Thickness of Aquifer given Discharge for Fully Penetrating Well Calculator

✖Discharge is the rate of flow of a liquid.ⓘ Discharge [Q]			+10% -10%
✖Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.ⓘ Radius of Influence [R]			+10% -10%
✖Radius of Well in Eviron. Engin. is defined as the distance from center of well to its outer boundary.ⓘ Radius of Well in Eviron. Engin. [r^']			+10% -10%
✖The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.ⓘ Coefficient of Permeability [k]			+10% -10%
✖Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.ⓘ Aquifer Thickness During Pumping [b_p]			+10% -10%
✖Depth of Water in the well measured above the impermeable layer.ⓘ Depth of Water [h_w]			+10% -10%

✖Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.ⓘ Thickness of Aquifer given Discharge for Fully Penetrating Well [H_i]

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Formula

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Thickness of Aquifer given Discharge for Fully Penetrating Well

Formula

`"H"_{"i"} = ((("Q"*log(("R"/"r"^{"'"}),e))/(pi*"k"))+("b"_{"p"})^2+("h"_{"w"})^2)/(2*"b"_{"p"})`

Example

`"4.372673m"=((("1.01m³/s"*log(("100m"/"2.94m"),e))/(pi*"0.01cm/s"))+("2.36m")^2+("2.44m")^2)/(2*"2.36m")`

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Thickness of Aquifer given Discharge for Fully Penetrating Well Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Aquifer Thickness = (((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2+(Depth of Water)^2)/(2*Aquifer Thickness During Pumping)
H_i = (((Q*log((R/r^'),e))/(pi*k))+(b_p)^2+(h_w)^2)/(2*b_p)
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 Aquifer Thickness - (Measured in Meter) - Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.
Discharge - (Measured in Cubic Meter per Second) - Discharge is the rate of flow of a liquid.
Radius of Influence - (Measured in Meter) - Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.
Radius of Well in Eviron. Engin. - (Measured in Meter) - Radius of Well in Eviron. Engin. is defined as the distance from center of well to its outer boundary.
Coefficient of Permeability - (Measured in Centimeter per Second) - The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.
Aquifer Thickness During Pumping - (Measured in Meter) - Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.
Depth of Water - (Measured in Meter) - Depth of Water in the well measured above the impermeable layer.

STEP 1: Convert Input(s) to Base Unit

Discharge: 1.01 Cubic Meter per Second --> 1.01 Cubic Meter per Second No Conversion Required
Radius of Influence: 100 Meter --> 100 Meter No Conversion Required
Radius of Well in Eviron. Engin.: 2.94 Meter --> 2.94 Meter No Conversion Required
Coefficient of Permeability: 0.01 Centimeter per Second --> 0.01 Centimeter per Second No Conversion Required
Aquifer Thickness During Pumping: 2.36 Meter --> 2.36 Meter No Conversion Required
Depth of Water: 2.44 Meter --> 2.44 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_i = (((Q*log((R/r^'),e))/(pi*k))+(b_p)^2+(h_w)^2)/(2*b_p) --> (((1.01*log((100/2.94),e))/(pi*0.01))+(2.36)^2+(2.44)^2)/(2*2.36)

Evaluating ... ...

H_i = 4.37267274658965

STEP 3: Convert Result to Output's Unit

4.37267274658965 Meter --> No Conversion Required

FINAL ANSWER

4.37267274658965 ≈ 4.372673 Meter <-- Initial Aquifer Thickness

(Calculation completed in 00.020 seconds)

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Depth of Water in Well given Discharge for Fully Penetrating Well

Go Depth of Water = sqrt((2*Aquifer Thickness During Pumping*Initial Aquifer Thickness)-((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2)

Thickness of Aquifer given Discharge for Fully Penetrating Well

Go Initial Aquifer Thickness = (((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2+(Depth of Water)^2)/(2*Aquifer Thickness During Pumping)

Radius of Influence of unconfined aquifer with known discharge

Go Radius of Influence in Eviron. Engin. = Radius of Well in Eviron. Engin.*exp((0.434*pi*Coefficient of Permeability*((Original Piezometric Head of the Well^2)-(Piezometric Head at Well)))/Discharge)

Radius of Well of unconfined Aquifer with known Discharge

Go Radius of Well in Eviron. Engin. = Radius of Influence in Eviron. Engin./exp((0.434*pi*Coefficient of Permeability*((Original Piezometric Head of the Well^2)-(Piezometric Head at Well)))/Discharge)

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 Aquifer Thickness = (((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2+(Depth of Water)^2)/(2*Aquifer Thickness During Pumping) to calculate the Initial Aquifer Thickness, The Thickness of Aquifer given Discharge for Fully Penetrating Well is defined as the value of thickness of aquifer when we have prior information of other parameters used. Initial Aquifer Thickness is denoted by H_i 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 (Q), Radius of Influence (R), Radius of Well in Eviron. Engin. (r^'), Coefficient of Permeability (k), Aquifer Thickness During Pumping (b_p) & Depth of Water (h_w) 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 -> 4.372673 = (((1.01*log((100/2.94),e))/(pi*0.0001))+(2.36)^2+(2.44)^2)/(2*2.36).

FAQ

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

The Thickness of Aquifer given Discharge for Fully Penetrating Well is defined as the value of thickness of aquifer when we have prior information of other parameters used and is represented as H_i = (((Q*log((R/r^'),e))/(pi*k))+(b_p)^2+(h_w)^2)/(2*b_p) or Initial Aquifer Thickness = (((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2+(Depth of Water)^2)/(2*Aquifer Thickness During Pumping). Discharge is the rate of flow of a liquid, Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table, Radius of Well in Eviron. Engin. is defined as the distance from center of well to its outer boundary, The Coefficient of Permeability of soil describes how easily a liquid will move through the soil, Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage & Depth of Water in the well measured above the impermeable layer.

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

The Thickness of Aquifer given Discharge for Fully Penetrating Well is defined as the value of thickness of aquifer when we have prior information of other parameters used is calculated using Initial Aquifer Thickness = (((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2+(Depth of Water)^2)/(2*Aquifer Thickness During Pumping). To calculate Thickness of Aquifer given Discharge for Fully Penetrating Well, you need Discharge (Q), Radius of Influence (R), Radius of Well in Eviron. Engin. (r^'), Coefficient of Permeability (k), Aquifer Thickness During Pumping (b_p) & Depth of Water (h_w). With our tool, you need to enter the respective value for Discharge, Radius of Influence, Radius of Well in Eviron. Engin, Coefficient of Permeability, Aquifer Thickness During Pumping & Depth of Water 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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