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

✖The coefficient of permeability (K) is the velocity in meters or centimetres per second of water through soils.ⓘ Coefficient of Permeability [K]			+10% -10%
✖Width of Aquifer measured from impermeable layer to the initial level of water table.ⓘ Width of Aquifer [H_a]			+10% -10%
✖Piezometric Head at Radial Distance r2 is important in calculating Thiem's equilibrium equation for steady flow.ⓘ Piezometric Head at Radial Distance r2 [h₂]			+10% -10%
✖Piezometric Head at Radial Distance r1 is important in calculating Thiem's equilibrium equation for steady flow.ⓘ Piezometric Head at Radial Distance r1 [h₁]			+10% -10%
✖Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used.ⓘ Radial Distance at Observation Well 2 [r₂]			+10% -10%
✖Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used.ⓘ Radial Distance at Observation Well 1 [r₁]			+10% -10%

✖Steady flow in a confined aquifer is the flow or discharge into the auifer.ⓘ Thiem's equilibrium equation for steady flow in confined aquifer [Q_sf]

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Thiem's equilibrium equation for steady flow in confined aquifer

Formula

`"Q"_{"sf"} = 2*pi*"K"*"H"_{"a"}*("h"_{"2"}-"h"_{"1"})/ln("r"_{"2"}/"r"_{"1"})`

Example

`"122.3737m³/s"=2*pi*"3.0cm/s"*"45m"*("25m"-"15m")/ln("10.0m"/"5.0m")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
Q_sf = 2*pi*K*H_a*(h₂-h₁)/ln(r₂/r₁)
This formula uses 1 Constants, 1 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Steady Flow in a Confined Aquifer - (Measured in Cubic Meter per Second) - Steady flow in a confined aquifer is the flow or discharge into the auifer.
Coefficient of Permeability - (Measured in Meter per Second) - The coefficient of permeability (K) is the velocity in meters or centimetres per second of water through soils.
Width of Aquifer - (Measured in Meter) - Width of Aquifer measured from impermeable layer to the initial level of water table.
Piezometric Head at Radial Distance r2 - (Measured in Meter) - Piezometric Head at Radial Distance r2 is important in calculating Thiem's equilibrium equation for steady flow.
Piezometric Head at Radial Distance r1 - (Measured in Meter) - Piezometric Head at Radial Distance r1 is important in calculating Thiem's equilibrium equation for steady flow.
Radial Distance at Observation Well 2 - (Measured in Meter) - Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used.
Radial Distance at Observation Well 1 - (Measured in Meter) - Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Permeability: 3 Centimeter per Second --> 0.03 Meter per Second (Check conversion here)
Width of Aquifer: 45 Meter --> 45 Meter No Conversion Required
Piezometric Head at Radial Distance r2: 25 Meter --> 25 Meter No Conversion Required
Piezometric Head at Radial Distance r1: 15 Meter --> 15 Meter No Conversion Required
Radial Distance at Observation Well 2: 10 Meter --> 10 Meter No Conversion Required
Radial Distance at Observation Well 1: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_sf = 2*pi*K*H_a*(h₂-h₁)/ln(r₂/r₁) --> 2*pi*0.03*45*(25-15)/ln(10/5)

Evaluating ... ...

Q_sf = 122.373723829334

STEP 3: Convert Result to Output's Unit

122.373723829334 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

122.373723829334 ≈ 122.3737 Cubic Meter per Second <-- Steady Flow in a Confined Aquifer

(Calculation completed in 00.004 seconds)

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Thiem's equilibrium equation for steady flow in confined aquifer

Go 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)

Equilibrium Equation for Flow in Confined Aquifer at Observation Well

Go Discharge entering cylindrical surface into Well = (2*pi*Transmissivity*(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)

Transmissivity when Discharge and Drawdowns are considered

Go Transmissivity = Steady Flow in a Confined Aquifer*ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1)/(2*pi*(Drawdown at the Start of Recuperation-Drawdown at a Time))

Discharge Observed at Edge of Zone of Influence

Go Discharge entering cylindrical surface into Well = 2*pi*Transmissivity*Possible Drawdown in Confined Aquifer/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1)

Discharge entering cylindrical surface to well discharge

Go Discharge entering cylindrical surface into Well = (2*pi*Radial Distance*Width of Aquifer)*(Coefficient of Permeability*(Change in the piezometric head/Change in Radial Distance))

Transmissivity when discharge at edge of zone of influence

Go Transmissivity = (Steady Flow in a Confined Aquifer*ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1))/(2*pi*Possible Drawdown in Confined Aquifer)

Velocity of flow by Darcy's Law at Radical Distance

Go Velocity of Flow at Radial Distance = Coefficient of Permeability*(Change in the piezometric head/Change in Radial Distance)

Change in Piezometric Head

Go Change in the piezometric head = Velocity of Flow at Radial Distance*Change in Radial Distance/Coefficient of Permeability

Change in Radial Distance

Go Change in Radial Distance = Coefficient of Permeability*Change in the piezometric head/Velocity of Flow at Radial Distance

Cylindrical Surface through which Velocity of Flow Occurs

Go Surface through which the Velocity of Flow Occurs = 2*pi*Radial Distance*Width of Aquifer

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

What is Coefficient of Permeability?

The Coefficient of Permeability of a soil describes how easily a liquid will move through a soil. It is also commonly referred to as the hydraulic conductivity of a soil. This factor can be affected by the viscosity, or thickness(fluidity) of a liquid and its density.

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

Thiem's equilibrium equation for steady flow in confined aquifer calculator 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 calculate the Steady Flow in a Confined Aquifer, The Thiem's equilibrium equation for steady flow in confined aquifer is used to determine piezometric head at any point at a radial distance r from the center of the well. Steady Flow in a Confined Aquifer is denoted by Q_sf symbol.

How to calculate Thiem's equilibrium equation for steady flow in confined aquifer using this online calculator? To use this online calculator 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. Here is how the Thiem's equilibrium equation for steady flow in confined aquifer calculation can be explained with given input values -> 122.3737 = 2*pi*0.03*45*(25-15)/ln(10/5).

FAQ

What is Thiem's equilibrium equation for steady flow in confined aquifer?

The Thiem's equilibrium equation for steady flow in confined aquifer is used to determine piezometric head at any point at a radial distance r from the center of the well and is represented as Q_sf = 2*pi*K*H_a*(h₂-h₁)/ln(r₂/r₁) or 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). The coefficient of permeability (K) is the velocity in meters or centimetres per second of water through soils, Width of Aquifer measured from impermeable layer to the initial level of water table, Piezometric Head at Radial Distance r2 is important in calculating Thiem's equilibrium equation for steady flow, Piezometric Head at Radial Distance r1 is important in calculating Thiem's equilibrium equation for steady flow, Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used & Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used.

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

The Thiem's equilibrium equation for steady flow in confined aquifer is used to determine piezometric head at any point at a radial distance r from the center of the well is calculated using 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 calculate Thiem's equilibrium equation for steady flow in confined aquifer, you need 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). With our tool, you need to enter the respective value for Coefficient of Permeability, Width of Aquifer, Piezometric Head at Radial Distance r2, Piezometric Head at Radial Distance r1, Radial Distance at Observation Well 2 & Radial Distance at Observation Well 1 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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