Discharge (hydrology)

Encyclopedia

In hydrology

,

flow, including any suspended solids (i.e. sediment), dissolved chemical species (i.e. CaCO

, whereas an engineer operating a reservoir system might define discharge as

.

GH Dury and MJ Bradshaw

are two hydrologists who devised models showing the relationship between discharge and other variables in a river. Bradshaw

reviewed how pebble size and other variables changed from source to mouth; whilst Dury considered the relationship between discharge and variable such as slope and friction are interrelated.

The units

that are typically used to express discharge include m³/s (cubic meters per second), ft³/s (cubic feet per second or cfs) and/or acre-feet per day. For example, the average discharge of the Rhine river in Europe is 2200 m3/s or 154000 acre.ft per day.

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 (), and is written as:

where

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 is mmm 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 rain, for example 1 cm over the entire catchment for a period of one hour. This represents a certain volume of water (depending on the area of the catchment) which must subsequently flow out of the river. Using this method either actual historical rainfalls or hypothetical "design storms" can be modeled mathematically to confirm characteristics of historical floods, or to predict a stream's reaction to a predited storm.

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.

Flows with larger discharges are able to transport

more sediment

downstream.

Hydrology

Hydrology is the study of the movement, distribution, and quality of water on Earth and other planets, including the hydrologic cycle, water resources and environmental watershed sustainability...

,

**discharge**is the volume rate of waterWater

Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

flow, including any suspended solids (i.e. sediment), dissolved chemical species (i.e. CaCO

_{3}_{(aq)}) and/or biologic material (i.e. diatoms), which is transported through a given cross-sectional area. Frequently, other terms synonymous with discharge are used to describe the volumetric flow rate of water and are typically discipline dependent. For example, a fluvial hydrologist studying natural river systems may define discharge as streamflowStreamflow

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...

, whereas an engineer operating a reservoir system might define discharge as

**outflow**, which is contrasted with inflowInflow (hydrology)

In hydrology, the inflow of a body of water is the source of the water in the body of water. It can also refer to the average volume of incoming water in unit time. It is contrasted with outflow....

.

GH Dury and MJ Bradshaw

Bradshaw model

The Bradshaw Model is a geographical model which describes how a river's characteristics vary between the upper course and lower course of a river. It shows that discharge, occupied channel width, channel depth and average load quantity increases downstream...

are two hydrologists who devised models showing the relationship between discharge and other variables in a river. Bradshaw

Bradshaw model

The Bradshaw Model is a geographical model which describes how a river's characteristics vary between the upper course and lower course of a river. It shows that discharge, occupied channel width, channel depth and average load quantity increases downstream...

reviewed how pebble size and other variables changed from source to mouth; whilst Dury considered the relationship between discharge and variable such as slope and friction are interrelated.

The units

Units of measurement

A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

that are typically used to express discharge include m³/s (cubic meters per second), ft³/s (cubic feet per second or cfs) and/or acre-feet per day. For example, the average discharge of the Rhine river in Europe is 2200 m3/s or 154000 acre.ft per day.

A commonly applied methodology for measuring, and estimating, the discharge of a river is based on a simplified form of the continuity equation

Continuity equation

A continuity equation in physics is a differential equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described...

. 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 (), and is written as:

where

- is the discharge ([L
^{3}T^{−1}]; m^{3}/s or ft^{3}/s) - is the cross-sectional areaAreaArea is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

of the portion of the channel occupied by the flow ([L^{2}]; m^{2}or ft^{2}) - is the average flow velocityVelocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

([LT^{−1}]; m/s or ft/s)

## Catchment discharge

The catchmentDrainage basin

A drainage basin is an extent or an area of land where surface water from rain and melting snow or ice converges to a single point, usually the exit of the basin, where the waters join another waterbody, such as a river, lake, reservoir, estuary, wetland, sea, or ocean...

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

Recession

In economics, a recession is a business cycle contraction, a general slowdown in economic activity. During recessions, many macroeconomic indicators vary in a similar way...

. 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 is mmm 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 rain, for example 1 cm over the entire catchment for a period of one hour. This represents a certain volume of water (depending on the area of the catchment) which must subsequently flow out of the river. Using this method either actual historical rainfalls or hypothetical "design storms" can be modeled mathematically to confirm characteristics of historical floods, or to predict a stream's reaction to a predited storm.

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

Rating curve

In hydrology, a Rating curve is a graph of discharge versus stage for a given point on a stream, usually at gauging stations, where the stream discharge is measured across the stream channel with a flow meter . Numerous measurements of stream discharge are made over a range of stream stages...

. 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.

Flows with larger discharges are able to transport

Sediment transport

Sediment transport is the movement of solid particles , typically due to a combination of the force of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained...

more sediment

Sediment

Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....

downstream.

## See also

- List of rivers by average discharge
- Volumetric flow rateVolumetric flow rateThe volumetric flow rate in fluid dynamics and hydrometry, is the volume of fluid which passes through a given surface per unit time...
- Groundwater discharge
- Submarine groundwater dischargeSubmarine groundwater dischargeSubmarine groundwater discharge is the net inflow of fresh water through an aquifer medium to the sea. Depending upon the hydrogeology, nutrient loads, and location, the SGD may vary. It is greatly dependent on the tides. Especially in the estuary regions, SGD is more relevant. It is important in...

## External links

- USDA NRCS National Engineering Handbook, Stage Discharge Relationships, Ch. 14
- USDA NRCS National Engineering Handbook