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

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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. Check FAQs

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

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

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

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Here is how the Depth of Water in Well given Discharge for Fully Penetrating Well equation looks like.

17.984 = \sqrt{(2 \cdot 15 \cdot 20) - (\frac{60 \cdot \log ((\frac{100}{2.94}), e)}{3.1416 \cdot 0.105}) - {(15)}^{2}}

17.984m = \sqrt{(2 \cdot 15m \cdot 20m) - (\frac{60m³/s \cdot \log ((\frac{100m}{2.94m}), e)}{3.1416 \cdot 0.105cm/s}) - {(15m)}^{2}}

17.984 = \sqrt{(2 \cdot 15 \cdot 20) - (\frac{60 \cdot \log ((\frac{100}{2.94}), e)}{3.1416 \cdot 0.105}) - {(15)}^{2}}

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

Follow our step by step solution on how to calculate Depth of Water in Well given Discharge for Fully Penetrating Well?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h fw = \sqrt{(2 \cdot 15m \cdot 20m) - (\frac{60m³/s \cdot \log ((\frac{100m}{2.94m}), e)}{π \cdot 0.105cm/s}) - {(15m)}^{2}}

Next Step Substitute values of Constants

∴

h fw = \sqrt{(2 \cdot 15m \cdot 20m) - (\frac{60m³/s \cdot \log ((\frac{100m}{2.94m}), e)}{3.1416 \cdot 0.105cm/s}) - {(15m)}^{2}}

Next Step Prepare to Evaluate

∴

h fw = \sqrt{(2 \cdot 15 \cdot 20) - (\frac{60 \cdot \log ((\frac{100}{2.94}), e)}{3.1416 \cdot 0.105}) - {(15)}^{2}}

Next Step Evaluate

∴

h fw = 17.9840310488038m

LAST Step Rounding Answer

∴

h fw = 17.984m

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

Variables

Constants

Functions

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

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

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

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

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.

Syntax: sqrt(Number)

log

Logarithmic function is an inverse function to exponentiation.

Syntax: log(Base, Number)

Other formulas in Fully Penetrating Artesian Gravity Well category

Go Thickness of Aquifer given Discharge for Fully Penetrating Well

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

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

Depth of Water in Well given Discharge for Fully Penetrating Well evaluator 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 evaluate 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 evaluate Depth of Water in Well given Discharge for Fully Penetrating Well using this online evaluator? To use this online evaluator 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.

FAQs on Depth of Water in Well given Discharge for Fully Penetrating Well

What is the formula to find Depth of Water in Well given Discharge for Fully Penetrating Well?

The formula of Depth of Water in Well given Discharge for Fully Penetrating Well is expressed as 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). Here is an example- 17.98403 = sqrt((2*15*20)-((60*log((100/2.94),e))/(pi*0.00105))-(15)^2).

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

With 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) we can find Depth of Water in Well given Discharge for Fully Penetrating Well using the formula - 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). This formula also uses Archimedes' constant and , Square Root (sqrt), Logarithmic Inverse (log) function(s).

Can the Depth of Water in Well given Discharge for Fully Penetrating Well be negative?

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

Which unit is used to measure Depth of Water in Well given Discharge for Fully Penetrating Well?

Depth of Water in Well 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 Depth of Water in Well given Discharge for Fully Penetrating Well can be measured.

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

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

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

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

Other formulas in Fully Penetrating Artesian Gravity Well category

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

FAQs on Depth of Water in Well given Discharge for Fully Penetrating Well

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