Radius of Well given Discharge for Partially Penetrating Well Calculator

✖The radius of influence is the distance from a pumping well to the point where the drawdown, or lowering of the water table, becomes negligible.ⓘ Radius of Influence [R]			+10% -10%
✖Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces.ⓘ Coefficient of Permeability [K]			+10% -10%
✖Aquifer Thickness (at Midpoint between Equipotential lines) or otherwise is the thickness of aquifer in which the pore spaces of rock forming the aquifer may or may not be with water.ⓘ Aquifer Thickness [b]			+10% -10%
✖The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.ⓘ Initial Piezometric Surface [H]			+10% -10%
✖Depth of Water is the depth in the well measured above the impermeable layer.ⓘ Depth of Water [h_w]			+10% -10%
✖Correction Factor refers to the reduced efficiency and altered flow patterns due to the well not extending through the entire aquifer thickness.ⓘ Correction Factor [G]			+10% -10%
✖Discharge for Partially Penetrating Well refers to the volume of water extracted from an aquifer when the well does not extend through the entire thickness of the aquifer.ⓘ Discharge for Partially Penetrating Well [Q_v]			+10% -10%

✖The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius.ⓘ Radius of Well given Discharge for Partially Penetrating Well [r]

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Formula

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Radius of Well given Discharge for Partially Penetrating Well

Formula

r = \frac{R}{\exp (\frac{2 \cdot π \cdot K \cdot b \cdot (H - h w) \cdot G}{Q v})}

Example

75.28252 m = \frac{100 m}{\exp (\frac{2 \cdot π \cdot 0.105 cm/s \cdot 15.0 m \cdot (20 m - 2.44 m) \cdot 0.83}{5.08 m³/s})}

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Radius of Well given Discharge for Partially Penetrating Well Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Well = Radius of Influence/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well))
r = R/(exp((2*pi*K*b*(H-h_w)*G)/Q_v))
This formula uses 1 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Radius of Well - (Measured in Meter) - The radius of well refers to the horizontal distance from the center of the well to its inner wall, essentially the well’s radius.
Radius of Influence - (Measured in Meter) - The radius of influence is the distance from a pumping well to the point where the drawdown, or lowering of the water table, becomes negligible.
Coefficient of Permeability - (Measured in Meter per Second) - Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces.
Aquifer Thickness - (Measured in Meter) - Aquifer Thickness (at Midpoint between Equipotential lines) or otherwise is the thickness of aquifer in which the pore spaces of rock forming the aquifer may or may not be with water.
Initial Piezometric Surface - (Measured in Meter) - The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence.
Depth of Water - (Measured in Meter) - Depth of Water is the depth in the well measured above the impermeable layer.
Correction Factor - Correction Factor refers to the reduced efficiency and altered flow patterns due to the well not extending through the entire aquifer thickness.
Discharge for Partially Penetrating Well - (Measured in Cubic Meter per Second) - Discharge for Partially Penetrating Well refers to the volume of water extracted from an aquifer when the well does not extend through the entire thickness of the aquifer.

STEP 1: Convert Input(s) to Base Unit

Radius of Influence: 100 Meter --> 100 Meter No Conversion Required
Coefficient of Permeability: 0.105 Centimeter per Second --> 0.00105 Meter per Second (Check conversion here)
Aquifer Thickness: 15 Meter --> 15 Meter No Conversion Required
Initial Piezometric Surface: 20 Meter --> 20 Meter No Conversion Required
Depth of Water: 2.44 Meter --> 2.44 Meter No Conversion Required
Correction Factor: 0.83 --> No Conversion Required
Discharge for Partially Penetrating Well: 5.08 Cubic Meter per Second --> 5.08 Cubic Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = R/(exp((2*pi*K*b*(H-h_w)*G)/Q_v)) --> 100/(exp((2*pi*0.00105*15*(20-2.44)*0.83)/5.08))

Evaluating ... ...

r = 75.2825228658548

STEP 3: Convert Result to Output's Unit

75.2825228658548 Meter --> No Conversion Required

FINAL ANSWER

75.2825228658548 ≈ 75.28252 Meter <-- Radius of Well

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Water Resources Ground Water » Flow in Wells » Partially Penetrating Artesian Well » Radius of Well given Discharge for Partially Penetrating Well

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Birsa Institute of Technology (BIT), Sindri

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< Partially Penetrating Artesian Well Calculators

Coefficient of Permeability given Discharge for Partially Penetrating Well

Go Coefficient of Permeability = Discharge for Partially Penetrating Well/((2*pi*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/(log((Radius of Influence/Radius of Well),e)))

Aquifer Thickness given Discharge for Partially Penetrating Well

Go Aquifer Thickness = Discharge for Partially Penetrating Well/((2*pi*Coefficient of Permeability*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/(log((Radius of Influence/Radius of Well),e)))

Thickness of Aquifer given Discharge for Partially Penetrating Well

Go Initial Piezometric Surface = Depth of Water+(Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well),e)))/(2*pi*Coefficient of Permeability*Aquifer Thickness*Correction Factor)

Discharge for Partially Penetrating Well

Go Discharge for Partially Penetrating Well = (2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/(log((Radius of Influence/Radius of Well),e))

Radius of Well given Discharge for Partially Penetrating Well Formula

What is Discharge?

The amount of fluid passing a section of a stream in unit time is called the discharge. If v is the mean velocity and A is the cross sectional area, the discharge Q is defined by Q = Av which is known as volume flow rate.

How to Calculate Radius of Well given Discharge for Partially Penetrating Well?

Radius of Well given Discharge for Partially Penetrating Well calculator uses Radius of Well = Radius of Influence/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well)) to calculate the Radius of Well, Radius of Well given Discharge for Partially Penetrating Well formula is defined as the effective radius of a partially penetrating well in a confined aquifer, which is influenced by the discharge rate, hydraulic conductivity, and thickness of the aquifer, as well as the distance from the well to the water table. Radius of Well is denoted by r symbol.

How to calculate Radius of Well given Discharge for Partially Penetrating Well using this online calculator? To use this online calculator for Radius of Well given Discharge for Partially Penetrating Well, enter Radius of Influence (R), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w), Correction Factor (G) & Discharge for Partially Penetrating Well (Q_v) and hit the calculate button. Here is how the Radius of Well given Discharge for Partially Penetrating Well calculation can be explained with given input values -> 75.28252 = 100/(exp((2*pi*0.00105*15*(20-2.44)*0.83)/5.08)).

FAQ

What is Radius of Well given Discharge for Partially Penetrating Well?

Radius of Well given Discharge for Partially Penetrating Well formula is defined as the effective radius of a partially penetrating well in a confined aquifer, which is influenced by the discharge rate, hydraulic conductivity, and thickness of the aquifer, as well as the distance from the well to the water table and is represented as r = R/(exp((2*pi*K*b*(H-h_w)*G)/Q_v)) or Radius of Well = Radius of Influence/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well)). The radius of influence is the distance from a pumping well to the point where the drawdown, or lowering of the water table, becomes negligible, Coefficient of Permeability refers to the ease with which water can flow through the aquifer's pore spaces, Aquifer Thickness (at Midpoint between Equipotential lines) or otherwise is the thickness of aquifer in which the pore spaces of rock forming the aquifer may or may not be with water, The initial piezometric surface refers to the level at which groundwater naturally stands in a confined aquifer before any pumping or external influence, Depth of Water is the depth in the well measured above the impermeable layer, Correction Factor refers to the reduced efficiency and altered flow patterns due to the well not extending through the entire aquifer thickness & Discharge for Partially Penetrating Well refers to the volume of water extracted from an aquifer when the well does not extend through the entire thickness of the aquifer.

How to calculate Radius of Well given Discharge for Partially Penetrating Well?

Radius of Well given Discharge for Partially Penetrating Well formula is defined as the effective radius of a partially penetrating well in a confined aquifer, which is influenced by the discharge rate, hydraulic conductivity, and thickness of the aquifer, as well as the distance from the well to the water table is calculated using Radius of Well = Radius of Influence/(exp((2*pi*Coefficient of Permeability*Aquifer Thickness*(Initial Piezometric Surface-Depth of Water)*Correction Factor)/Discharge for Partially Penetrating Well)). To calculate Radius of Well given Discharge for Partially Penetrating Well, you need Radius of Influence (R), Coefficient of Permeability (K), Aquifer Thickness (b), Initial Piezometric Surface (H), Depth of Water (h_w), Correction Factor (G) & Discharge for Partially Penetrating Well (Q_v). With our tool, you need to enter the respective value for Radius of Influence, Coefficient of Permeability, Aquifer Thickness, Initial Piezometric Surface, Depth of Water, Correction Factor & Discharge for Partially Penetrating Well 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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