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Radius of Influence when Interference among Well is Present Formula

GoRadius of Influence when Interference among Three Well is Present 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 = \sqrt{(r \cdot B) \cdot \exp (\frac{2 \cdot π \cdot K \cdot b \cdot (H - h w)}{Q t})}

R - Radius of Influence?r - Radius of Well?B - Distance Between Wells?K - Coefficient of Permeability?b - Aquifer Thickness?H - Initial Piezometric Surface?h_w - Depth of Water?Q_t - Discharge by Each Well when Two Well Interference?π - Archimedes' constant?

Radius of Influence when Interference among Well is Present Example

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Here is how the Radius of Influence when Interference among Well is Present equation looks like with Values.

Here is how the Radius of Influence when Interference among Well is Present equation looks like with Units.

Here is how the Radius of Influence when Interference among Well is Present equation looks like.

3.1505 = \sqrt{(2.94 \cdot 2.93) \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105 \cdot 15 \cdot (20 - 2.44)}{12.26})}

3.1505m = \sqrt{(2.94m \cdot 2.93m) \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m)}{12.26m³/s})}

3.1505 = \sqrt{(2.94 \cdot 2.93) \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105 \cdot 15 \cdot (20 - 2.44)}{12.26})}

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Radius of Influence when Interference among Well is Present Solution

Follow our step by step solution on how to calculate Radius of Influence when Interference among Well is Present?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R = \sqrt{(2.94m \cdot 2.93m) \cdot \exp (\frac{2 \cdot π \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m)}{12.26m³/s})}

Next Step Substitute values of Constants

∴

R = \sqrt{(2.94m \cdot 2.93m) \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m)}{12.26m³/s})}

Next Step Convert Units

∴

R = \sqrt{(2.94m \cdot 2.93m) \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.001m/s \cdot 15m \cdot (20m - 2.44m)}{12.26m³/s})}

Next Step Prepare to Evaluate

∴

R = \sqrt{(2.94 \cdot 2.93) \cdot \exp (\frac{2 \cdot 3.1416 \cdot 0.001 \cdot 15 \cdot (20 - 2.44)}{12.26})}

Next Step Evaluate

∴

R = 3.15054777642181m

LAST Step Rounding Answer

∴

R = 3.1505m

Radius of Influence when Interference among Well is Present 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

Distance Between Wells

Distance Between Wells refers to the center to center distance between the well.

Symbol: B

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance Between Wells

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

Discharge by Each Well when Two Well Interference

Discharge by Each Well when Two Well Interference is the sum of the individual well rates, adjusted for interference.

Symbol: Q_t

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge by Each Well when Two Well Interference

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)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Radius of Influence

Go Radius of Influence when Interference among Three Well is Present

R = {((r \cdot B^{2}) \cdot \exp (\frac{2 \cdot π \cdot K \cdot b \cdot (H - h w)}{Q th}))}^{\frac{1}{3}}

Other formulas in Interference Among Wells category

Go Discharge through Each Well when Interference among Well is Present

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

Go Coefficient of Permeability when Interference among Well is Present

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

How to Evaluate Radius of Influence when Interference among Well is Present?

Radius of Influence when Interference among Well is Present evaluator uses Radius of Influence = sqrt((Radius of Well*Distance Between Wells)*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well when Two Well Interference)) to evaluate the Radius of Influence, Radius of Influence when Interference among Well is Present formula is defined as a measure of the distance from the pumping well to the point where the drawdown of the water table is negligible, considering the interference effects of nearby wells in a groundwater flow system. Radius of Influence is denoted by R symbol.

How to evaluate Radius of Influence when Interference among Well is Present using this online evaluator? To use this online evaluator for Radius of Influence when Interference among Well is Present, enter Radius of Well (r), Distance Between Wells (B), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w) & Discharge by Each Well when Two Well Interference (Q_t) and hit the calculate button.

FAQs on Radius of Influence when Interference among Well is Present

What is the formula to find Radius of Influence when Interference among Well is Present?

The formula of Radius of Influence when Interference among Well is Present is expressed as Radius of Influence = sqrt((Radius of Well*Distance Between Wells)*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well when Two Well Interference)). Here is an example- 3.150548 = sqrt((2.94*2.93)*exp((2*pi*0.00105*15*(20-2.44))/12.26)).

How to calculate Radius of Influence when Interference among Well is Present?

With Radius of Well (r), Distance Between Wells (B), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w) & Discharge by Each Well when Two Well Interference (Q_t) we can find Radius of Influence when Interference among Well is Present using the formula - Radius of Influence = sqrt((Radius of Well*Distance Between Wells)*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well when Two Well Interference)). This formula also uses Archimedes' constant and , Exponential Growth (exp), Square Root (sqrt) function(s).

What are the other ways to Calculate Radius of Influence?

Here are the different ways to Calculate Radius of Influence-

Radius of Influence=((Radius of Well*Distance Between Wells^2)*exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well at Three Well Interference))^(1/3)

Can the Radius of Influence when Interference among Well is Present be negative?

No, the Radius of Influence when Interference among Well is Present, measured in Length cannot be negative.

Which unit is used to measure Radius of Influence when Interference among Well is Present?

Radius of Influence when Interference among Well is Present 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 when Interference among Well is Present can be measured.

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Radius of Influence when Interference among Well is Present Formula

​GoRadius of Influence when Interference among Three Well is Present Formula

Radius of Influence when Interference among Well is Present Example

Radius of Influence when Interference among Well is Present Solution

Radius of Influence when Interference among Well is Present Formula Elements

Other Formulas to find Radius of Influence

Other formulas in Interference Among Wells category

How to Evaluate Radius of Influence when Interference among Well is Present?

FAQs on Radius of Influence when Interference among Well is Present

Variable Name

GoRadius of Influence when Interference among Three Well is Present Formula