Discharge at Edge of Zone of Influence Calculator

✖The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.ⓘ Coefficient of Permeability [K]			+10% -10%
✖The Saturated Thickness of the Aquifer refers to the vertical height of the aquifer in which the pore spaces are completely filled with water.ⓘ Saturated Thickness of the Aquifer [H]			+10% -10%
✖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.ⓘ Depth of Water in the Pumping Well [h_w]			+10% -10%
✖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.ⓘ Radius at the Edge of Zone of Influence [r]			+10% -10%
✖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.ⓘ Radius of the Pumping Well [R_w]			+10% -10%

✖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.ⓘ Discharge at Edge of Zone of Influence [Q_u]

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Formula

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Discharge at Edge of Zone of Influence

Formula

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

Example

64.38969 m³/s = π \cdot 9 cm/s \cdot \frac{{35 m}^{2} - {30 m}^{2}}{\ln (\frac{25 m}{6 m})}

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Discharge at Edge of Zone of Influence Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Q_u = pi*K*(H^2-h_w^2)/ln(r/R_w)
This formula uses 1 Constants, 1 Functions, 6 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 of an Unconfined Aquifer - (Measured in Cubic Meter per Second) - 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.
Coefficient of Permeability - (Measured in Meter per Second) - The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.
Saturated Thickness of the Aquifer - (Measured in Meter) - The Saturated Thickness of the Aquifer refers to the vertical height of the aquifer in which the pore spaces are completely filled with water.
Depth of Water in the Pumping Well - (Measured in Meter) - 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.
Radius at the Edge of Zone of Influence - (Measured in Meter) - 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.
Radius of the Pumping Well - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Permeability: 9 Centimeter per Second --> 0.09 Meter per Second (Check conversion here)
Saturated Thickness of the Aquifer: 35 Meter --> 35 Meter No Conversion Required
Depth of Water in the Pumping Well: 30 Meter --> 30 Meter No Conversion Required
Radius at the Edge of Zone of Influence: 25 Meter --> 25 Meter No Conversion Required
Radius of the Pumping Well: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_u = pi*K*(H^2-h_w^2)/ln(r/R_w) --> pi*0.09*(35^2-30^2)/ln(25/6)

Evaluating ... ...

Q_u = 64.3896937725745

STEP 3: Convert Result to Output's Unit

64.3896937725745 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

64.3896937725745 ≈ 64.38969 Cubic Meter per Second <-- Steady Flow of an Unconfined Aquifer

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

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National Institute of Technology (NIT), Warangal

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< Unconfined Flow Calculators

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

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

Discharge at Edge of Zone of Influence

Go 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)

Coefficient of Permeability when Equilibrium Equation for Well in Unconfined Aquifer

Go Coefficient of Permeability = Steady Flow of an Unconfined Aquifer/(pi*(Water Table Depth 2^2-Water Table Depth^2)/ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1))

Equilibrium Equation for Well in Unconfined Aquifer

Go 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)

Discharge at Edge of Zone of Influence Formula

What are the Zones of Groundwater?

Groundwater is found in two zones. The unsaturated zone, immediately below the land surface, contains water and air in the open spaces, or pores. The saturated zone, a zone in which all the pores and rock fractures are filled with water, underlies the unsaturated zone.

How to Calculate Discharge at Edge of Zone of Influence?

Discharge at Edge of Zone of Influence calculator uses 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) to calculate the Steady Flow of an Unconfined Aquifer, The Discharge at Edge of Zone of Influence formula is defined as the volumetric flow rate of water that is transported through a given cross-sectional area. Steady Flow of an Unconfined Aquifer is denoted by Q_u symbol.

How to calculate Discharge at Edge of Zone of Influence using this online calculator? To use this online calculator for Discharge at Edge of Zone of Influence, enter Coefficient of Permeability (K), Saturated Thickness of the Aquifer (H), Depth of Water in the Pumping Well (h_w), Radius at the Edge of Zone of Influence (r) & Radius of the Pumping Well (R_w) and hit the calculate button. Here is how the Discharge at Edge of Zone of Influence calculation can be explained with given input values -> 64.38969 = pi*0.09*(35^2-30^2)/ln(25/6).

FAQ

What is Discharge at Edge of Zone of Influence?

The Discharge at Edge of Zone of Influence formula is defined as the volumetric flow rate of water that is transported through a given cross-sectional area and is represented as Q_u = pi*K*(H^2-h_w^2)/ln(r/R_w) or 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). The Coefficient of Permeability of soil describes how easily a liquid will move through the soil, The Saturated Thickness of the Aquifer refers to the vertical height of the aquifer in which the pore spaces are completely filled with water, 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, 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 & 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.

How to calculate Discharge at Edge of Zone of Influence?

The Discharge at Edge of Zone of Influence formula is defined as the volumetric flow rate of water that is transported through a given cross-sectional area is calculated using 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). To calculate Discharge at Edge of Zone of Influence, you need Coefficient of Permeability (K), Saturated Thickness of the Aquifer (H), Depth of Water in the Pumping Well (h_w), Radius at the Edge of Zone of Influence (r) & Radius of the Pumping Well (R_w). With our tool, you need to enter the respective value for Coefficient of Permeability, Saturated Thickness of the Aquifer, Depth of Water in the Pumping Well, Radius at the Edge of Zone of Influence & Radius of the Pumping Well and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Steady Flow of an Unconfined Aquifer?

In this formula, Steady Flow of an Unconfined Aquifer uses Coefficient of Permeability, Saturated Thickness of the Aquifer, Depth of Water in the Pumping Well, Radius at the Edge of Zone of Influence & Radius of the Pumping Well. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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