# Discharge (hydrology)

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In hydrology, discharge is the volumetric flow rate of water that is transported through a given cross-sectional area. [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.

## Contents

Synonyms vary by discipline. For example, a fluvial hydrologist studying natural river systems may define discharge as streamflow, whereas an engineer operating a reservoir system might define discharge as outflow, which is contrasted with inflow.

## Theory and calculation

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.

## 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.

## Catchement effects on river discharge and morphology

GH Dury and MJ 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' [3] and on land use affecting river discharge and bedload supply [4] .

## Related Research Articles

A stream gauge, streamgage or 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 location 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 in a variety of ways. The common types of flowmeters with industrial applications are listed below:

In geography and geology, fluvial processes are associated with rivers and streams and the deposits and landforms created by them. When the stream or rivers are associated with glaciers, ice sheets, or ice caps, the term glaciofluvial or fluvioglacial is used.

In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate is the volume of fluid which passes per unit time; usually represented by the symbol Q. The SI unit is cubic metres per second (m3/s). Another unit used is standard cubic centimetres per minute (sccm).

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 . 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.

The Manning formula is an empirical formula estimating the average velocity of a liquid flowing in a conduit that does not completely enclose the liquid, i.e., open channel flow. However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also possess a free surface like that of open channel flow. All flow in so-called open channels is driven by gravity. It was first presented by the French engineer Philippe Gauckler in 1867, and later re-developed by the Irish engineer Robert Manning in 1890.

Streamflow, or channel runoff, is the flow of water in streams, rivers, and other channels, and is a major element of the water cycle. It is one component of the runoff 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. Baseflow is the portion of streamflow delayed shallow subsurface flow". It should not be confused with groundwater flow. Fair weather flow is called as Base flow.

The wetted perimeter is the perimeter of the cross sectional area that is "wet". 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 a derived SI unit of volumetric flow rate equal to that of a stere or cube with sides of one metre 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.

Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are clastic rocks, mud, or clay; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in rivers, oceans, lakes, seas, and other bodies of water due to currents and tides. Transport is also caused by glaciers as they flow, and on terrestrial surfaces under the influence of wind. Sediment transport due only to gravity can occur on sloping surfaces in general, including hillslopes, scarps, cliffs, and the continental shelf—continental slope boundary.

River regime can describe one of two characteristics of a reach of an alluvial river:

A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases a river flows into the ground and becomes dry at the end of its course without reaching another body of water. Small rivers can be referred to using names such as stream, creek, brook, rivulet, and rill. 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.

The depth–slope product is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow. It is widely used in river engineering, stream restoration, sedimentology, and fluvial geomorphology. It is the product of the water depth and the mean bed slope, along with the acceleration due to gravity and density of the fluid.

Stream power is the rate of energy dissipation against the bed and banks of a river or stream per unit downstream length. It is given by the equation:

An alluvial river is one in which the bed and banks are made up of mobile sediment and/or soil. Alluvial rivers are self-formed, meaning that their channels are shaped by the magnitude and frequency of the floods that they experience, and the ability of these floods to erode, deposit, and transport sediment. For this reason, alluvial rivers can assume a number of forms based on the properties of their banks; the flows they experience; the local riparian ecology; and the amount, size, and type of sediment that they carry.

Bank erosion is the wearing away of the banks of a stream or river. This is distinguished from erosion of the bed of the watercourse, which is referred to as scour.

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. Leopold, L.B., Wolman, M.G. and Miller, J.P. Fluvial Processes in geomorphology, W.H. Freeman, San Francisco 1964
4. Kondolf, GM, Piégay, H, Landon, N. 2002. Channel response to increased and decreased bedload supply from land use change: contrasts between two catchments. Geomorphology, 45, 1-2, 35-51
• "Chapter 14: Stage-Discharge Relationships" (PDF). USDA NRCS National Engineering Handbook. Part 630: Hydrology. USDA. April 2012.
• USDA NRCS National Engineering Handbook. Part 630: Hydrology. USDA. May 2012.