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Discharge at Downstream Water Body of Catchment Formula

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The Discharge at Downstream Side refers to the volume of water flowing past a specific point in a river per unit of time, measured at a location further along the river’s course, away from its source. Check FAQs

q 1 = (\frac{R \cdot L stream}{2}) + ((\frac{K}{2 \cdot L stream}) \cdot ({h o}^{2} - {h 1}^{2}))

q₁ - Discharge at Downstream Side?R - Natural Recharge?L_stream - Length between Upstream and Downstream?K - Coefficient of Permeability?h_o - Piezometric Head at Upstream End?h₁ - Piezometric Head at Downstream End?

Discharge at Downstream Water Body of Catchment Example

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Here is how the Discharge at Downstream Water Body of Catchment equation looks like with Values.

Here is how the Discharge at Downstream Water Body of Catchment equation looks like with Units.

Here is how the Discharge at Downstream Water Body of Catchment equation looks like.

34.0293 = (\frac{16 \cdot 4.09}{2}) + ((\frac{9}{2 \cdot 4.09}) \cdot (12^{2} - 5^{2}))

34.0293m³/s = (\frac{16m³/s \cdot 4.09m}{2}) + ((\frac{9cm/s}{2 \cdot 4.09m}) \cdot ({12m}^{2} - {5m}^{2}))

34.0293 = (\frac{16 \cdot 4.09}{2}) + ((\frac{9}{2 \cdot 4.09}) \cdot (12^{2} - 5^{2}))

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Discharge at Downstream Water Body of Catchment Solution

Follow our step by step solution on how to calculate Discharge at Downstream Water Body of Catchment?

FIRST Step Consider the formula

q 1 = (\frac{R \cdot L stream}{2}) + ((\frac{K}{2 \cdot L stream}) \cdot ({h o}^{2} - {h 1}^{2}))

Next Step Substitute values of Variables

∴

q 1 = (\frac{16m³/s \cdot 4.09m}{2}) + ((\frac{9cm/s}{2 \cdot 4.09m}) \cdot ({12m}^{2} - {5m}^{2}))

Next Step Convert Units

∴

q 1 = (\frac{16m³/s \cdot 4.09m}{2}) + ((\frac{0.09m/s}{2 \cdot 4.09m}) \cdot ({12m}^{2} - {5m}^{2}))

Next Step Prepare to Evaluate

∴

q 1 = (\frac{16 \cdot 4.09}{2}) + ((\frac{0.09}{2 \cdot 4.09}) \cdot (12^{2} - 5^{2}))

Next Step Evaluate

∴

q 1 = 34.0292909535452m³/s

LAST Step Rounding Answer

∴

q 1 = 34.0293m³/s

Discharge at Downstream Water Body of Catchment Formula Elements

Variables

Discharge at Downstream Side

Symbol: q₁

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge at Downstream Side

Natural Recharge

The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table.

Symbol: R

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Natural Recharge

Length between Upstream and Downstream

The Length between Upstream and Downstream refers to the horizontal base with a difference in surface elevations.

Symbol: L_stream

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length between Upstream and Downstream

Coefficient of Permeability

The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.

Symbol: K

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Formulas to find Coefficient of Permeability

Piezometric Head at Upstream End

The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum.

Symbol: h_o

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Piezometric Head at Upstream End

Piezometric Head at Downstream End

The Piezometric Head at Downstream End refers to the specific measurement of liquid pressure above a vertical datum.

Symbol: h₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Piezometric Head at Downstream End

Other formulas in One Dimensional Dupit's Flow with Recharge category

Go Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

h = \sqrt{(\frac{- R \cdot x^{2}}{K}) - ((\frac{{h o}^{2} - {h 1}^{2} - (\frac{R \cdot {L stream}^{2}}{K})}{L stream}) \cdot x) + {h o}^{2}}

Go Equation for Water Divide

a = (\frac{L stream}{2}) - (\frac{K}{R}) \cdot (\frac{{h o}^{2} - {h 1}^{2}}{2} \cdot L stream)

Go Discharge per Unit Width of Aquifer at any Location x

q x = R \cdot (x - (\frac{L stream}{2})) + (\frac{K}{2} \cdot L stream) \cdot ({h o}^{2} - {h 1}^{2})

Go Discharge Entering Drain per Unit Length of Drain

q d = 2 \cdot (R \cdot (\frac{L}{2}))

How to Evaluate Discharge at Downstream Water Body of Catchment?

Discharge at Downstream Water Body of Catchment evaluator uses Discharge at Downstream Side = ((Natural Recharge*Length between Upstream and Downstream)/2)+((Coefficient of Permeability/(2*Length between Upstream and Downstream))*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)) to evaluate the Discharge at Downstream Side, The Discharge at Downstream Water Body of Catchment formula is defined as the volumetric flow rate of water that is transported through a given cross-sectional area at the downstream water body. Discharge at Downstream Side is denoted by q₁ symbol.

How to evaluate Discharge at Downstream Water Body of Catchment using this online evaluator? To use this online evaluator for Discharge at Downstream Water Body of Catchment, enter Natural Recharge (R), Length between Upstream and Downstream (L_stream), Coefficient of Permeability (K), Piezometric Head at Upstream End (h_o) & Piezometric Head at Downstream End (h₁) and hit the calculate button.

FAQs on Discharge at Downstream Water Body of Catchment

What is the formula to find Discharge at Downstream Water Body of Catchment?

The formula of Discharge at Downstream Water Body of Catchment is expressed as Discharge at Downstream Side = ((Natural Recharge*Length between Upstream and Downstream)/2)+((Coefficient of Permeability/(2*Length between Upstream and Downstream))*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)). Here is an example- 34.02929 = ((16*4.09)/2)+((0.09/(2*4.09))*(12^2-5^2)).

How to calculate Discharge at Downstream Water Body of Catchment?

With Natural Recharge (R), Length between Upstream and Downstream (L_stream), Coefficient of Permeability (K), Piezometric Head at Upstream End (h_o) & Piezometric Head at Downstream End (h₁) we can find Discharge at Downstream Water Body of Catchment using the formula - Discharge at Downstream Side = ((Natural Recharge*Length between Upstream and Downstream)/2)+((Coefficient of Permeability/(2*Length between Upstream and Downstream))*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)).

Can the Discharge at Downstream Water Body of Catchment be negative?

No, the Discharge at Downstream Water Body of Catchment, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Discharge at Downstream Water Body of Catchment?

Discharge at Downstream Water Body of Catchment is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Discharge at Downstream Water Body of Catchment can be measured.

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Discharge at Downstream Water Body of Catchment Formula

Discharge at Downstream Water Body of Catchment Example

Discharge at Downstream Water Body of Catchment Solution

Discharge at Downstream Water Body of Catchment Formula Elements

Other formulas in One Dimensional Dupit's Flow with Recharge category

How to Evaluate Discharge at Downstream Water Body of Catchment?

FAQs on Discharge at Downstream Water Body of Catchment

Variable Name