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Equilibrium Equation for Well in Unconfined Aquifer Formula

GoDischarge at Edge of Zone of Influence Formula

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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. Check FAQs

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

Q_u - Steady Flow of an Unconfined Aquifer?K - Coefficient of Permeability?H₂ - Water Table Depth 2?H₁ - Water Table Depth?r₂ - Radial Distance at Observation Well 2?r₁ - Radial Distance at Observation Well 1?π - Archimedes' constant?

Equilibrium Equation for Well in Unconfined Aquifer Example

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Here is how the Equilibrium Equation for Well in Unconfined Aquifer equation looks like with Values.

Here is how the Equilibrium Equation for Well in Unconfined Aquifer equation looks like with Units.

Here is how the Equilibrium Equation for Well in Unconfined Aquifer equation looks like.

71.7926 = 3.1416 \cdot 9 \cdot \frac{45^{2} - 43^{2}}{\ln (\frac{10}{5})}

71.7926m³/s = 3.1416 \cdot 9cm/s \cdot \frac{{45m}^{2} - {43m}^{2}}{\ln (\frac{10m}{5m})}

71.7926 = 3.1416 \cdot 9 \cdot \frac{45^{2} - 43^{2}}{\ln (\frac{10}{5})}

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Home » Engineering » Civil » Engineering Hydrology » Equilibrium Equation for Well in Unconfined Aquifer

Equilibrium Equation for Well in Unconfined Aquifer Solution

Follow our step by step solution on how to calculate Equilibrium Equation for Well in Unconfined Aquifer?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Q u = π \cdot 9cm/s \cdot \frac{{45m}^{2} - {43m}^{2}}{\ln (\frac{10m}{5m})}

Next Step Substitute values of Constants

∴

Q u = 3.1416 \cdot 9cm/s \cdot \frac{{45m}^{2} - {43m}^{2}}{\ln (\frac{10m}{5m})}

Next Step Convert Units

∴

Q u = 3.1416 \cdot 0.09m/s \cdot \frac{{45m}^{2} - {43m}^{2}}{\ln (\frac{10m}{5m})}

Next Step Prepare to Evaluate

∴

Q u = 3.1416 \cdot 0.09 \cdot \frac{45^{2} - 43^{2}}{\ln (\frac{10}{5})}

Next Step Evaluate

∴

Q u = 71.7925846465427m³/s

LAST Step Rounding Answer

∴

Q u = 71.7926m³/s

Equilibrium Equation for Well in Unconfined Aquifer Formula Elements

Variables

Constants

Functions

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.

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.

Water Table Depth 2

The Water Table Depth 2 refers to the vertical distance from the ground surface down to the water table, which is the upper surface of the zone of saturation where the soil or rock is fully saturated.

Symbol: H₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Water Table Depth

The Water Table Depth refers to the vertical distance from the ground surface down to the water table, which is the upper surface of the zone of saturation where the soil or rock is fully saturated.

Symbol: H₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Radial Distance at Observation Well 2

The Radial Distance at Observation Well 2 refers to the refers to the horizontal distance from the center of a pumping well to the observation well.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Radial Distance at Observation Well 1

The Radial Distance at Observation Well 1 refers to the refers to the horizontal distance from the center of a pumping well to the observation well.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

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)

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Formula and 2000+ more formulas!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

Other Formulas to find Steady Flow of an Unconfined Aquifer

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})}

Other formulas in Unconfined Flow category

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 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}}

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

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

How to Evaluate Equilibrium Equation for Well in Unconfined Aquifer?

Equilibrium Equation for Well in Unconfined Aquifer evaluator uses Steady Flow of an Unconfined Aquifer = pi*Coefficient of Permeability*(Water Table Depth 2^2-Water Table Depth^2)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1) to evaluate the Steady Flow of an Unconfined Aquifer, The Equilibrium Equation for Well in Unconfined Aquifer formula is defined as the volumetric flow rate of water that is transported through given cross-sectional area. Steady Flow of an Unconfined Aquifer is denoted by Q_u symbol.

How to evaluate Equilibrium Equation for Well in Unconfined Aquifer using this online evaluator? To use this online evaluator for Equilibrium Equation for Well in Unconfined Aquifer, enter Coefficient of Permeability (K), Water Table Depth 2 (H₂), Water Table Depth (H₁), Radial Distance at Observation Well 2 (r₂) & Radial Distance at Observation Well 1 (r₁) and hit the calculate button.

FAQs on Equilibrium Equation for Well in Unconfined Aquifer

What is the formula to find Equilibrium Equation for Well in Unconfined Aquifer?

The formula of Equilibrium Equation for Well in Unconfined Aquifer is expressed as Steady Flow of an Unconfined Aquifer = pi*Coefficient of Permeability*(Water Table Depth 2^2-Water Table Depth^2)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1). Here is an example- 71.79258 = pi*0.09*(45^2-43^2)/ln(10/5).

How to calculate Equilibrium Equation for Well in Unconfined Aquifer?

With Coefficient of Permeability (K), Water Table Depth 2 (H₂), Water Table Depth (H₁), Radial Distance at Observation Well 2 (r₂) & Radial Distance at Observation Well 1 (r₁) we can find Equilibrium Equation for Well in Unconfined Aquifer using the formula - Steady Flow of an Unconfined Aquifer = pi*Coefficient of Permeability*(Water Table Depth 2^2-Water Table Depth^2)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Steady Flow of an Unconfined Aquifer?

Here are the different ways to Calculate Steady Flow of an Unconfined Aquifer-

Steady Flow of an Unconfined Aquifer=pi*Coefficient of Permeability*(Saturated Thickness of the Aquifer^2-Depth of Water in the Pumping Well^2)/ln(Radius at the Edge of Zone of Influence/Radius of the Pumping Well)

Can the Equilibrium Equation for Well in Unconfined Aquifer be negative?

No, the Equilibrium Equation for Well in Unconfined Aquifer, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Equilibrium Equation for Well in Unconfined Aquifer?

Equilibrium Equation for Well in Unconfined Aquifer is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Equilibrium Equation for Well in Unconfined Aquifer can be measured.