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Radius of Influence given Discharge by Spherical Flow Formula

GoRadius of Influence given Ratio of Discharge Formula

GoRadius of Influence given Ratio of Discharge with Base 10 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{(\frac{Q s}{Q fe}) \cdot b}{r})

R - Radius of Influence?r - Radius of Well?Q_s - Discharge by Spherical Flow?Q_fe - Discharge for Fully Penetrating Gravity Well?b - Aquifer Thickness?

Radius of Influence given Discharge by Spherical Flow Example

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Here is how the Radius of Influence given Discharge by Spherical Flow equation looks like with Values.

Here is how the Radius of Influence given Discharge by Spherical Flow equation looks like with Units.

Here is how the Radius of Influence given Discharge by Spherical Flow equation looks like.

3.9034 = 2.94 \cdot \exp (\frac{(\frac{0.34}{6.12}) \cdot 15}{2.94})

3.9034m = 2.94m \cdot \exp (\frac{(\frac{0.34m³/s}{6.12m³/s}) \cdot 15m}{2.94m})

3.9034 = 2.94 \cdot \exp (\frac{(\frac{0.34}{6.12}) \cdot 15}{2.94})

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Radius of Influence given Discharge by Spherical Flow Solution

Follow our step by step solution on how to calculate Radius of Influence given Discharge by Spherical Flow?

FIRST Step Consider the formula

R = r \cdot \exp (\frac{(\frac{Q s}{Q fe}) \cdot b}{r})

Next Step Substitute values of Variables

∴

R = 2.94m \cdot \exp (\frac{(\frac{0.34m³/s}{6.12m³/s}) \cdot 15m}{2.94m})

Next Step Prepare to Evaluate

∴

R = 2.94 \cdot \exp (\frac{(\frac{0.34}{6.12}) \cdot 15}{2.94})

Next Step Evaluate

∴

R = 3.90343249654048m

LAST Step Rounding Answer

∴

R = 3.9034m

Radius of Influence given Discharge by Spherical Flow Formula Elements

Variables

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

Discharge by Spherical Flow

Discharge by Spherical Flow refers to when water moves radially towards the well in a three-dimensional pattern, typical in confined aquifers or near partially penetrating wells.

Symbol: Q_s

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge by Spherical Flow

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

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

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 Influence

Go Radius of Influence given Ratio of Discharge

R = r \cdot \exp (\frac{QsQ ratio \cdot b}{r})

Go Radius of Influence given Ratio of Discharge with Base 10

R = r \cdot 10^{\frac{QsQ ratio \cdot b}{2.3 \cdot r}}

Go Radius of Influence given Discharge by Spherical Flow with Base 10

R = r \cdot 10^{\frac{(\frac{Q s}{Q fe}) \cdot b}{2.3 \cdot r}}

Other formulas in Spherical Flow in a Well category

Go Discharge due to Spherical Flow in Well

Q s = 2 \cdot π \cdot K \cdot r \cdot (H - h w)

Go Coefficient of Permeability given Discharge due to Spherical Flow in Well

K = \frac{Q s}{2 \cdot π \cdot r \cdot (H - h w)}

Go Radius of Well given Discharge due to Spherical Flow in Well

r = \frac{Q s}{2 \cdot π \cdot K \cdot (H - h w)}

Go Thickness of Aquifer given Discharge due to Spherical Flow in Well

H = h w + (\frac{Q s}{2 \cdot π \cdot K \cdot r})

How to Evaluate Radius of Influence given Discharge by Spherical Flow?

Radius of Influence given Discharge by Spherical Flow evaluator uses Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well) to evaluate the Radius of Influence, Radius of Influence given Discharge by Spherical Flow formula is defined as a method to estimate the radial distance from the pumping well to the point where the drawdown is negligible, which is essential in understanding the flow of fluids in wells and aquifers. Radius of Influence is denoted by R symbol.

How to evaluate Radius of Influence given Discharge by Spherical Flow using this online evaluator? To use this online evaluator for Radius of Influence given Discharge by Spherical Flow, enter Radius of Well (r), Discharge by Spherical Flow (Q_s), Discharge for Fully Penetrating Gravity Well (Q_fe) & Aquifer Thickness (b) and hit the calculate button.

FAQs on Radius of Influence given Discharge by Spherical Flow

What is the formula to find Radius of Influence given Discharge by Spherical Flow?

The formula of Radius of Influence given Discharge by Spherical Flow is expressed as Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well). Here is an example- 3.903432 = 2.94*exp(((0.34/6.12)*15)/2.94).

How to calculate Radius of Influence given Discharge by Spherical Flow?

With Radius of Well (r), Discharge by Spherical Flow (Q_s), Discharge for Fully Penetrating Gravity Well (Q_fe) & Aquifer Thickness (b) we can find Radius of Influence given Discharge by Spherical Flow using the formula - Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well). This formula also uses Exponential Growth (exp) 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*exp((Ratio of Discharge*Aquifer Thickness)/Radius of Well)
Radius of Influence=Radius of Well*10^((Ratio of Discharge*Aquifer Thickness)/(2.3*Radius of Well))
Radius of Influence=Radius of Well*10^(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/(2.3*Radius of Well))

Can the Radius of Influence given Discharge by Spherical Flow be negative?

No, the Radius of Influence given Discharge by Spherical Flow, measured in Length cannot be negative.

Which unit is used to measure Radius of Influence given Discharge by Spherical Flow?

Radius of Influence given Discharge by Spherical Flow 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 by Spherical Flow can be measured.

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Radius of Influence given Discharge by Spherical Flow Formula

​GoRadius of Influence given Ratio of Discharge Formula

​GoRadius of Influence given Ratio of Discharge with Base 10 Formula

Radius of Influence given Discharge by Spherical Flow Example

Radius of Influence given Discharge by Spherical Flow Solution

Radius of Influence given Discharge by Spherical Flow Formula Elements

Other Formulas to find Radius of Influence

Other formulas in Spherical Flow in a Well category

How to Evaluate Radius of Influence given Discharge by Spherical Flow?

FAQs on Radius of Influence given Discharge by Spherical Flow

Variable Name

GoRadius of Influence given Ratio of Discharge Formula

GoRadius of Influence given Ratio of Discharge with Base 10 Formula