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Thickness of Aquifer given Discharge for Fully Penetrating Well Formula

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The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence. Check FAQs

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

H - Initial Piezometric Surface?Q_fw - Discharge by Fully Penetrating Well?R - Radius of Influence?r - Radius of Well?K - Coefficient of Permeability?b - Aquifer Thickness?h_fw - Depth of Water in Fully Penetrating Gravity Well?π - Archimedes' constant?

Thickness of Aquifer given Discharge for Fully Penetrating Well Example

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Here is how the Thickness of Aquifer given Discharge for Fully Penetrating Well equation looks like with Values.

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Here is how the Thickness of Aquifer given Discharge for Fully Penetrating Well equation looks like.

19.9952 = \frac{(\frac{60 \cdot \log ((\frac{100}{2.94}), e)}{3.1416 \cdot 0.105}) + {(15)}^{2} + {(17.98)}^{2}}{2 \cdot 15}

19.9952m = \frac{(\frac{60m³/s \cdot \log ((\frac{100m}{2.94m}), e)}{3.1416 \cdot 0.105cm/s}) + {(15m)}^{2} + {(17.98m)}^{2}}{2 \cdot 15m}

19.9952 = \frac{(\frac{60 \cdot \log ((\frac{100}{2.94}), e)}{3.1416 \cdot 0.105}) + {(15)}^{2} + {(17.98)}^{2}}{2 \cdot 15}

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Thickness of Aquifer given Discharge for Fully Penetrating Well Solution

Follow our step by step solution on how to calculate Thickness of Aquifer given Discharge for Fully Penetrating Well?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

H = \frac{(\frac{60m³/s \cdot \log ((\frac{100m}{2.94m}), e)}{π \cdot 0.105cm/s}) + {(15m)}^{2} + {(17.98m)}^{2}}{2 \cdot 15m}

Next Step Substitute values of Constants

∴

H = \frac{(\frac{60m³/s \cdot \log ((\frac{100m}{2.94m}), e)}{3.1416 \cdot 0.105cm/s}) + {(15m)}^{2} + {(17.98m)}^{2}}{2 \cdot 15m}

Next Step Prepare to Evaluate

∴

H = \frac{(\frac{60 \cdot \log ((\frac{100}{2.94}), e)}{3.1416 \cdot 0.105}) + {(15)}^{2} + {(17.98)}^{2}}{2 \cdot 15}

Next Step Evaluate

∴

H = 19.995167574522m

LAST Step Rounding Answer

∴

H = 19.9952m

Thickness of Aquifer given Discharge for Fully Penetrating Well Formula Elements

Variables

Constants

Functions

Initial Piezometric Surface

The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Initial Piezometric Surface

Discharge by Fully Penetrating Well

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.

Symbol: Q_fw

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge by Fully Penetrating Well

Radius of Influence

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.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Influence

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.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Well

Coefficient of Permeability

Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces.

Symbol: K

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Formulas to find Coefficient of Permeability

Aquifer Thickness

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.

Symbol: b

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Aquifer Thickness

Depth of Water in Fully Penetrating Gravity Well

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.

Symbol: h_fw

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Water in Fully Penetrating Gravity Well

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

log

Logarithmic function is an inverse function to exponentiation.

Syntax: log(Base, Number)

Other formulas in Fully Penetrating Artesian Gravity Well category

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

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

Go Radius of Influence of unconfined aquifer with known discharge

R = r \cdot \exp (\frac{0.434 \cdot π \cdot K \cdot (H^{2} - {h fw}^{2})}{Q fe})

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

Thickness of Aquifer given Discharge for Fully Penetrating Well evaluator 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 evaluate 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 evaluate Thickness of Aquifer given Discharge for Fully Penetrating Well using this online evaluator? To use this online evaluator 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.

FAQs on Thickness of Aquifer given Discharge for Fully Penetrating Well

What is the formula to find Thickness of Aquifer given Discharge for Fully Penetrating Well?

The formula of Thickness of Aquifer given Discharge for Fully Penetrating Well is expressed as 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). Here is an example- 19.99517 = (((60*log((100/2.94),e))/(pi*0.00105))+(15)^2+(17.98)^2)/(2*15).

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

With 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) we can find Thickness of Aquifer given Discharge for Fully Penetrating Well using the formula - 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). This formula also uses Archimedes' constant and Logarithmic Inverse (log) function(s).

Can the Thickness of Aquifer given Discharge for Fully Penetrating Well be negative?

No, the Thickness of Aquifer given Discharge for Fully Penetrating Well, measured in Length cannot be negative.

Which unit is used to measure Thickness of Aquifer given Discharge for Fully Penetrating Well?

Thickness of Aquifer given Discharge for Fully Penetrating Well is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Thickness of Aquifer given Discharge for Fully Penetrating Well can be measured.

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Thickness of Aquifer given Discharge for Fully Penetrating Well Formula

Thickness of Aquifer given Discharge for Fully Penetrating Well Example

Thickness of Aquifer given Discharge for Fully Penetrating Well Solution

Thickness of Aquifer given Discharge for Fully Penetrating Well Formula Elements

Other formulas in Fully Penetrating Artesian Gravity Well category

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

FAQs on Thickness of Aquifer given Discharge for Fully Penetrating Well

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