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Depth of Water in Well given Discharge in Unconfined Aquifer Formula

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Depth of Water in Well given Discharge is the depth or water level inside a well that can sustain a specific discharge rate. Check FAQs

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

h'' - Depth of Water in Well given Discharge?H - Thickness of Unconfined Aquifer?Q - Discharge?R_w - Radius of Influence?r - Radius of Well?K_WH - Coefficient of Permeability in Well Hydraulics?π - Archimedes' constant?

Depth of Water in Well given Discharge in Unconfined Aquifer Example

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Here is how the Depth of Water in Well given Discharge in Unconfined Aquifer equation looks like with Values.

Here is how the Depth of Water in Well given Discharge in Unconfined Aquifer equation looks like with Units.

Here is how the Depth of Water in Well given Discharge in Unconfined Aquifer equation looks like.

1.2285 = \sqrt{5^{2} - \frac{1.01 \cdot \log ((\frac{8.6}{7.5}), e)}{3.1416 \cdot 10}}

1.2285m = \sqrt{{5m}^{2} - \frac{1.01m³/s \cdot \log ((\frac{8.6m}{7.5m}), e)}{3.1416 \cdot 10cm/s}}

1.2285 = \sqrt{5^{2} - \frac{1.01 \cdot \log ((\frac{8.6}{7.5}), e)}{3.1416 \cdot 10}}

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Depth of Water in Well given Discharge in Unconfined Aquifer Solution

Follow our step by step solution on how to calculate Depth of Water in Well given Discharge in Unconfined Aquifer?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h'' = \sqrt{{5m}^{2} - \frac{1.01m³/s \cdot \log ((\frac{8.6m}{7.5m}), e)}{π \cdot 10cm/s}}

Next Step Substitute values of Constants

∴

h'' = \sqrt{{5m}^{2} - \frac{1.01m³/s \cdot \log ((\frac{8.6m}{7.5m}), e)}{3.1416 \cdot 10cm/s}}

Next Step Convert Units

∴

h'' = \sqrt{{5m}^{2} - \frac{1.01m³/s \cdot \log ((\frac{8.6m}{7.5m}), e)}{3.1416 \cdot 0.1m/s}}

Next Step Prepare to Evaluate

∴

h'' = \sqrt{5^{2} - \frac{1.01 \cdot \log ((\frac{8.6}{7.5}), e)}{3.1416 \cdot 0.1}}

Next Step Evaluate

∴

h'' = 1.228500482931m

LAST Step Rounding Answer

∴

h'' = 1.2285m

Depth of Water in Well given Discharge in Unconfined Aquifer Formula Elements

Variables

Constants

Functions

Depth of Water in Well given Discharge

Depth of Water in Well given Discharge is the depth or water level inside a well that can sustain a specific discharge rate.

Symbol: h''

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Water in Well given Discharge

Thickness of Unconfined Aquifer

Thickness of Unconfined Aquifer is measured from impermeable layer to the initial level of water table.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Thickness of Unconfined Aquifer

Discharge

Discharge is the flow rate of water that is extracted from or injected into a well.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Discharge

Radius of Influence

Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.

Symbol: R_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Influence

Radius of Well

Radius of Well is defined as the distance from center of well to its outer boundary.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Well

Coefficient of Permeability in Well Hydraulics

Coefficient of Permeability in Well Hydraulics of soil in well hydraulics describes how easily a liquid will move through the soil.

Symbol: K_WH

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Formulas to find Coefficient of Permeability in Well Hydraulics

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 Depth of Water in Well category

Go Depth of Water at Point 1 given Discharge of Two Wells under Consideration

h 1 = \sqrt{{h 2}^{2} - \frac{Q \cdot \log ((\frac{r 2}{r 1}), e)}{π \cdot K WH}}

Go Depth of Water at Point 2 given Discharge of Two Wells under Consideration

h 2 = \sqrt{{h 1}^{2} + \frac{Q \cdot \log ((\frac{r 2}{r 1}), e)}{π \cdot K WH}}

Go Depth of Water at Point 1 given Discharge from Two Wells with Base 10

h 1 = \sqrt{{h 2}^{2} - \frac{Q \cdot \log ((\frac{r 2}{r 1}), 10)}{1.36 \cdot K WH}}

Go Depth of Water at Point 2 given Discharge from Two Wells with Base 10

h 2 = \sqrt{{h 1}^{2} + \frac{Q \cdot \log ((\frac{r 2}{r 1}), 10)}{1.36 \cdot K WH}}

How to Evaluate Depth of Water in Well given Discharge in Unconfined Aquifer?

Depth of Water in Well given Discharge in Unconfined Aquifer evaluator uses Depth of Water in Well given Discharge = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability in Well Hydraulics)) to evaluate the Depth of Water in Well given Discharge, The Depth of Water in Well given Discharge in Unconfined Aquifer formula is defined as the calculation of the value of depth of water when we have prior information of discharge in unconfined aquifer. Depth of Water in Well given Discharge is denoted by h'' symbol.

How to evaluate Depth of Water in Well given Discharge in Unconfined Aquifer using this online evaluator? To use this online evaluator for Depth of Water in Well given Discharge in Unconfined Aquifer, enter Thickness of Unconfined Aquifer (H), Discharge (Q), Radius of Influence (R_w), Radius of Well (r) & Coefficient of Permeability in Well Hydraulics (K_WH) and hit the calculate button.

FAQs on Depth of Water in Well given Discharge in Unconfined Aquifer

What is the formula to find Depth of Water in Well given Discharge in Unconfined Aquifer?

The formula of Depth of Water in Well given Discharge in Unconfined Aquifer is expressed as Depth of Water in Well given Discharge = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability in Well Hydraulics)). Here is an example- 1.2285 = sqrt(5^2-(1.01*log((8.6/7.5),e))/(pi*0.1)).

How to calculate Depth of Water in Well given Discharge in Unconfined Aquifer?

With Thickness of Unconfined Aquifer (H), Discharge (Q), Radius of Influence (R_w), Radius of Well (r) & Coefficient of Permeability in Well Hydraulics (K_WH) we can find Depth of Water in Well given Discharge in Unconfined Aquifer using the formula - Depth of Water in Well given Discharge = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of Well),e))/(pi*Coefficient of Permeability in Well Hydraulics)). This formula also uses Archimedes' constant and , Square Root (sqrt), Logarithmic Inverse (log) function(s).

Can the Depth of Water in Well given Discharge in Unconfined Aquifer be negative?

No, the Depth of Water in Well given Discharge in Unconfined Aquifer, measured in Length cannot be negative.

Which unit is used to measure Depth of Water in Well given Discharge in Unconfined Aquifer?

Depth of Water in Well given Discharge in Unconfined Aquifer 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 in Unconfined Aquifer can be measured.

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Depth of Water in Well given Discharge in Unconfined Aquifer Formula

Depth of Water in Well given Discharge in Unconfined Aquifer Example

Depth of Water in Well given Discharge in Unconfined Aquifer Solution

Depth of Water in Well given Discharge in Unconfined Aquifer Formula Elements

Other formulas in Depth of Water in Well category

How to Evaluate Depth of Water in Well given Discharge in Unconfined Aquifer?

FAQs on Depth of Water in Well given Discharge in Unconfined Aquifer

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