area of all land which drains toward the river from above that point. The river's discharge at that location depends on the rainfall on the catchment or drainage area and the inflow or outflow of groundwater to or from the area, stream modifications such as dams and irrigation diversions, as well as evaporation and evapotranspiration from the area's land and plant surfaces. In storm hydrology, an important consideration is the stream's discharge hydrograph, a record of how the discharge varies over time after a precipitation event. The stream rises to a peak flow after each precipitation event, then falls in a slow recession. Because the peak flow also corresponds to the maximum water level reached during the event, it is of interest in flood studies. Analysis of the relationship between precipitation intensity and duration and the response of the stream discharge are aided by the concept of the unit hydrograph, which represents the response of stream discharge over time to the application of a hypothetical "unit" amount and duration of rainfall (e.g., half an inch over one hour). The amount of precipitation correlates to the volume of water (depending on the area of the catchment) that subsequently flows out of the river. Using the unit hydrograph method, actual historical rainfalls can be modeled mathematically to confirm characteristics of historical floods, and hypothetical "design storms" can be created for comparison to observed stream responses.

The relationship between the discharge in the stream at a given cross-section and the level of the stream is described by a rating curve. Average velocities and the cross-sectional area of the stream are measured for a given stream level. The velocity and the area give the discharge for that level. After measurements are made for several different levels, a rating table or rating curve may be developed. Once rated, the discharge in the stream may be determined by measuring the level, and determining the corresponding discharge from the rating curve. If a continuous level-recording device is located at a rated cross-section, the stream's discharge may be continuously determined.

Larger flows (higher discharges) can transport more sediment and larger particles downstream than smaller flows due to their greater force. Larger flows can also erode stream banks and damage public infrastructure.

## Catchment effects on discharge and morphology

G. H. Dury and M. J. Bradshaw are two geographers who devised models showing the relationship between discharge and other variables in a river. The Bradshaw model described how pebble size and other variables change from source to mouth; while Dury considered the relationships between discharge and variables such as stream slope and friction. These follow from the ideas presented by Leopold, Wolman and Miller in Fluvial Processes in Geomorphology. [4] and on land use affecting river discharge and bedload supply. [5]

## Inflow

Inflow is the sum of processes within the hydrologic cycle that increase the water levels of bodies of water. [6] Most precipitation occurs directly over bodies of water such as the oceans, or on land as surface runoff. [7] A portion of runoff enters streams and rivers, and another portion soaks into the ground as groundwater seepage. [8] The rest soaks into the ground as infiltration, some of which infiltrates deep into the ground to replenish aquifers. [9]

## Related Research Articles

A stream gauge, streamgage or stream gauging station is a location used by hydrologists or environmental scientists to monitor and test terrestrial bodies of water. Hydrometric measurements of water level surface elevation ("stage") and/or volumetric discharge (flow) are generally taken and observations of biota and water quality may also be made. The locations of gauging stations are often found on topographical maps. Some gauging stations are highly automated and may include telemetry capability transmitted to a central data logging facility.

Flow measurement is the quantification of bulk fluid movement. Flow can be measured using devices called flowmeters in various ways. The common types of flowmeters with industrial applications are listed below:

In physics and engineering, in particular fluid dynamics, the volumetric flow rate is the volume of fluid which passes per unit time; usually it is represented by the symbol Q. It contrasts with mass flow rate, which is the other main type of fluid flow rate. In most contexts a mention of rate of fluid flow is likely to refer to the volumetric rate. In hydrometry, the volumetric flow rate is known as discharge.

A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel, or conduit carrying flow. The rate of flow is typically expressed in cubic meters or cubic feet per second . Hydrographs often relate changes of precipitation to changes in discharge over time. It can also refer to a graph showing the volume of water reaching a particular outfall, or location in a sewerage network. Graphs are commonly used in the design of sewerage, more specifically, the design of surface water sewerage systems and combined sewers.

Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum.

In hydrology, there are two similar but distinct definitions in use for the word drawdown:

Ecohydrology is an interdisciplinary scientific field studying the interactions between water and ecological systems. It is considered a sub discipline of hydrology, with an ecological focus. These interactions may take place within water bodies, such as rivers and lakes, or on land, in forests, deserts, and other terrestrial ecosystems. Areas of research in ecohydrology include transpiration and plant water use, adaption of organisms to their water environment, influence of vegetation and benthic plants on stream flow and function, and feedbacks between ecological processes, the soil carbon sponge and the hydrological cycle.

Drainage density is a quantity used to describe physical parameters of a drainage basin. First described by Robert E. Horton, drainage density is defined as the total length of channel in a drainage basin divided by the total area, represented by the following equation:

The United States Environmental Protection Agency (EPA) Storm Water Management Model (SWMM) is a dynamic rainfall–runoff–subsurface runoff simulation model used for single-event to long-term (continuous) simulation of the surface/subsurface hydrology quantity and quality from primarily urban/suburban areas.

The law of water balance states that the inflows to any water system or area is equal to its outflows plus change in storage during a time interval. In hydrology, a water balance equation can be used to describe the flow of water in and out of a system. A system can be one of several hydrological or water domains, such as a column of soil, a drainage basin, an irrigation area or a city.

Streamflow, or channel runoff, is the flow of water in streams and other channels, and is a major element of the water cycle. It is one runoff component, the movement of water from the land to waterbodies, the other component being surface runoff. Water flowing in channels comes from surface runoff from adjacent hillslopes, from groundwater flow out of the ground, and from water discharged from pipes. The discharge of water flowing in a channel is measured using stream gauges or can be estimated by the Manning equation. The record of flow over time is called a hydrograph. Flooding occurs when the volume of water exceeds the capacity of the channel.

Baseflow is the portion of the streamflow that is sustained between precipitation events, fed to streams by delayed pathways. It should not be confused with groundwater flow. Fair weather flow is also called base flow.

The wetted perimeter is the perimeter of the cross sectional area that is "wet". The length of line of the intersection of channel wetted surface with a cross sectional plane normal to the flow direction. The term wetted perimeter is common in civil engineering, environmental engineering, hydrology, geomorphology, and heat transfer applications; it is associated with the hydraulic diameter or hydraulic radius. Engineers commonly cite the cross sectional area of a river.

A cubic metre per second is the unit of volumetric flow rate in the International System of Units (SI) equal to that of a stere or cube with sides of one metre (39.37 in) in length exchanged or moving each second. It is popularly used for water flow, especially in rivers and streams, and fractions for HVAC values measuring air flow.

The river regime generally describes the character of the typical fluctuations of flow of a river, but can also refer to the mathematical relationship between the river discharge and its width, depth and slope. Thus, "river regime" can describe one of two characteristics of a reach of an alluvial river:

A perennial stream is a stream that has continuous flow of surface water throughout the year in at least parts of its catchment during seasons of normal rainfall, as opposed to one whose flow is intermittent. In the absence of irregular, prolonged or extreme drought, a perennial stream is a watercourse, or segment, element or emerging body of water which continually delivers groundwater. For example, an artificial disruption of stream, variability in flow or stream selection associated with the activity in hydropower installations, do not affect this status. Perennial streams do not include stagnant water, reservoirs, cutoff lakes and ponds that persist throughout the year. All other streams, or parts of them, should be considered seasonal rivers or lakes. The stream can cycle from intermittent to perpetual through multiple iterations.

The groundwater energy balance is the energy balance of a groundwater body in terms of incoming hydraulic energy associated with groundwater inflow into the body, energy associated with the outflow, energy conversion into heat due to friction of flow, and the resulting change of energy status and groundwater level.

A river is a natural flowing watercourse, usually a freshwater stream, flowing on the Earth's land surface or inside caves towards another waterbody at a lower elevation, such as an ocean, sea, bay, lake, wetland, or another river. In some cases, a river flows into the ground or becomes dry at the end of its course without reaching another body of water. Small rivers can be referred to by names such as creek, brook, and rivulet. There are no official definitions for the generic term river as applied to geographic features, although in some countries or communities, a stream is defined by its size. Many names for small rivers are specific to geographic location; examples are "run" in some parts of the United States, "burn" in Scotland and Northeast England, and "beck" in Northern England. Sometimes a river is defined as being larger than a creek, but not always; the language is vague.

Stream power, originally derived by R. A. Bagnold in the 1960s, is the amount of energy the water in a river or stream is exerting on the sides and bottom of the river. Stream power is the result of multiplying the density of the water, the acceleration of the water due to gravity, the volume of water flowing through the river, and the slope of that water. There are many forms of the stream power formula with varying utilities, such as comparing rivers of various widths or quantifying the energy required to move sediment of a certain size. Stream power is closely related to other criteria such as stream competency and shear stress. Stream power is a valuable measurement for hydrologists and geomorphologists tackling sediment transport issues as well as for civil engineers, who use it in the planning and construction of roads, bridges, dams, and culverts.

In hydrology stream competency, also known as stream competence, is a measure of the maximum size of particles a stream can transport. The particles are made up of grain sizes ranging from large to small and include boulders, rocks, pebbles, sand, silt, and clay. These particles make up the bed load of the stream. Stream competence was originally simplified by the “sixth-power-law,” which states the mass of a particle that can be moved is proportional to the velocity of the river raised to the sixth power. This refers to the stream bed velocity which is difficult to measure or estimate due to the many factors that cause slight variances in stream velocities.

## References

1. Buchanan, T.J. and Somers, W.P., 1969, Discharge Measurements at Gaging Stations: U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3, Chapter A8, p. 1.
2. Dunne, T., and Leopold, L.B., 1978, Water in Environmental Planning: San Francisco, Calif., W.H. Freeman, pp. 257–258.
3. Sherman, LeRoy K. (1932). "The relation of hydrographs of runoff to size and character of drainage-basins". Transactions, American Geophysical Union. 13 (1): 332. doi:10.1029/TR013i001p00332. ISSN   0002-8606.
4. L. B. Leopold, M. G. Wolman J. P. and Miller, Fluvial Processes in Geomorphology, W. H. Freeman, San Francisco, 1964.
5. G. M. Kondolf, H. Piégay and N. Landon, "Channel response to increased and decreased bedload supply from land use change: contrasts between two catchments", Geomorphology, 45/1–2, pp. 35–51.
6. "The Hydrologic Cycle | Freshwater Inflows". freshwaterinflow.org. Retrieved 2020-12-09.
7. DOC, NOAA. "Description of the Hydrologic Cycle". www.nwrfc.noaa.gov. Retrieved 2020-12-09.
8. "Groundwater Flows Underground". usgs.gov. Retrieved 2020-12-09.
9. "Precipitation and the Water Cycle". usgs.gov. Retrieved 2020-12-09.