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Radius of Influence of unconfined aquifer with known discharge Formula

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The radius of influence is the distance from a pumping well to the point where the drawdown, or lowering of the water table, becomes negligible. Check FAQs

R = r \cdot \exp (\frac{0.434 \cdot π \cdot K \cdot (H^{2} - {h fw}^{2})}{Q fe})

R - Radius of Influence?r - Radius of Well?K - Coefficient of Permeability?H - Initial Piezometric Surface?h_fw - Depth of Water in Fully Penetrating Gravity Well?Q_fe - Discharge for Fully Penetrating Gravity Well?π - Archimedes' constant?

Radius of Influence of unconfined aquifer with known discharge Example

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Here is how the Radius of Influence of unconfined aquifer with known discharge equation looks like with Values.

Here is how the Radius of Influence of unconfined aquifer with known discharge equation looks like with Units.

Here is how the Radius of Influence of unconfined aquifer with known discharge equation looks like.

2.9932 = 2.94 \cdot \exp (\frac{0.434 \cdot 3.1416 \cdot 0.105 \cdot (20^{2} - {17.98}^{2})}{6.12})

2.9932m = 2.94m \cdot \exp (\frac{0.434 \cdot 3.1416 \cdot 0.105cm/s \cdot ({20m}^{2} - {17.98m}^{2})}{6.12m³/s})

2.9932 = 2.94 \cdot \exp (\frac{0.434 \cdot 3.1416 \cdot 0.105 \cdot (20^{2} - {17.98}^{2})}{6.12})

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Radius of Influence of unconfined aquifer with known discharge Solution

Follow our step by step solution on how to calculate Radius of Influence of unconfined aquifer with known discharge?

FIRST Step Consider the formula

R = r \cdot \exp (\frac{0.434 \cdot π \cdot K \cdot (H^{2} - {h fw}^{2})}{Q fe})

Next Step Substitute values of Variables

∴

R = 2.94m \cdot \exp (\frac{0.434 \cdot π \cdot 0.105cm/s \cdot ({20m}^{2} - {17.98m}^{2})}{6.12m³/s})

Next Step Substitute values of Constants

∴

R = 2.94m \cdot \exp (\frac{0.434 \cdot 3.1416 \cdot 0.105cm/s \cdot ({20m}^{2} - {17.98m}^{2})}{6.12m³/s})

Next Step Convert Units

∴

R = 2.94m \cdot \exp (\frac{0.434 \cdot 3.1416 \cdot 0.001m/s \cdot ({20m}^{2} - {17.98m}^{2})}{6.12m³/s})

Next Step Prepare to Evaluate

∴

R = 2.94 \cdot \exp (\frac{0.434 \cdot 3.1416 \cdot 0.001 \cdot (20^{2} - {17.98}^{2})}{6.12})

Next Step Evaluate

∴

R = 2.99323950843247m

LAST Step Rounding Answer

∴

R = 2.9932m

Radius of Influence of unconfined aquifer with known discharge Formula Elements

Variables

Constants

Functions

Radius of Influence

The radius of influence is the distance from a pumping well to the point where the drawdown, or lowering of the water table, becomes negligible.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Influence

Radius of Well

The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Well

Coefficient of Permeability

Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces.

Symbol: K

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Formulas to find Coefficient of Permeability

Initial Piezometric Surface

The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Initial Piezometric Surface

Depth of Water in Fully Penetrating Gravity Well

Depth of Water in Fully Penetrating Gravity Well refers to the vertical distance from the water table to the bottom of the well, which extends through the entire thickness of the unconfined aquifer.

Symbol: h_fw

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Water in Fully Penetrating Gravity Well

Discharge for Fully Penetrating Gravity Well

Discharge for Fully Penetrating Gravity Well refers to the volume of water extracted from an unconfined aquifer where the well reaches the entire thickness of the aquifer.

Symbol: Q_fe

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge for Fully Penetrating Gravity 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

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in Fully Penetrating Artesian Gravity Well category

Go Thickness of Aquifer given Discharge for Fully Penetrating Well

H = \frac{(\frac{Q fw \cdot \log ((\frac{R}{r}), e)}{π \cdot K}) + {(b)}^{2} + {(h fw)}^{2}}{2 \cdot b}

Go Depth of Water in Well given Discharge for Fully Penetrating Well

h fw = \sqrt{(2 \cdot b \cdot H) - (\frac{Q fw \cdot \log ((\frac{R}{r}), e)}{π \cdot K}) - {(b)}^{2}}

Go Radius of Well of unconfined Aquifer with known Discharge

r = \frac{R}{\exp (\frac{0.434 \cdot π \cdot K \cdot ((H^{2}) - ({h w}^{2}))}{Q fe})}

How to Evaluate Radius of Influence of unconfined aquifer with known discharge?

Radius of Influence of unconfined aquifer with known discharge evaluator uses Radius of Influence = Radius of Well*exp((0.434*pi*Coefficient of Permeability*(Initial Piezometric Surface^2-Depth of Water in Fully Penetrating Gravity Well^2))/Discharge for Fully Penetrating Gravity Well) to evaluate the Radius of Influence, Radius of Influence of unconfined aquifer with known discharge formula is defined as the distance from the center of a pumping well to the point where the drawdown of the water table is negligible, which is a critical parameter in understanding the flow of groundwater in unconfined aquifers. Radius of Influence is denoted by R symbol.

How to evaluate Radius of Influence of unconfined aquifer with known discharge using this online evaluator? To use this online evaluator for Radius of Influence of unconfined aquifer with known discharge, enter Radius of Well (r), Coefficient of Permeability (K), Initial Piezometric Surface (H), Depth of Water in Fully Penetrating Gravity Well (h_fw) & Discharge for Fully Penetrating Gravity Well (Q_fe) and hit the calculate button.

FAQs on Radius of Influence of unconfined aquifer with known discharge

What is the formula to find Radius of Influence of unconfined aquifer with known discharge?

The formula of Radius of Influence of unconfined aquifer with known discharge is expressed as Radius of Influence = Radius of Well*exp((0.434*pi*Coefficient of Permeability*(Initial Piezometric Surface^2-Depth of Water in Fully Penetrating Gravity Well^2))/Discharge for Fully Penetrating Gravity Well). Here is an example- 2.99324 = 2.94*exp((0.434*pi*0.00105*(20^2-17.98^2))/6.12).

How to calculate Radius of Influence of unconfined aquifer with known discharge?

With Radius of Well (r), Coefficient of Permeability (K), Initial Piezometric Surface (H), Depth of Water in Fully Penetrating Gravity Well (h_fw) & Discharge for Fully Penetrating Gravity Well (Q_fe) we can find Radius of Influence of unconfined aquifer with known discharge using the formula - Radius of Influence = Radius of Well*exp((0.434*pi*Coefficient of Permeability*(Initial Piezometric Surface^2-Depth of Water in Fully Penetrating Gravity Well^2))/Discharge for Fully Penetrating Gravity Well). This formula also uses Archimedes' constant and Exponential Growth (exp) function(s).

Can the Radius of Influence of unconfined aquifer with known discharge be negative?

No, the Radius of Influence of unconfined aquifer with known discharge, measured in Length cannot be negative.

Which unit is used to measure Radius of Influence of unconfined aquifer with known discharge?

Radius of Influence of unconfined aquifer with known discharge is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius of Influence of unconfined aquifer with known discharge can be measured.

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Radius of Influence of unconfined aquifer with known discharge Formula

Radius of Influence of unconfined aquifer with known discharge Example

Radius of Influence of unconfined aquifer with known discharge Solution

Radius of Influence of unconfined aquifer with known discharge Formula Elements

Other formulas in Fully Penetrating Artesian Gravity Well category

How to Evaluate Radius of Influence of unconfined aquifer with known discharge?

FAQs on Radius of Influence of unconfined aquifer with known discharge

Variable Name