Discharge by Spherical Flow Calculator

✖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%
✖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%
✖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 [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]

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Discharge by Spherical Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

log - Logarithmic function is an inverse function to exponentiation., log(Base, Number)

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Discharge for Fully Penetrating Gravity Well: 6.12 Cubic Meter per Second --> 6.12 Cubic Meter per Second No Conversion Required
Radius of Well: 2.94 Meter --> 2.94 Meter No Conversion Required
Aquifer Thickness: 15 Meter --> 15 Meter No Conversion Required
Radius of Influence: 100 Meter --> 100 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_s = Q_fe*(r/b)*log((R/r),e) --> 6.12*(2.94/15)*log((100/2.94),e)

Evaluating ... ...

Q_s = 0.34011948483906

STEP 3: Convert Result to Output's Unit

0.34011948483906 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

0.34011948483906 ≈ 0.340119 Cubic Meter per Second <-- Discharge by Spherical Flow

(Calculation completed in 00.017 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)

Discharge by Spherical Flow Formula

LaTeX Go

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

What is Radius of Well?

The radius of a well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius. This dimension is crucial in groundwater studies for calculating various hydraulic properties such as the well's capacity, discharge rate, and drawdown. It also plays a role in determining the well's design and construction parameters, ensuring proper water flow and minimizing the effects of clogging. The radius of the well impacts the efficiency of water extraction and the overall performance of the well in an aquifer.

How to Calculate Discharge by Spherical Flow?

Discharge by Spherical Flow calculator uses Discharge by Spherical Flow = Discharge for Fully Penetrating Gravity Well*(Radius of Well/Aquifer Thickness)*log((Radius of Influence/Radius of Well),e) to calculate the Discharge by Spherical Flow, Discharge by Spherical Flow formula is defined as a measure of the rate of fluid flow from a well or a spherical source, taking into account the radius of the well, the distance from the well to the point of measurement, and the properties of the surrounding porous medium. Discharge by Spherical Flow is denoted by Q_s symbol.

How to calculate Discharge by Spherical Flow using this online calculator? To use this online calculator for Discharge by Spherical Flow, enter Discharge for Fully Penetrating Gravity Well (Q_fe), Radius of Well (r), Aquifer Thickness (b) & Radius of Influence (R) and hit the calculate button. Here is how the Discharge by Spherical Flow calculation can be explained with given input values -> 0.340119 = 6.12*(2.94/15)*log((100/2.94),e).

FAQ

What is Discharge by Spherical Flow?

Discharge by Spherical Flow formula is defined as a measure of the rate of fluid flow from a well or a spherical source, taking into account the radius of the well, the distance from the well to the point of measurement, and the properties of the surrounding porous medium and is represented as Q_s = Q_fe*(r/b)*log((R/r),e) or Discharge by Spherical Flow = Discharge for Fully Penetrating Gravity Well*(Radius of Well/Aquifer Thickness)*log((Radius of Influence/Radius of Well),e). 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, The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius, 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 & 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.

How to calculate Discharge by Spherical Flow?

Discharge by Spherical Flow formula is defined as a measure of the rate of fluid flow from a well or a spherical source, taking into account the radius of the well, the distance from the well to the point of measurement, and the properties of the surrounding porous medium is calculated using Discharge by Spherical Flow = Discharge for Fully Penetrating Gravity Well*(Radius of Well/Aquifer Thickness)*log((Radius of Influence/Radius of Well),e). To calculate Discharge by Spherical Flow, you need Discharge for Fully Penetrating Gravity Well (Q_fe), Radius of Well (r), Aquifer Thickness (b) & Radius of Influence (R). With our tool, you need to enter the respective value for Discharge for Fully Penetrating Gravity Well, Radius of Well, Aquifer Thickness & Radius of Influence 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 Discharge by Spherical Flow?

In this formula, Discharge by Spherical Flow uses Discharge for Fully Penetrating Gravity Well, Radius of Well, Aquifer Thickness & Radius of Influence. We can use 2 other way(s) to calculate the same, which is/are as follows -

Discharge by Spherical Flow = 2*pi*Coefficient of Permeability*Radius of Well*(Initial Piezometric Surface-Depth of Water)
Discharge by Spherical Flow = 2.3*Discharge for Fully Penetrating Gravity Well*(Radius of Well/Aquifer Thickness)*log((Radius of Influence/Radius of Well),10)

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