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

✖Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.ⓘ Aquifer Thickness During Pumping [b_p]			+10% -10%
✖Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.ⓘ Initial Aquifer Thickness [H_i]			+10% -10%
✖Discharge is the rate of flow of a liquid.ⓘ Discharge [Q]			+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%

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

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Formula

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Depth of Water in Well given Discharge for Fully Penetrating Well

Formula

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

Example

`"2.905613m"=sqrt((2*"2.36m"*"2.54m")- (("1.01m³/s"*log(("100m"/"2.94m"),e))/(pi*"0.01cm/s"))+("2.36m")^2)`

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

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Water = sqrt((2*Aquifer Thickness During Pumping*Initial Aquifer Thickness)- ((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2)
h_w = sqrt((2*b_p*H_i)- ((Q*log((R/r^'),e))/(pi*k))+(b_p)^2)
This formula uses 2 Constants, 2 Functions, 7 Variables

Constants Used

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

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
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.
Aquifer Thickness During Pumping - (Measured in Meter) - Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage.
Initial Aquifer Thickness - (Measured in Meter) - Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping.
Discharge - (Measured in Cubic Meter per Second) - Discharge is the rate of flow of a liquid.
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 Centimeter per Second) - The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.

STEP 1: Convert Input(s) to Base Unit

Aquifer Thickness During Pumping: 2.36 Meter --> 2.36 Meter No Conversion Required
Initial Aquifer Thickness: 2.54 Meter --> 2.54 Meter No Conversion Required
Discharge: 1.01 Cubic Meter per Second --> 1.01 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 --> 0.01 Centimeter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_w = sqrt((2*b_p*H_i)- ((Q*log((R/r^'),e))/(pi*k))+(b_p)^2) --> sqrt((2*2.36*2.54)- ((1.01*log((100/2.94),e))/(pi*0.01))+(2.36)^2)

Evaluating ... ...

h_w = 2.90561260943314

STEP 3: Convert Result to Output's Unit

2.90561260943314 Meter --> No Conversion Required

FINAL ANSWER

2.90561260943314 ≈ 2.905613 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 » Fully Penetrating Artesian - Gravity Well » Depth of Water in Well given Discharge for Fully Penetrating Well

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< 4 Fully Penetrating Artesian - Gravity Well Calculators

Depth of Water in Well given Discharge for Fully Penetrating Well

Go Depth of Water = sqrt((2*Aquifer Thickness During Pumping*Initial Aquifer Thickness)- ((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2)

Thickness of Aquifer given Discharge for Fully Penetrating Well

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

Radius of Influence of unconfined aquifer with known discharge

Go Radius of Influence in Eviron. Engin. = Radius of Well in Eviron. Engin.*exp((0.434*pi*Coefficient of Permeability*((Original Piezometric Head of the Well^2)-(Piezometric Head at Well)))/Discharge)

Radius of Well of unconfined Aquifer with known Discharge

Go Radius of Well in Eviron. Engin. = Radius of Influence in Eviron. Engin./exp((0.434*pi*Coefficient of Permeability*((Original Piezometric Head of the Well^2)-(Piezometric Head at Well)))/Discharge)

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

Depth of Water in Well given Discharge for Fully Penetrating Well calculator uses Depth of Water = sqrt((2*Aquifer Thickness During Pumping*Initial Aquifer Thickness)- ((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2) to calculate the Depth of Water, The Depth of Water in Well given Discharge for Fully Penetrating Well is defined as the value of depth of water 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 Fully Penetrating Well using this online calculator? To use this online calculator for Depth of Water in Well given Discharge for Fully Penetrating Well, enter Aquifer Thickness During Pumping (b_p), Initial Aquifer Thickness (H_i), Discharge (Q), Radius of Influence (R), Radius of Well in Eviron. Engin. (r^') & Coefficient of Permeability (k) and hit the calculate button. Here is how the Depth of Water in Well given Discharge for Fully Penetrating Well calculation can be explained with given input values -> 9.531725 = sqrt((2*2.36*2.54)- ((1.01*log((100/2.94),e))/(pi*0.0001))+(2.36)^2).

FAQ

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

The Depth of Water in Well given Discharge for Fully Penetrating Well is defined as the value of depth of water when we have prior information of other parameters used and is represented as h_w = sqrt((2*b_p*H_i)- ((Q*log((R/r^'),e))/(pi*k))+(b_p)^2) or Depth of Water = sqrt((2*Aquifer Thickness During Pumping*Initial Aquifer Thickness)- ((Discharge*log((Radius of Influence/Radius of Well in Eviron. Engin.),e))/(pi*Coefficient of Permeability))+(Aquifer Thickness During Pumping)^2). Aquifer Thickness During Pumping is the thickness of aquifer during pumping stage, Initial Aquifer Thickness is the aquifer thickness at initial stage before pumping, Discharge is the rate of flow of a liquid, 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.

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

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