Thickness of Aquifer given Discharge for Fully Penetrating Well Calculator

✖Discharge by Fully Penetrating Well refers to the volume of water extracted from an unconfined aquifer where the well reaches the entire thickness of the aquifer.ⓘ Discharge by Fully Penetrating Well [Q_fw]			+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%
✖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%
✖Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces.ⓘ Coefficient of Permeability [K]			+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%
✖Depth of Water in Fully Penetrating Gravity Well refers to the vertical distance from the water table to the bottom of the well, which extends through the entire thickness of the unconfined aquifer.ⓘ Depth of Water in Fully Penetrating Gravity Well [h_fw]			+10% -10%

✖The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.ⓘ Thickness of Aquifer given Discharge for Fully Penetrating Well [H]

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Formula

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Thickness of Aquifer given Discharge for Fully Penetrating Well

Formula

H = \frac{(\frac{Q fw \cdot \log ((\frac{R}{r}), e)}{π \cdot K}) + {(b)}^{2} + {(h fw)}^{2}}{2 \cdot b}

Example

19.99517 m = \frac{(\frac{60 m³/s \cdot \log ((\frac{100 m}{2.94 m}), e)}{π \cdot 0.105 cm/s}) + {(15.0 m)}^{2} + {(17.98 m)}^{2}}{2 \cdot 15.0 m}

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Thickness of Aquifer given Discharge for Fully Penetrating Well Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Piezometric Surface = (((Discharge by Fully Penetrating Well*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness)^2+(Depth of Water in Fully Penetrating Gravity Well)^2)/(2*Aquifer Thickness)
H = (((Q_fw*log((R/r),e))/(pi*K))+(b)^2+(h_fw)^2)/(2*b)
This formula uses 2 Constants, 1 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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

Initial Piezometric Surface - (Measured in Meter) - The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.
Discharge by Fully Penetrating Well - (Measured in Cubic Meter per Second) - Discharge by Fully Penetrating Well refers to the volume of water extracted from an unconfined aquifer where the well reaches the entire thickness of the aquifer.
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.
Coefficient of Permeability - (Measured in Centimeter per Second) - Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces.
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.
Depth of Water in Fully Penetrating Gravity Well - (Measured in Meter) - Depth of Water in Fully Penetrating Gravity Well refers to the vertical distance from the water table to the bottom of the well, which extends through the entire thickness of the unconfined aquifer.

STEP 1: Convert Input(s) to Base Unit

Discharge by Fully Penetrating Well: 60 Cubic Meter per Second --> 60 Cubic Meter per Second No Conversion Required
Radius of Influence: 100 Meter --> 100 Meter No Conversion Required
Radius of Well: 2.94 Meter --> 2.94 Meter No Conversion Required
Coefficient of Permeability: 0.105 Centimeter per Second --> 0.105 Centimeter per Second No Conversion Required
Aquifer Thickness: 15 Meter --> 15 Meter No Conversion Required
Depth of Water in Fully Penetrating Gravity Well: 17.98 Meter --> 17.98 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = (((Q_fw*log((R/r),e))/(pi*K))+(b)^2+(h_fw)^2)/(2*b) --> (((60*log((100/2.94),e))/(pi*0.105))+(15)^2+(17.98)^2)/(2*15)

Evaluating ... ...

H = 19.995167574522

STEP 3: Convert Result to Output's Unit

19.995167574522 Meter --> No Conversion Required

FINAL ANSWER

19.995167574522 ≈ 19.99517 Meter <-- Initial Piezometric Surface

(Calculation completed in 00.004 seconds)

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< Fully Penetrating Artesian Gravity Well Calculators

Depth of Water in Well given Discharge for Fully Penetrating Well

Go Depth of Water in Fully Penetrating Gravity Well = sqrt((2*Aquifer Thickness*Initial Piezometric Surface)-((Discharge by Fully Penetrating Well*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability))-(Aquifer Thickness)^2)

Thickness of Aquifer given Discharge for Fully Penetrating Well

Go Initial Piezometric Surface = (((Discharge by Fully Penetrating Well*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness)^2+(Depth of Water in Fully Penetrating Gravity Well)^2)/(2*Aquifer Thickness)

Radius of Influence of unconfined aquifer with known discharge

Go Radius of Influence = Radius of Well*exp((0.434*pi*Coefficient of Permeability*(Initial Piezometric Surface^2-Depth of Water in Fully Penetrating Gravity Well^2))/Discharge for Fully Penetrating Gravity Well)

Radius of Well of unconfined Aquifer with known Discharge

Go Radius of Well = Radius of Influence/exp((0.434*pi*Coefficient of Permeability*((Initial Piezometric Surface^2)-(Depth of Water^2)))/Discharge for Fully Penetrating Gravity Well)

Thickness of Aquifer given Discharge for Fully Penetrating Well Formula

What is Aquifer ?

An aquifer is a body of rock and/or sediment that holds groundwater. Groundwater is the word used to describe precipitation that has infiltrated the soil beyond the surface and collected in empty spaces underground.

How to Calculate Thickness of Aquifer given Discharge for Fully Penetrating Well?

Thickness of Aquifer given Discharge for Fully Penetrating Well calculator uses Initial Piezometric Surface = (((Discharge by Fully Penetrating Well*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness)^2+(Depth of Water in Fully Penetrating Gravity Well)^2)/(2*Aquifer Thickness) to calculate the Initial Piezometric Surface, Thickness of Aquifer given Discharge for Fully Penetrating Well formula is defined as the height of a layer of permeable rock that supplies water to a well, which is essential in understanding the flow of fluids in aquifers and determining the yield of a well. Initial Piezometric Surface is denoted by H symbol.

How to calculate Thickness of Aquifer given Discharge for Fully Penetrating Well using this online calculator? To use this online calculator for Thickness of Aquifer given Discharge for Fully Penetrating Well, enter Discharge by Fully Penetrating Well (Q_fw), Radius of Influence (R), Radius of Well (r), Coefficient of Permeability (K), Aquifer Thickness (b) & Depth of Water in Fully Penetrating Gravity Well (h_fw) and hit the calculate button. Here is how the Thickness of Aquifer given Discharge for Fully Penetrating Well calculation can be explained with given input values -> 19.99517 = (((60*log((100/2.94),e))/(pi*0.00105))+(15)^2+(17.98)^2)/(2*15).

FAQ

What is Thickness of Aquifer given Discharge for Fully Penetrating Well?

Thickness of Aquifer given Discharge for Fully Penetrating Well formula is defined as the height of a layer of permeable rock that supplies water to a well, which is essential in understanding the flow of fluids in aquifers and determining the yield of a well and is represented as H = (((Q_fw*log((R/r),e))/(pi*K))+(b)^2+(h_fw)^2)/(2*b) or Initial Piezometric Surface = (((Discharge by Fully Penetrating Well*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness)^2+(Depth of Water in Fully Penetrating Gravity Well)^2)/(2*Aquifer Thickness). Discharge by Fully Penetrating 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 influence is the distance from a pumping well to the point where the drawdown, or lowering of the water table, becomes negligible, The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius, Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces, 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 & Depth of Water in Fully Penetrating Gravity Well refers to the vertical distance from the water table to the bottom of the well, which extends through the entire thickness of the unconfined aquifer.

How to calculate Thickness of Aquifer given Discharge for Fully Penetrating Well?

Thickness of Aquifer given Discharge for Fully Penetrating Well formula is defined as the height of a layer of permeable rock that supplies water to a well, which is essential in understanding the flow of fluids in aquifers and determining the yield of a well is calculated using Initial Piezometric Surface = (((Discharge by Fully Penetrating Well*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness)^2+(Depth of Water in Fully Penetrating Gravity Well)^2)/(2*Aquifer Thickness). To calculate Thickness of Aquifer given Discharge for Fully Penetrating Well, you need Discharge by Fully Penetrating Well (Q_fw), Radius of Influence (R), Radius of Well (r), Coefficient of Permeability (K), Aquifer Thickness (b) & Depth of Water in Fully Penetrating Gravity Well (h_fw). With our tool, you need to enter the respective value for Discharge by Fully Penetrating Well, Radius of Influence, Radius of Well, Coefficient of Permeability, Aquifer Thickness & Depth of Water in Fully Penetrating Gravity Well and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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