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Radius of Well when Interference among three well is present Formula

GoRadius of Well when Interference among well is present Formula

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

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

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

Radius of Well when Interference among three well is present Example

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Here is how the Radius of Well when Interference among three well is present equation looks like with Values.

Here is how the Radius of Well when Interference among three well is present equation looks like with Units.

Here is how the Radius of Well when Interference among three well is present equation looks like.

105984.4739 = \frac{100^{3}}{\exp (\frac{2 \cdot 3.1416 \cdot 0.105 \cdot 15 \cdot (20 - 2.44)}{18.397}) \cdot {2.93}^{2}}

105984.4739m = \frac{{100m}^{3}}{\exp (\frac{2 \cdot 3.1416 \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m)}{18.397m³/s}) \cdot {2.93m}^{2}}

105984.4739 = \frac{100^{3}}{\exp (\frac{2 \cdot 3.1416 \cdot 0.105 \cdot 15 \cdot (20 - 2.44)}{18.397}) \cdot {2.93}^{2}}

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Radius of Well when Interference among three well is present Solution

Follow our step by step solution on how to calculate Radius of Well when Interference among three well is present?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r = \frac{{100m}^{3}}{\exp (\frac{2 \cdot π \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m)}{18.397m³/s}) \cdot {2.93m}^{2}}

Next Step Substitute values of Constants

∴

r = \frac{{100m}^{3}}{\exp (\frac{2 \cdot 3.1416 \cdot 0.105cm/s \cdot 15m \cdot (20m - 2.44m)}{18.397m³/s}) \cdot {2.93m}^{2}}

Next Step Convert Units

∴

r = \frac{{100m}^{3}}{\exp (\frac{2 \cdot 3.1416 \cdot 0.001m/s \cdot 15m \cdot (20m - 2.44m)}{18.397m³/s}) \cdot {2.93m}^{2}}

Next Step Prepare to Evaluate

∴

r = \frac{100^{3}}{\exp (\frac{2 \cdot 3.1416 \cdot 0.001 \cdot 15 \cdot (20 - 2.44)}{18.397}) \cdot {2.93}^{2}}

Next Step Evaluate

∴

r = 105984.473867m

LAST Step Rounding Answer

∴

r = 105984.4739m

Radius of Well when Interference among three well is present Formula Elements

Variables

Constants

Functions

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

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

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 at Three Well Interference

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

Symbol: Q_th

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge by Each Well at Three Well Interference

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

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 to find Radius of Well

Go Radius of Well when Interference among well is present

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

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 Well when Interference among three well is present?

Radius of Well when Interference among three well is present evaluator uses Radius of Well = (Radius of Influence^3)/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well at Three Well Interference)*Distance Between Wells^2) to evaluate the Radius of Well, Radius of Well when Interference among three well is present formula is defined as a measure of the effective radius of a well in a multi-well system, considering the interference effects between the three wells, which is essential in understanding the flow behavior in wells and optimizing the production from these wells. Radius of Well is denoted by r symbol.

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

FAQs on Radius of Well when Interference among three well is present

What is the formula to find Radius of Well when Interference among three well is present?

The formula of Radius of Well when Interference among three well is present is expressed as Radius of Well = (Radius of Influence^3)/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well at Three Well Interference)*Distance Between Wells^2). Here is an example- 105984.5 = (100^3)/(exp((2*pi*0.00105*15*(20-2.44))/18.397)*2.93^2).

How to calculate Radius of Well when Interference among three well is present?

With Radius of Influence (R), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w), Discharge by Each Well at Three Well Interference (Q_th) & Distance Between Wells (B) we can find Radius of Well when Interference among three well is present using the formula - Radius of Well = (Radius of Influence^3)/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water))/Discharge by Each Well at Three Well Interference)*Distance Between Wells^2). This formula also uses Archimedes' constant and Exponential Growth (exp) function(s).

What are the other ways to Calculate Radius of Well?

Here are the different ways to Calculate Radius of Well-

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

Can the Radius of Well when Interference among three well is present be negative?

No, the Radius of Well when Interference among three well is present, measured in Length cannot be negative.

Which unit is used to measure Radius of Well when Interference among three well is present?

Radius of Well when Interference among three 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 Well when Interference among three well is present can be measured.

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Radius of Well when Interference among three well is present Formula

​GoRadius of Well when Interference among well is present Formula

Radius of Well when Interference among three well is present Example

Radius of Well when Interference among three well is present Solution

Radius of Well when Interference among three well is present Formula Elements

Other Formulas to find Radius of Well

Other formulas in Interference Among Wells category

How to Evaluate Radius of Well when Interference among three well is present?

FAQs on Radius of Well when Interference among three well is present

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GoRadius of Well when Interference among well is present Formula