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Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Formula

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The Depth of Water in the Pumping Well refers to the well in which pumping is required to increase the formation pressure to allow the free production flow. Check FAQs

h w = \sqrt{{(H)}^{2} - (\frac{Q u \cdot \ln (\frac{r}{R w})}{π \cdot K})}

h_w - Depth of Water in the Pumping Well?H - Saturated Thickness of the Aquifer?Q_u - Steady Flow of an Unconfined Aquifer?r - Radius at the Edge of Zone of Influence?R_w - Radius of the Pumping Well?K - Coefficient of Permeability?π - Archimedes' constant?

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Example

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Here is how the Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered equation looks like with Values.

Here is how the Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered equation looks like with Units.

Here is how the Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered equation looks like.

29.9486 = \sqrt{{(35)}^{2} - (\frac{65 \cdot \ln (\frac{25}{6})}{3.1416 \cdot 9})}

29.9486m = \sqrt{{(35m)}^{2} - (\frac{65m³/s \cdot \ln (\frac{25m}{6m})}{3.1416 \cdot 9cm/s})}

29.9486 = \sqrt{{(35)}^{2} - (\frac{65 \cdot \ln (\frac{25}{6})}{3.1416 \cdot 9})}

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Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Solution

Follow our step by step solution on how to calculate Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered?

FIRST Step Consider the formula

h w = \sqrt{{(H)}^{2} - (\frac{Q u \cdot \ln (\frac{r}{R w})}{π \cdot K})}

Next Step Substitute values of Variables

∴

h w = \sqrt{{(35m)}^{2} - (\frac{65m³/s \cdot \ln (\frac{25m}{6m})}{π \cdot 9cm/s})}

Next Step Substitute values of Constants

∴

h w = \sqrt{{(35m)}^{2} - (\frac{65m³/s \cdot \ln (\frac{25m}{6m})}{3.1416 \cdot 9cm/s})}

Next Step Convert Units

∴

h w = \sqrt{{(35m)}^{2} - (\frac{65m³/s \cdot \ln (\frac{25m}{6m})}{3.1416 \cdot 0.09m/s})}

Next Step Prepare to Evaluate

∴

h w = \sqrt{{(35)}^{2} - (\frac{65 \cdot \ln (\frac{25}{6})}{3.1416 \cdot 0.09})}

Next Step Evaluate

∴

h w = 29.9486150843287m

LAST Step Rounding Answer

∴

h w = 29.9486m

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Formula Elements

Variables

Constants

Functions

Depth of Water in the Pumping Well

The Depth of Water in the Pumping Well refers to the well in which pumping is required to increase the formation pressure to allow the free production flow.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Water in the Pumping Well

Saturated Thickness of the Aquifer

The Saturated Thickness of the Aquifer refers to the vertical height of the aquifer in which the pore spaces are completely filled with water.

Symbol: H

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Saturated Thickness of the Aquifer

Steady Flow of an Unconfined Aquifer

The Steady Flow of an Unconfined Aquifer refers to a condition where the groundwater flow rate and the water table level remain constant over time.

Symbol: Q_u

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Steady Flow of an Unconfined Aquifer

Radius at the Edge of Zone of Influence

The Radius at the Edge of Zone of Influence refers to the maximum distance from a pumping well where the effects of drawdown (lowering of the water table) can be detected.

Symbol: r

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius at the Edge of Zone of Influence

Radius of the Pumping Well

The Radius of the Pumping Well refers to the physical radius of the well itself, typically measured from the center of the well to its outer edge.

Symbol: R_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of the Pumping Well

Coefficient of Permeability

The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.

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

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

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)

Other formulas in Unconfined Flow category

Go Equilibrium Equation for Well in Unconfined Aquifer

Q u = π \cdot K \cdot \frac{{H 2}^{2} - {H 1}^{2}}{\ln (\frac{r 2}{r 1})}

Go Coefficient of Permeability when Equilibrium Equation for Well in Unconfined Aquifer

K = \frac{Q u}{π \cdot \frac{{H 2}^{2} - {H 1}^{2}}{\ln (\frac{r 2}{r 1})}}

Go Discharge at Edge of Zone of Influence

Q u = π \cdot K \cdot \frac{H^{2} - {h w}^{2}}{\ln (\frac{r}{R w})}

Go Saturated Thickness of Aquifer when Steady Flow of Unconfined Aquifer is Considered

H = \sqrt{\frac{Q u \cdot \ln (\frac{r}{R w})}{π \cdot K} + {h w}^{2}}

How to Evaluate Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered?

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered evaluator uses Depth of Water in the Pumping Well = sqrt((Saturated Thickness of the Aquifer)^2-((Steady Flow of an Unconfined Aquifer*ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well))/(pi*Coefficient of Permeability))) to evaluate the Depth of Water in the Pumping Well, The Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered formula is defined as water level in well of certain radius in catchment under study. Depth of Water in the Pumping Well is denoted by h_w symbol.

How to evaluate Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered using this online evaluator? To use this online evaluator for Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered, enter Saturated Thickness of the Aquifer (H), Steady Flow of an Unconfined Aquifer (Q_u), Radius at the Edge of Zone of Influence (r), Radius of the Pumping Well (R_w) & Coefficient of Permeability (K) and hit the calculate button.

FAQs on Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered

What is the formula to find Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered?

The formula of Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered is expressed as Depth of Water in the Pumping Well = sqrt((Saturated Thickness of the Aquifer)^2-((Steady Flow of an Unconfined Aquifer*ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well))/(pi*Coefficient of Permeability))). Here is an example- 29.94862 = sqrt((35)^2-((65*ln(25/6))/(pi*0.09))).

How to calculate Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered?

With Saturated Thickness of the Aquifer (H), Steady Flow of an Unconfined Aquifer (Q_u), Radius at the Edge of Zone of Influence (r), Radius of the Pumping Well (R_w) & Coefficient of Permeability (K) we can find Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered using the formula - Depth of Water in the Pumping Well = sqrt((Saturated Thickness of the Aquifer)^2-((Steady Flow of an Unconfined Aquifer*ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well))/(pi*Coefficient of Permeability))). This formula also uses Archimedes' constant and , Natural Logarithm (ln), Square Root (sqrt) function(s).

Can the Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered be negative?

Yes, the Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered, measured in Length can be negative.

Which unit is used to measure Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered?

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered 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 Pumping Well when Steady Flow in Unconfined Aquifer is Considered can be measured.

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Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Formula

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Example

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Solution

Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered Formula Elements

Other formulas in Unconfined Flow category

How to Evaluate Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered?

FAQs on Depth of Water in Pumping Well when Steady Flow in Unconfined Aquifer is Considered

Variable Name