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Radius of Well given Discharge in Confined Aquifer Formula

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GoRadius of Well for Discharge in Confined Aquifer with Base 10 Formula

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GoRadius of Well given Coefficient of Transmissibility Formula

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Radius of Well given Discharge is the radial distance from the center of the well to the outer boundary of the aquifer, where the effects of pumping or water withdrawal are observed. Check FAQs

r w = \frac{R w}{\exp (\frac{2 \cdot π \cdot K WH \cdot b p \cdot (H i - h w)}{Q 0})}

r_w - Radius of Well given Discharge?R_w - Radius of Influence?K_WH - Coefficient of Permeability in Well Hydraulics?b_p - Aquifer Thickness During Pumping?H_i - Initial Aquifer Thickness?h_w - Depth of Water?Q₀ - Discharge at Time t=0?π - Archimedes' constant?

Radius of Well given Discharge in Confined Aquifer Example

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Here is how the Radius of Well given Discharge in Confined Aquifer equation looks like with Values.

Here is how the Radius of Well given Discharge in Confined Aquifer equation looks like with Units.

Here is how the Radius of Well given Discharge in Confined Aquifer equation looks like.

8.5898 = \frac{8.6}{\exp (\frac{2 \cdot 3.1416 \cdot 10 \cdot 2.36 \cdot (2.48 - 2.44)}{50})}

8.5898m = \frac{8.6m}{\exp (\frac{2 \cdot 3.1416 \cdot 10cm/s \cdot 2.36m \cdot (2.48m - 2.44m)}{50m³/s})}

8.5898 = \frac{8.6}{\exp (\frac{2 \cdot 3.1416 \cdot 10 \cdot 2.36 \cdot (2.48 - 2.44)}{50})}

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Home » Engineering » Civil » Environmental Engineering » Radius of Well given Discharge in Confined Aquifer

Radius of Well given Discharge in Confined Aquifer Solution

Follow our step by step solution on how to calculate Radius of Well given Discharge in Confined Aquifer?

FIRST Step Consider the formula

r w = \frac{R w}{\exp (\frac{2 \cdot π \cdot K WH \cdot b p \cdot (H i - h w)}{Q 0})}

Next Step Substitute values of Variables

∴

r w = \frac{8.6m}{\exp (\frac{2 \cdot π \cdot 10cm/s \cdot 2.36m \cdot (2.48m - 2.44m)}{50m³/s})}

Next Step Substitute values of Constants

∴

r w = \frac{8.6m}{\exp (\frac{2 \cdot 3.1416 \cdot 10cm/s \cdot 2.36m \cdot (2.48m - 2.44m)}{50m³/s})}

Next Step Convert Units

∴

r w = \frac{8.6m}{\exp (\frac{2 \cdot 3.1416 \cdot 0.1m/s \cdot 2.36m \cdot (2.48m - 2.44m)}{50m³/s})}

Next Step Prepare to Evaluate

∴

r w = \frac{8.6}{\exp (\frac{2 \cdot 3.1416 \cdot 0.1 \cdot 2.36 \cdot (2.48 - 2.44)}{50})}

Next Step Evaluate

∴

r w = 8.58980416635836m

LAST Step Rounding Answer

∴

r w = 8.5898m

Radius of Well given Discharge in Confined Aquifer Formula Elements

Variables

Constants

Functions

Radius of Well given Discharge

Radius of Well given Discharge is the radial distance from the center of the well to the outer boundary of the aquifer, where the effects of pumping or water withdrawal are observed.

Symbol: r_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Radius of Influence

Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.

Symbol: R_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Coefficient of Permeability in Well Hydraulics

Coefficient of Permeability in Well Hydraulics of soil in well hydraulics describes how easily a liquid will move through the soil.

Symbol: K_WH

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Aquifer Thickness During Pumping

Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.

Symbol: b_p

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Initial Aquifer Thickness

Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.

Symbol: H_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Depth of Water

Depth of Water is the depth in the well measured above the impermeable layer.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Discharge at Time t=0

Discharge at Time t=0 is the rate of flow of a liquid that moves over a designated point over a fixed period.

Symbol: Q₀

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

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

exp

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

Syntax: exp(Number)

Credits

Creator Image

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verifier Image

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other Formulas to find Radius of Well given Discharge

Go Radius of Well for Discharge in Confined Aquifer with Base 10

r w = \frac{R w}{\frac{10^{2.72 \cdot K swh \cdot b \cdot (H i - h w)}}{Q}}

Go Radius of Well given Coefficient of Transmissibility

r w = \frac{R w}{\exp (\frac{2 \cdot π \cdot T envi \cdot (H i - h w)}{Q 0})}

Other formulas in Radial Distance and Radius of well category

Go Radius of Well given Confined Aquifer Discharge

r' = \frac{R w}{\exp (\frac{2 \cdot π \cdot K WH \cdot b p \cdot s t}{Q})}

Go Radius of Well given Confined Aquifer Discharge with Base 10

r' = \frac{R w}{10^{\frac{2.72 \cdot K WH \cdot b p \cdot s t}{Q}}}

See More

How to Evaluate Radius of Well given Discharge in Confined Aquifer?

Radius of Well given Discharge in Confined Aquifer evaluator uses Radius of Well given Discharge = Radius of Influence/exp((2*pi*Coefficient of Permeability in Well Hydraulics*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water))/Discharge at Time t=0) to evaluate the Radius of Well given Discharge, The Radius of Well given Discharge in Confined Aquifer is defined as the value of radius of well when we have prior information of other parameters used. Radius of Well given Discharge is denoted by r_w symbol.

How to evaluate Radius of Well given Discharge in Confined Aquifer using this online evaluator? To use this online evaluator for Radius of Well given Discharge in Confined Aquifer, enter Radius of Influence (R_w), Coefficient of Permeability in Well Hydraulics (K_WH), Aquifer Thickness During Pumping (b_p), Initial Aquifer Thickness (H_i), Depth of Water (h_w) & Discharge at Time t=0 (Q₀) and hit the calculate button.

FAQs on Radius of Well given Discharge in Confined Aquifer

What is the formula to find Radius of Well given Discharge in Confined Aquifer?

The formula of Radius of Well given Discharge in Confined Aquifer is expressed as Radius of Well given Discharge = Radius of Influence/exp((2*pi*Coefficient of Permeability in Well Hydraulics*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water))/Discharge at Time t=0). Here is an example- 8.589804 = 8.6/exp((2*pi*0.1*2.36*(2.48-2.44))/50).

How to calculate Radius of Well given Discharge in Confined Aquifer?

With Radius of Influence (R_w), Coefficient of Permeability in Well Hydraulics (K_WH), Aquifer Thickness During Pumping (b_p), Initial Aquifer Thickness (H_i), Depth of Water (h_w) & Discharge at Time t=0 (Q₀) we can find Radius of Well given Discharge in Confined Aquifer using the formula - Radius of Well given Discharge = Radius of Influence/exp((2*pi*Coefficient of Permeability in Well Hydraulics*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water))/Discharge at Time t=0). This formula also uses Archimedes' constant and Exponential Growth (exp) function(s).

What are the other ways to Calculate Radius of Well given Discharge?

Here are the different ways to Calculate Radius of Well given Discharge-

Radius of Well given Discharge=Radius of Influence/(10^(2.72*Standard Coefficient of Permeability*Thickness of Aquifer*(Initial Aquifer Thickness-Depth of Water))/Discharge)
Radius of Well given Discharge=Radius of Influence/exp((2*pi*Coefficient of Transmissibility*(Initial Aquifer Thickness-Depth of Water))/Discharge at Time t=0)
Radius of Well given Discharge=Radius of Influence/10^((2.72*Coefficient of Transmissibility*(Initial Aquifer Thickness-Depth of Water))/Discharge at Time t=0)

Can the Radius of Well given Discharge in Confined Aquifer be negative?

No, the Radius of Well given Discharge in Confined Aquifer, measured in Length cannot be negative.

Which unit is used to measure Radius of Well given Discharge in Confined Aquifer?

Radius of Well given Discharge in Confined Aquifer is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius of Well given Discharge in Confined Aquifer can be measured.

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