Radius of Influence given Discharge by Spherical Flow Calculator

✖The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius.ⓘ Radius of Well [r]			+10% -10%
✖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.ⓘ Discharge by Spherical Flow [Q_s]			+10% -10%
✖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.ⓘ Discharge for Fully Penetrating Gravity Well [Q_fe]			+10% -10%
✖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.ⓘ Aquifer Thickness [b]			+10% -10%

✖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.ⓘ Radius of Influence given Discharge by Spherical Flow [R]

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Radius of Influence given Discharge by Spherical Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well)
R = r*exp(((Q_s/Q_fe)*b)/r)
This formula uses 1 Functions, 5 Variables

Functions Used

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

Variables Used

Radius of Influence - (Measured in Meter) - 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.
Radius of Well - (Measured in Meter) - The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius.
Discharge by Spherical Flow - (Measured in Cubic Meter per Second) - 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.
Discharge for Fully Penetrating Gravity Well - (Measured in Cubic Meter per Second) - 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.
Aquifer Thickness - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Radius of Well: 2.94 Meter --> 2.94 Meter No Conversion Required
Discharge by Spherical Flow: 0.34 Cubic Meter per Second --> 0.34 Cubic Meter per Second No Conversion Required
Discharge for Fully Penetrating Gravity Well: 6.12 Cubic Meter per Second --> 6.12 Cubic Meter per Second No Conversion Required
Aquifer Thickness: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = r*exp(((Q_s/Q_fe)*b)/r) --> 2.94*exp(((0.34/6.12)*15)/2.94)

Evaluating ... ...

R = 3.90343249654048

STEP 3: Convert Result to Output's Unit

3.90343249654048 Meter --> No Conversion Required

FINAL ANSWER

3.90343249654048 ≈ 3.903432 Meter <-- Radius of Influence

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< Spherical Flow in a Well Calculators

Coefficient of Permeability given Discharge due to Spherical Flow in Well

LaTeX Go Coefficient of Permeability = Discharge by Spherical Flow/(2*pi*Radius of Well*(Initial Piezometric Surface-Depth of Water))

Thickness of Aquifer given Discharge due to Spherical Flow in Well

LaTeX Go Initial Piezometric Surface = Depth of Water+(Discharge by Spherical Flow/(2*pi*Coefficient of Permeability*Radius of Well))

Radius of Well given Discharge due to Spherical Flow in Well

LaTeX Go Radius of Well = Discharge by Spherical Flow/(2*pi*Coefficient of Permeability*(Initial Piezometric Surface-Depth of Water))

Discharge due to Spherical Flow in Well

LaTeX Go Discharge by Spherical Flow = 2*pi*Coefficient of Permeability*Radius of Well*(Initial Piezometric Surface-Depth of Water)

Radius of Influence given Discharge by Spherical Flow Formula

LaTeX Go

Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well)
R = r*exp(((Q_s/Q_fe)*b)/r)

What is Discharge by Spherical Flow?

Discharge due to spherical flow in a well occurs when water moves radially towards the well in a three-dimensional pattern, typical in confined aquifers or near partially penetrating wells. It is influenced by factors like aquifer properties, well radius, drawdown, and the radius of influence. The discharge rate is determined using equations that account for the changing cross-sectional area of flow and the variation in hydraulic gradient with distance from the well. This flow pattern results in a more complex relationship between discharge and drawdown compared to linear or radial flow.

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

Radius of Influence given Discharge by Spherical Flow calculator uses Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well) to calculate 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 calculate Radius of Influence given Discharge by Spherical Flow using this online calculator? To use this online calculator 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. Here is how the Radius of Influence given Discharge by Spherical Flow calculation can be explained with given input values -> 3.903432 = 2.94*exp(((0.34/6.12)*15)/2.94).

FAQ

What is Radius of Influence given Discharge by Spherical Flow?

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 and is represented as R = r*exp(((Q_s/Q_fe)*b)/r) or Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/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, 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, 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 & 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.

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

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 is calculated using Radius of Influence = Radius of Well*exp(((Discharge by Spherical Flow/Discharge for Fully Penetrating Gravity Well)*Aquifer Thickness)/Radius of Well). To calculate Radius of Influence given Discharge by Spherical Flow, you need Radius of Well (r), Discharge by Spherical Flow (Q_s), Discharge for Fully Penetrating Gravity Well (Q_fe) & Aquifer Thickness (b). With our tool, you need to enter the respective value for Radius of Well, Discharge by Spherical Flow, Discharge for Fully Penetrating Gravity Well & Aquifer Thickness and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radius of Influence?

In this formula, Radius of Influence uses Radius of Well, Discharge by Spherical Flow, Discharge for Fully Penetrating Gravity Well & Aquifer Thickness. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))

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