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Radius of Influence given Discharge for Partially Penetrating Well 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{2 \cdot π \cdot K \cdot b \cdot (H - h w) \cdot G}{Q v}))

R - Radius of Influence?r - Radius of Well?K - Coefficient of Permeability?b - Aquifer Thickness?H - Initial Piezometric Surface?h_w - Depth of Water?G - Correction Factor?Q_v - Discharge for Partially Penetrating Well?π - Archimedes' constant?

Radius of Influence given Discharge for Partially Penetrating Well Example

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Here is how the Radius of Influence given Discharge for Partially Penetrating Well equation looks like with Values.

Here is how the Radius of Influence given Discharge for Partially Penetrating Well equation looks like with Units.

Here is how the Radius of Influence given Discharge for Partially Penetrating Well equation looks like.

3.9053 = (2.94 \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105 \cdot 15 \cdot (20 - 2.44) \cdot 0.83}{5.08}))

3.9053m = (2.94m \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m) \cdot 0.83}{5.08m³/s}))

3.9053 = (2.94 \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105 \cdot 15 \cdot (20 - 2.44) \cdot 0.83}{5.08}))

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Radius of Influence given Discharge for Partially Penetrating Well Solution

Follow our step by step solution on how to calculate Radius of Influence given Discharge for Partially Penetrating Well?

FIRST Step Consider the formula

R = (r \cdot \exp (\frac{2 \cdot π \cdot K \cdot b \cdot (H - h w) \cdot G}{Q v}))

Next Step Substitute values of Variables

∴

R = (2.94m \cdot \exp (\frac{2 \cdot π \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m) \cdot 0.83}{5.08m³/s}))

Next Step Substitute values of Constants

∴

R = (2.94m \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m) \cdot 0.83}{5.08m³/s}))

Next Step Convert Units

∴

R = (2.94m \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.001m/s \cdot 15m \cdot (20m - 2.44m) \cdot 0.83}{5.08m³/s}))

Next Step Prepare to Evaluate

∴

R = (2.94 \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.001 \cdot 15 \cdot (20 - 2.44) \cdot 0.83}{5.08}))

Next Step Evaluate

∴

R = 3.90528888788538m

LAST Step Rounding Answer

∴

R = 3.9053m

Radius of Influence given Discharge for Partially Penetrating Well 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

Aquifer Thickness

Aquifer Thickness (at Midpoint between Equipotential lines) or otherwise is the thickness of aquifer in which the pore spaces of rock forming the aquifer may or may not be with water.

Symbol: b

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Aquifer Thickness

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

Depth of Water is the depth in the well measured above the impermeable layer.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Water

Correction Factor

Correction Factor refers to the reduced efficiency and altered flow patterns due to the well not extending through the entire aquifer thickness.

Symbol: G

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Correction Factor

Discharge for Partially Penetrating Well

Discharge for Partially Penetrating Well refers to the volume of water extracted from an aquifer when the well does not extend through the entire thickness of the aquifer.

Symbol: Q_v

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge for Partially Penetrating 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 Partially Penetrating Artesian Well category

Go Discharge for Partially Penetrating Well

Q v = \frac{2 \cdot π \cdot K \cdot b \cdot (H - h w) \cdot G}{\log ((\frac{R}{r}), e)}

Go Coefficient of Permeability given Discharge for Partially Penetrating Well

K = \frac{Q v}{\frac{2 \cdot π \cdot b \cdot (H - h w) \cdot G}{\log ((\frac{R}{r}), e)}}

How to Evaluate Radius of Influence given Discharge for Partially Penetrating Well?

Radius of Influence given Discharge for Partially Penetrating Well evaluator uses Radius of Influence = (Radius of Well*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well)) to evaluate the Radius of Influence, Radius of Influence given Discharge for Partially Penetrating Well formula is defined as the maximum radial distance from the well at which the influence of the well's discharge is felt, and is a critical parameter in evaluating the impact of pumping on groundwater flow in partially penetrating wells. Radius of Influence is denoted by R symbol.

How to evaluate Radius of Influence given Discharge for Partially Penetrating Well using this online evaluator? To use this online evaluator for Radius of Influence given Discharge for Partially Penetrating Well, enter Radius of Well (r), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w), Correction Factor (G) & Discharge for Partially Penetrating Well (Q_v) and hit the calculate button.

FAQs on Radius of Influence given Discharge for Partially Penetrating Well

What is the formula to find Radius of Influence given Discharge for Partially Penetrating Well?

The formula of Radius of Influence given Discharge for Partially Penetrating Well is expressed as Radius of Influence = (Radius of Well*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well)). Here is an example- 3.905289 = (2.94*exp((2*pi*0.00105*15*(20-2.44)*0.83)/5.08)).

How to calculate Radius of Influence given Discharge for Partially Penetrating Well?

With Radius of Well (r), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w), Correction Factor (G) & Discharge for Partially Penetrating Well (Q_v) we can find Radius of Influence given Discharge for Partially Penetrating Well using the formula - Radius of Influence = (Radius of Well*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well)). This formula also uses Archimedes' constant and Exponential Growth (exp) function(s).

Can the Radius of Influence given Discharge for Partially Penetrating Well be negative?

No, the Radius of Influence given Discharge for Partially Penetrating Well, measured in Length cannot be negative.

Which unit is used to measure Radius of Influence given Discharge for Partially Penetrating Well?

Radius of Influence given Discharge for Partially Penetrating Well 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 given Discharge for Partially Penetrating Well can be measured.

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Radius of Influence given Discharge for Partially Penetrating Well Formula

Radius of Influence given Discharge for Partially Penetrating Well Example

Radius of Influence given Discharge for Partially Penetrating Well Solution

Radius of Influence given Discharge for Partially Penetrating Well Formula Elements

Other formulas in Partially Penetrating Artesian Well category

How to Evaluate Radius of Influence given Discharge for Partially Penetrating Well?

FAQs on Radius of Influence given Discharge for Partially Penetrating Well

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