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Discharge per Unit Width of Aquifer at any Location x Formula

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The Discharge of Aquifer at any Location x refers to the volumetric flow rate of water that is transported through a given cross-sectional area. Check FAQs

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

q_x - Discharge of Aquifer at any Location x?R - Natural Recharge?x - Flow in 'x' Direction?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 per Unit Width of Aquifer at any Location x Example

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Here is how the Discharge per Unit Width of Aquifer at any Location x equation looks like with Values.

Here is how the Discharge per Unit Width of Aquifer at any Location x equation looks like with Units.

Here is how the Discharge per Unit Width of Aquifer at any Location x equation looks like.

21.182 = 16 \cdot (2 - (\frac{4.09}{2})) + (\frac{9}{2} \cdot 4.09) \cdot (12^{2} - 5^{2})

21.182m³/s = 16m³/s \cdot (2m³/s - (\frac{4.09m}{2})) + (\frac{9cm/s}{2} \cdot 4.09m) \cdot ({12m}^{2} - {5m}^{2})

21.182 = 16 \cdot (2 - (\frac{4.09}{2})) + (\frac{9}{2} \cdot 4.09) \cdot (12^{2} - 5^{2})

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Discharge per Unit Width of Aquifer at any Location x Solution

Follow our step by step solution on how to calculate Discharge per Unit Width of Aquifer at any Location x?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

q x = 21.18195m³/s

LAST Step Rounding Answer

∴

q x = 21.182m³/s

Discharge per Unit Width of Aquifer at any Location x Formula Elements

Variables

Discharge of Aquifer at any Location x

The Discharge of Aquifer at any Location x refers to the volumetric flow rate of water that is transported through a given cross-sectional area.

Symbol: q_x

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Discharge of Aquifer at any Location x

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

Flow in 'x' Direction

The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation.

Symbol: x

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Flow in 'x' Direction

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)

How to Evaluate Discharge per Unit Width of Aquifer at any Location x?

Discharge per Unit Width of Aquifer at any Location x evaluator uses Discharge of Aquifer at any Location x = Natural Recharge*(Flow in 'x' Direction-(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 of Aquifer at any Location x, The Discharge per Unit Width of Aquifer at any Location x is defined as the volumetric flow rate of water that is transported through a given cross-sectional area. Discharge of Aquifer at any Location x is denoted by q_x symbol.

How to evaluate Discharge per Unit Width of Aquifer at any Location x using this online evaluator? To use this online evaluator for Discharge per Unit Width of Aquifer at any Location x, enter Natural Recharge (R), Flow in 'x' Direction (x), 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 per Unit Width of Aquifer at any Location x

What is the formula to find Discharge per Unit Width of Aquifer at any Location x?

The formula of Discharge per Unit Width of Aquifer at any Location x is expressed as Discharge of Aquifer at any Location x = Natural Recharge*(Flow in 'x' Direction-(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- 21.18195 = 16*(2-(4.09/2))+(0.09/2*4.09)*(12^2-5^2).

How to calculate Discharge per Unit Width of Aquifer at any Location x?

With Natural Recharge (R), Flow in 'x' Direction (x), 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 per Unit Width of Aquifer at any Location x using the formula - Discharge of Aquifer at any Location x = Natural Recharge*(Flow in 'x' Direction-(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 per Unit Width of Aquifer at any Location x be negative?

Yes, the Discharge per Unit Width of Aquifer at any Location x, measured in Volumetric Flow Rate can be negative.

Which unit is used to measure Discharge per Unit Width of Aquifer at any Location x?

Discharge per Unit Width of Aquifer at any Location x 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 per Unit Width of Aquifer at any Location x can be measured.

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Discharge per Unit Width of Aquifer at any Location x Formula

Discharge per Unit Width of Aquifer at any Location x Example

Discharge per Unit Width of Aquifer at any Location x Solution

Discharge per Unit Width of Aquifer at any Location x Formula Elements

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

How to Evaluate Discharge per Unit Width of Aquifer at any Location x?

FAQs on Discharge per Unit Width of Aquifer at any Location x

Variable Name