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Discharge at Edge of Zone of Influence Formula

GoEquilibrium Equation for Well in Unconfined Aquifer Formula

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The Steady Flow of an Unconfined Aquifer refers to a condition where the groundwater flow rate and the water table level remain constant over time. Check FAQs

Q u = π \cdot K \cdot \frac{H^{2} - {h w}^{2}}{\ln (\frac{r}{R w})}

Q_u - Steady Flow of an Unconfined Aquifer?K - Coefficient of Permeability?H - Saturated Thickness of the Aquifer?h_w - Depth of Water in the Pumping Well?r - Radius at the Edge of Zone of Influence?R_w - Radius of the Pumping Well?π - Archimedes' constant?

Discharge at Edge of Zone of Influence Example

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Here is how the Discharge at Edge of Zone of Influence equation looks like with Values.

Here is how the Discharge at Edge of Zone of Influence equation looks like with Units.

Here is how the Discharge at Edge of Zone of Influence equation looks like.

64.3897 = 3.1416 \cdot 9 \cdot \frac{35^{2} - 30^{2}}{\ln (\frac{25}{6})}

64.3897m³/s = 3.1416 \cdot 9cm/s \cdot \frac{{35m}^{2} - {30m}^{2}}{\ln (\frac{25m}{6m})}

64.3897 = 3.1416 \cdot 9 \cdot \frac{35^{2} - 30^{2}}{\ln (\frac{25}{6})}

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Discharge at Edge of Zone of Influence Solution

Follow our step by step solution on how to calculate Discharge at Edge of Zone of Influence?

FIRST Step Consider the formula

Q u = π \cdot K \cdot \frac{H^{2} - {h w}^{2}}{\ln (\frac{r}{R w})}

Next Step Substitute values of Variables

∴

Q u = π \cdot 9cm/s \cdot \frac{{35m}^{2} - {30m}^{2}}{\ln (\frac{25m}{6m})}

Next Step Substitute values of Constants

∴

Q u = 3.1416 \cdot 9cm/s \cdot \frac{{35m}^{2} - {30m}^{2}}{\ln (\frac{25m}{6m})}

Next Step Convert Units

∴

Q u = 3.1416 \cdot 0.09m/s \cdot \frac{{35m}^{2} - {30m}^{2}}{\ln (\frac{25m}{6m})}

Next Step Prepare to Evaluate

∴

Q u = 3.1416 \cdot 0.09 \cdot \frac{35^{2} - 30^{2}}{\ln (\frac{25}{6})}

Next Step Evaluate

∴

Q u = 64.3896937725745m³/s

LAST Step Rounding Answer

∴

Q u = 64.3897m³/s

Discharge at Edge of Zone of Influence Formula Elements

Variables

Constants

Functions

Steady Flow of an Unconfined Aquifer

The Steady Flow of an Unconfined Aquifer refers to a condition where the groundwater flow rate and the water table level remain constant over time.

Symbol: Q_u

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Steady Flow of an Unconfined Aquifer

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

Saturated Thickness of the Aquifer

The Saturated Thickness of the Aquifer refers to the vertical height of the aquifer in which the pore spaces are completely filled with water.

Symbol: H

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Saturated Thickness of the Aquifer

Depth of Water in the Pumping Well

The Depth of Water in the Pumping Well refers to the well in which pumping is required to increase the formation pressure to allow the free production flow.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Water in the Pumping Well

Radius at the Edge of Zone of Influence

The Radius at the Edge of Zone of Influence refers to the maximum distance from a pumping well where the effects of drawdown (lowering of the water table) can be detected.

Symbol: r

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius at the Edge of Zone of Influence

Radius of the Pumping Well

The Radius of the Pumping Well refers to the physical radius of the well itself, typically measured from the center of the well to its outer edge.

Symbol: R_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of the Pumping Well

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Steady Flow of an Unconfined Aquifer

Go Equilibrium Equation for Well in Unconfined Aquifer

Q u = π \cdot K \cdot \frac{{H 2}^{2} - {H 1}^{2}}{\ln (\frac{r 2}{r 1})}

Other formulas in Unconfined Flow category

Go Coefficient of Permeability when Equilibrium Equation for Well in Unconfined Aquifer

K = \frac{Q u}{π \cdot \frac{{H 2}^{2} - {H 1}^{2}}{\ln (\frac{r 2}{r 1})}}

Go Saturated Thickness of Aquifer when Steady Flow of Unconfined Aquifer is Considered

H = \sqrt{\frac{Q u \cdot \ln (\frac{r}{R w})}{π \cdot K} + {h w}^{2}}

Go Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered

h w = \sqrt{{(H)}^{2} - (\frac{Q u \cdot \ln (\frac{r}{R w})}{π \cdot K})}

How to Evaluate Discharge at Edge of Zone of Influence?

Discharge at Edge of Zone of Influence evaluator uses Steady Flow of an Unconfined Aquifer = pi*Coefficient of Permeability*(Saturated Thickness of the Aquifer^2-Depth of Water in the Pumping Well^2)/ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well) to evaluate the Steady Flow of an Unconfined Aquifer, The Discharge at Edge of Zone of Influence formula is defined as the volumetric flow rate of water that is transported through a given cross-sectional area. Steady Flow of an Unconfined Aquifer is denoted by Q_u symbol.

How to evaluate Discharge at Edge of Zone of Influence using this online evaluator? To use this online evaluator for Discharge at Edge of Zone of Influence, enter Coefficient of Permeability (K), Saturated Thickness of the Aquifer (H), Depth of Water in the Pumping Well (h_w), Radius at the Edge of Zone of Influence (r) & Radius of the Pumping Well (R_w) and hit the calculate button.

FAQs on Discharge at Edge of Zone of Influence

What is the formula to find Discharge at Edge of Zone of Influence?

The formula of Discharge at Edge of Zone of Influence is expressed as Steady Flow of an Unconfined Aquifer = pi*Coefficient of Permeability*(Saturated Thickness of the Aquifer^2-Depth of Water in the Pumping Well^2)/ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well). Here is an example- 64.38969 = pi*0.09*(35^2-30^2)/ln(25/6).

How to calculate Discharge at Edge of Zone of Influence?

With Coefficient of Permeability (K), Saturated Thickness of the Aquifer (H), Depth of Water in the Pumping Well (h_w), Radius at the Edge of Zone of Influence (r) & Radius of the Pumping Well (R_w) we can find Discharge at Edge of Zone of Influence using the formula - Steady Flow of an Unconfined Aquifer = pi*Coefficient of Permeability*(Saturated Thickness of the Aquifer^2-Depth of Water in the Pumping Well^2)/ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Steady Flow of an Unconfined Aquifer?

Here are the different ways to Calculate Steady Flow of an Unconfined Aquifer-

Steady Flow of an Unconfined Aquifer=pi*Coefficient of Permeability*(Water Table Depth 2^2-Water Table Depth^2)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1)

Can the Discharge at Edge of Zone of Influence be negative?

No, the Discharge at Edge of Zone of Influence, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Discharge at Edge of Zone of Influence?

Discharge at Edge of Zone of Influence 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 Edge of Zone of Influence can be measured.

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Discharge at Edge of Zone of Influence Formula

​GoEquilibrium Equation for Well in Unconfined Aquifer Formula

Discharge at Edge of Zone of Influence Example

Discharge at Edge of Zone of Influence Solution

Discharge at Edge of Zone of Influence Formula Elements

Other Formulas to find Steady Flow of an Unconfined Aquifer

Other formulas in Unconfined Flow category

How to Evaluate Discharge at Edge of Zone of Influence?

FAQs on Discharge at Edge of Zone of Influence

Variable Name

GoEquilibrium Equation for Well in Unconfined Aquifer Formula