Depth of Water in Well given Discharge for Partially Penetrating Well Calculator

✖Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.ⓘ Initial Aquifer Thickness [H_i]			+10% -10%
✖Discharge for Partially Penetrating Well is in terms of volumetric flow rate.ⓘ Discharge for Partially Penetrating Well [Q_v]			+10% -10%
✖Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.ⓘ Radius of Influence [R]			+10% -10%
✖Radius of Well in Eviron. Engin. is defined as the distance from center of well to its outer boundary.ⓘ Radius of Well in Eviron. Engin. [r^']			+10% -10%
✖The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.ⓘ Coefficient of Permeability [k]			+10% -10%
✖Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.ⓘ Aquifer Thickness During Pumping [b_p]			+10% -10%
✖Correction Factor is a factor that is applied for the correction in the Partial Penetration.ⓘ Correction Factor [G]			+10% -10%

✖Depth of Water in the well measured above the impermeable layer.ⓘ Depth of Water in Well given Discharge for Partially Penetrating Well [h_w]

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Formula

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Depth of Water in Well given Discharge for Partially Penetrating Well

Formula

`"h"_{"w"} = "H"_{"i"}-(("Q"_{"v"}*(log(("R"/"r"^{"'"}),e)))/(2*pi*"k"*"b"_{"p"}*"G"))`

Example

`"2.440976m"="2.54m"-(("0.0029m³/s"*(log(("100m"/"2.94m"),e)))/(2*pi*"0.01cm/s"*"2.36m"*"5.6"))`

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Depth of Water in Well given Discharge for Partially Penetrating Well Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Water = Initial Aquifer Thickness-((Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))/(2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*Correction Factor))
h_w = H_i-((Q_v*(log((R/r^'),e)))/(2*pi*k*b_p*G))
This formula uses 2 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

log - Logarithmic function is an inverse function to exponentiation., log(Base, Number)

Variables Used

Depth of Water - (Measured in Meter) - Depth of Water in the well measured above the impermeable layer.
Initial Aquifer Thickness - (Measured in Meter) - Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.
Discharge for Partially Penetrating Well - (Measured in Cubic Meter per Second) - Discharge for Partially Penetrating Well is in terms of volumetric flow rate.
Radius of Influence - (Measured in Meter) - Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.
Radius of Well in Eviron. Engin. - (Measured in Meter) - Radius of Well in Eviron. Engin. is defined as the distance from center of well to its outer boundary.
Coefficient of Permeability - (Measured in Meter per Second) - The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.
Aquifer Thickness During Pumping - (Measured in Meter) - Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.
Correction Factor - Correction Factor is a factor that is applied for the correction in the Partial Penetration.

STEP 1: Convert Input(s) to Base Unit

Initial Aquifer Thickness: 2.54 Meter --> 2.54 Meter No Conversion Required
Discharge for Partially Penetrating Well: 0.0029 Cubic Meter per Second --> 0.0029 Cubic Meter per Second No Conversion Required
Radius of Influence: 100 Meter --> 100 Meter No Conversion Required
Radius of Well in Eviron. Engin.: 2.94 Meter --> 2.94 Meter No Conversion Required
Coefficient of Permeability: 0.01 Centimeter per Second --> 0.0001 Meter per Second (Check conversion here)
Aquifer Thickness During Pumping: 2.36 Meter --> 2.36 Meter No Conversion Required
Correction Factor: 5.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_w = H_i-((Q_v*(log((R/r^'),e)))/(2*pi*k*b_p*G)) --> 2.54-((0.0029*(log((100/2.94),e)))/(2*pi*0.0001*2.36*5.6))

Evaluating ... ...

h_w = 2.44097562302475

STEP 3: Convert Result to Output's Unit

2.44097562302475 Meter --> No Conversion Required

FINAL ANSWER

2.44097562302475 ≈ 2.440976 Meter <-- Depth of Water

(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 » Depth of Water in Well given Discharge for Partially Penetrating Well

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Birsa Institute of Technology (BIT), Sindri

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< 11 Partially Penetrating Artesian Well Calculators

Thickness of Aquifer given Discharge for Partially Penetrating Well

Go Initial Aquifer Thickness = Depth of Water+(Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))/(2*pi*Coefficient of Permeability in Environ. Engin.*Aquifer Thickness During Pumping*Correction Factor)

Correction Factor for Partial Penetration given Discharge for Partially Penetrating Well

Go Correction Factor = Discharge for Partially Penetrating Well/((2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water))/(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))

Coefficient of Permeability given Discharge for Partially Penetrating Well

Go Coefficient of Permeability = Discharge for Partially Penetrating Well/((2*pi*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water)*Correction Factor)/(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))

Depth of Water in Well given Discharge for Partially Penetrating Well

Go Depth of Water = Initial Aquifer Thickness-((Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))/(2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*Correction Factor))

Aquifer Thickness given Discharge for Partially Penetrating Well

Go Aquifer Thickness During Pumping = Discharge for Partially Penetrating Well/((2*pi*Coefficient of Permeability*(Initial Aquifer Thickness-Depth of Water)*Correction Factor)/(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))

Discharge for Partially Penetrating Well

Go Discharge for Partially Penetrating Well = (2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water)*Correction Factor)/(log((Radius of Influence/Radius of Well in Eviron. Engin.),e))

Radius of Influence given Discharge for Partially Penetrating Well

Go Radius of Influence in Eviron. Engin. = (Radius of Well in Eviron. Engin.*exp((2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water)*Correction Factor)/Discharge at Time t=0))

Radius of Well given Discharge for Partially Penetrating Well

Go Radius of Well in Eviron. Engin. = Radius of Influence in Eviron. Engin./(exp((2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*(Initial Aquifer Thickness-Depth of Water)*Correction Factor)/Discharge))

Correction Factor for Partial Penetration given Discharge for Fully Penetrating Well

Go Correction Factor = Discharge for Partially Penetrating Well/Discharge in Enviro. Engin.

Discharge for Partially Penetrating Well given Correction Factor

Go Discharge for Partially Penetrating Well = Correction Factor*Discharge in Enviro. Engin.

Discharge for Fully Penetrating Well given Correction Factor

Go Discharge in Enviro. Engin. = Discharge for Partially Penetrating Well/Correction Factor

Depth of Water in 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 Depth of Water in Well given Discharge for Partially Penetrating Well?

Depth of Water in Well given Discharge for Partially Penetrating Well calculator uses Depth of Water = Initial Aquifer Thickness-((Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))/(2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*Correction Factor)) to calculate the Depth of Water, The Depth of Water in Well given Discharge for Partially Penetrating Well is defined as the value of depth of water in well when we have prior information of other parameters used. Depth of Water is denoted by h_w symbol.

How to calculate Depth of Water in Well given Discharge for Partially Penetrating Well using this online calculator? To use this online calculator for Depth of Water in Well given Discharge for Partially Penetrating Well, enter Initial Aquifer Thickness (H_i), Discharge for Partially Penetrating Well (Q_v), Radius of Influence (R), Radius of Well in Eviron. Engin. (r^'), Coefficient of Permeability (k), Aquifer Thickness During Pumping (b_p) & Correction Factor (G) and hit the calculate button. Here is how the Depth of Water in Well given Discharge for Partially Penetrating Well calculation can be explained with given input values -> 19.90098 = 2.54-((0.0029*(log((100/2.94),e)))/(2*pi*0.0001*2.36*5.6)).

FAQ

What is Depth of Water in Well given Discharge for Partially Penetrating Well?

The Depth of Water in Well given Discharge for Partially Penetrating Well is defined as the value of depth of water in well when we have prior information of other parameters used and is represented as h_w = H_i-((Q_v*(log((R/r^'),e)))/(2*pi*k*b_p*G)) or Depth of Water = Initial Aquifer Thickness-((Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))/(2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*Correction Factor)). Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping, Discharge for Partially Penetrating Well is in terms of volumetric flow rate, Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table, Radius of Well in Eviron. Engin. is defined as the distance from center of well to its outer boundary, The Coefficient of Permeability of soil describes how easily a liquid will move through the soil, Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage & Correction Factor is a factor that is applied for the correction in the Partial Penetration.

How to calculate Depth of Water in Well given Discharge for Partially Penetrating Well?

The Depth of Water in Well given Discharge for Partially Penetrating Well is defined as the value of depth of water in well when we have prior information of other parameters used is calculated using Depth of Water = Initial Aquifer Thickness-((Discharge for Partially Penetrating Well*(log((Radius of Influence/Radius of Well in Eviron. Engin.),e)))/(2*pi*Coefficient of Permeability*Aquifer Thickness During Pumping*Correction Factor)). To calculate Depth of Water in Well given Discharge for Partially Penetrating Well, you need Initial Aquifer Thickness (H_i), Discharge for Partially Penetrating Well (Q_v), Radius of Influence (R), Radius of Well in Eviron. Engin. (r^'), Coefficient of Permeability (k), Aquifer Thickness During Pumping (b_p) & Correction Factor (G). With our tool, you need to enter the respective value for Initial Aquifer Thickness, Discharge for Partially Penetrating Well, Radius of Influence, Radius of Well in Eviron. Engin, Coefficient of Permeability, Aquifer Thickness During Pumping & Correction Factor 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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