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Thiem's equilibrium equation for steady flow in confined aquifer Formula

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Steady Flow in a Confined Aquifer is a condition where groundwater flows through an aquifer under conditions of steady-state equilibrium. Check FAQs

Q sf = 2 \cdot π \cdot K \cdot H a \cdot \frac{h 2 - h 1}{\ln (\frac{r 2}{r 1})}

Q_sf - Steady Flow in a Confined Aquifer?K - Coefficient of Permeability?H_a - Width of Aquifer?h₂ - Piezometric Head at Radial Distance r2?h₁ - Piezometric Head at Radial Distance r1?r₂ - Radial Distance at Observation Well 2?r₁ - Radial Distance at Observation Well 1?π - Archimedes' constant?

Thiem's equilibrium equation for steady flow in confined aquifer Example

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Here is how the Thiem's equilibrium equation for steady flow in confined aquifer equation looks like with Values.

Here is how the Thiem's equilibrium equation for steady flow in confined aquifer equation looks like with Units.

Here is how the Thiem's equilibrium equation for steady flow in confined aquifer equation looks like.

122.3737 = 2 \cdot 3.1416 \cdot 3 \cdot 45 \cdot \frac{25 - 15}{\ln (\frac{10}{5})}

122.3737m³/s = 2 \cdot 3.1416 \cdot 3cm/s \cdot 45m \cdot \frac{25m - 15m}{\ln (\frac{10m}{5m})}

122.3737 = 2 \cdot 3.1416 \cdot 3 \cdot 45 \cdot \frac{25 - 15}{\ln (\frac{10}{5})}

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Thiem's equilibrium equation for steady flow in confined aquifer Solution

Follow our step by step solution on how to calculate Thiem's equilibrium equation for steady flow in confined aquifer?

FIRST Step Consider the formula

Q sf = 2 \cdot π \cdot K \cdot H a \cdot \frac{h 2 - h 1}{\ln (\frac{r 2}{r 1})}

Next Step Substitute values of Variables

∴

Q sf = 2 \cdot π \cdot 3cm/s \cdot 45m \cdot \frac{25m - 15m}{\ln (\frac{10m}{5m})}

Next Step Substitute values of Constants

∴

Q sf = 2 \cdot 3.1416 \cdot 3cm/s \cdot 45m \cdot \frac{25m - 15m}{\ln (\frac{10m}{5m})}

Next Step Convert Units

∴

Q sf = 2 \cdot 3.1416 \cdot 0.03m/s \cdot 45m \cdot \frac{25m - 15m}{\ln (\frac{10m}{5m})}

Next Step Prepare to Evaluate

∴

Q sf = 2 \cdot 3.1416 \cdot 0.03 \cdot 45 \cdot \frac{25 - 15}{\ln (\frac{10}{5})}

Next Step Evaluate

∴

Q sf = 122.373723829334m³/s

LAST Step Rounding Answer

∴

Q sf = 122.3737m³/s

Thiem's equilibrium equation for steady flow in confined aquifer Formula Elements

Variables

Constants

Functions

Steady Flow in a Confined Aquifer

Steady Flow in a Confined Aquifer is a condition where groundwater flows through an aquifer under conditions of steady-state equilibrium.

Symbol: Q_sf

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Steady Flow in a Confined Aquifer

Coefficient of Permeability

Coefficient of Permeability is the measure of the ability of a porous material (such as soil or rock) to transmit fluids through it. It quantifies how easily water can flow through the material.

Symbol: K

Measurement: SpeedUnit: cm/s

Note: Value can be positive or negative.

Formulas to find Coefficient of Permeability

Width of Aquifer

Width of Aquifer is the horizontal extent or lateral dimension of the aquifer perpendicular to the direction of groundwater flow.

Symbol: H_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of Aquifer

Piezometric Head at Radial Distance r2

Piezometric Head at Radial Distance r2 is the hydraulic head measured at a specific radial distance r2 from a point of interest, typically a well or a pumping borehole.

Symbol: h₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Piezometric Head at Radial Distance r2

Piezometric Head at Radial Distance r1

Piezometric Head at Radial Distance r1 is the hydraulic head measured at a specific radial distance r1 from a point of interest, typically a well or a pumping borehole.

Symbol: h₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Piezometric Head at Radial Distance r1

Radial Distance at Observation Well 2

Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radial Distance at Observation Well 2

Radial Distance at Observation Well 1

Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radial Distance at Observation Well 1

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)

Other formulas in Steady Flow into a Well category

Go Velocity of Flow by Darcy's Law at Radical Distance

V r = K \cdot (\frac{dh}{dr})

Go Change in Piezometric Head

dh = V r \cdot \frac{dr}{K}

How to Evaluate Thiem's equilibrium equation for steady flow in confined aquifer?

Thiem's equilibrium equation for steady flow in confined aquifer evaluator uses Steady Flow in a Confined Aquifer = 2*pi*Coefficient of Permeability*Width of Aquifer*(Piezometric Head at Radial Distance r2-Piezometric Head at Radial Distance r1)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1) to evaluate the Steady Flow in a Confined Aquifer, The Thiem's Equilibrium Equation for Steady Flow in confined aquifer formula is defined as the steady-state flow of groundwater towards a well in a confined aquifer. Steady Flow in a Confined Aquifer is denoted by Q_sf symbol.

How to evaluate Thiem's equilibrium equation for steady flow in confined aquifer using this online evaluator? To use this online evaluator for Thiem's equilibrium equation for steady flow in confined aquifer, enter Coefficient of Permeability (K), Width of Aquifer (H_a), Piezometric Head at Radial Distance r2 (h₂), Piezometric Head at Radial Distance r1 (h₁), Radial Distance at Observation Well 2 (r₂) & Radial Distance at Observation Well 1 (r₁) and hit the calculate button.

FAQs on Thiem's equilibrium equation for steady flow in confined aquifer

What is the formula to find Thiem's equilibrium equation for steady flow in confined aquifer?

The formula of Thiem's equilibrium equation for steady flow in confined aquifer is expressed as Steady Flow in a Confined Aquifer = 2*pi*Coefficient of Permeability*Width of Aquifer*(Piezometric Head at Radial Distance r2-Piezometric Head at Radial Distance r1)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1). Here is an example- 122.3737 = 2*pi*0.03*45*(25-15)/ln(10/5).

How to calculate Thiem's equilibrium equation for steady flow in confined aquifer?

With Coefficient of Permeability (K), Width of Aquifer (H_a), Piezometric Head at Radial Distance r2 (h₂), Piezometric Head at Radial Distance r1 (h₁), Radial Distance at Observation Well 2 (r₂) & Radial Distance at Observation Well 1 (r₁) we can find Thiem's equilibrium equation for steady flow in confined aquifer using the formula - Steady Flow in a Confined Aquifer = 2*pi*Coefficient of Permeability*Width of Aquifer*(Piezometric Head at Radial Distance r2-Piezometric Head at Radial Distance r1)/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).

Can the Thiem's equilibrium equation for steady flow in confined aquifer be negative?

Yes, the Thiem's equilibrium equation for steady flow in confined aquifer, measured in Volumetric Flow Rate can be negative.

Which unit is used to measure Thiem's equilibrium equation for steady flow in confined aquifer?

Thiem's equilibrium equation for steady flow in confined 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 Thiem's equilibrium equation for steady flow in confined aquifer can be measured.

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Thiem's equilibrium equation for steady flow in confined aquifer Formula

Thiem's equilibrium equation for steady flow in confined aquifer Example

Thiem's equilibrium equation for steady flow in confined aquifer Solution

Thiem's equilibrium equation for steady flow in confined aquifer Formula Elements

Other formulas in Steady Flow into a Well category

How to Evaluate Thiem's equilibrium equation for steady flow in confined aquifer?

FAQs on Thiem's equilibrium equation for steady flow in confined aquifer

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