Depth of Water in Well given Discharge for Fully Penetrating Well Calculator

✖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 initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.ⓘ Initial Piezometric Surface [H]			+10% -10%
✖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%

✖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 Well given Discharge for Fully Penetrating Well [h_fw]

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Depth of Water in Well given Discharge for Fully Penetrating Well Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
h_fw = sqrt((2*b*H)-((Q_fw*log((R/r),e))/(pi*K))-(b)^2)
This formula uses 2 Constants, 2 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
log - Logarithmic function is an inverse function to exponentiation., log(Base, Number)

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Aquifer Thickness: 15 Meter --> 15 Meter No Conversion Required
Initial Piezometric Surface: 20 Meter --> 20 Meter No Conversion Required
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_fw = sqrt((2*b*H)-((Q_fw*log((R/r),e))/(pi*K))-(b)^2) --> sqrt((2*15*20)-((60*log((100/2.94),e))/(pi*0.105))-(15)^2)

Evaluating ... ...

h_fw = 17.9840310488038

STEP 3: Convert Result to Output's Unit

17.9840310488038 Meter --> No Conversion Required

FINAL ANSWER

17.9840310488038 ≈ 17.98403 Meter <-- Depth of Water in Fully Penetrating Gravity Well

(Calculation completed in 00.020 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< Fully Penetrating Artesian Gravity Well Calculators

Depth of Water in Well given Discharge for Fully Penetrating Well

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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)

Depth of Water in Well given Discharge for Fully Penetrating Well Formula

LaTeX Go

What is Discharge ?

The amount of fluid passing a section of a stream in unit time is called the discharge. If v is the mean velocity and A is the cross sectional area, the discharge Q is defined by Q = Av which is known as volume flow rate.

How to Calculate Depth of Water in Well given Discharge for Fully Penetrating Well?

Depth of Water in Well given Discharge for Fully Penetrating Well calculator uses 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) to calculate the Depth of Water in Fully Penetrating Gravity Well, Depth of Water in Well given Discharge for Fully Penetrating Well formula is defined as a measure of the water level in a fully penetrating well, considering the discharge rate, radius of the well, and other relevant parameters, to determine the water depth in the well. Depth of Water in Fully Penetrating Gravity Well is denoted by h_fw symbol.

How to calculate Depth of Water in Well given Discharge for Fully Penetrating Well using this online calculator? To use this online calculator for Depth of Water in Well given Discharge for Fully Penetrating Well, enter Aquifer Thickness (b), Initial Piezometric Surface (H), Discharge by Fully Penetrating Well (Q_fw), Radius of Influence (R), Radius of Well (r) & Coefficient of Permeability (K) and hit the calculate button. Here is how the Depth of Water in Well given Discharge for Fully Penetrating Well calculation can be explained with given input values -> 17.98403 = sqrt((2*15*20)-((60*log((100/2.94),e))/(pi*0.00105))-(15)^2).

FAQ

What is Depth of Water in Well given Discharge for Fully Penetrating Well?

Depth of Water in Well given Discharge for Fully Penetrating Well formula is defined as a measure of the water level in a fully penetrating well, considering the discharge rate, radius of the well, and other relevant parameters, to determine the water depth in the well and is represented as h_fw = sqrt((2*b*H)-((Q_fw*log((R/r),e))/(pi*K))-(b)^2) or 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). 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 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 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.

How to calculate Depth of Water in Well given Discharge for Fully Penetrating Well?

Depth of Water in Well given Discharge for Fully Penetrating Well formula is defined as a measure of the water level in a fully penetrating well, considering the discharge rate, radius of the well, and other relevant parameters, to determine the water depth in the well is calculated using 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). To calculate Depth of Water in Well given Discharge for Fully Penetrating Well, you need Aquifer Thickness (b), Initial Piezometric Surface (H), Discharge by Fully Penetrating Well (Q_fw), Radius of Influence (R), Radius of Well (r) & Coefficient of Permeability (K). With our tool, you need to enter the respective value for Aquifer Thickness, Initial Piezometric Surface, Discharge by Fully Penetrating Well, Radius of Influence, Radius of Well & Coefficient of Permeability 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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