Depth of Water in Well given Discharge in Unconfined Aquifer Solution

STEP 0: Pre-Calculation Summary
Formula Used
Depth of Water = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of well),e))/(pi*Coefficient of Permeability in Well Hydraulics))
hw = sqrt(H^2-(Q*log((Rw/r),e))/(pi*KWH))
This formula uses 2 Constants, 2 Functions, 6 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.
Thickness of Unconfined Aquifer - (Measured in Meter) - Thickness of Unconfined Aquifer is measured from impermeable layer to the initial level of water table.
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 - (Measured in Meter) - Radius of well is defined as the distance from center of well to its outer boundary.
Coefficient of Permeability in Well Hydraulics - (Measured in Meter per Second) - Coefficient of Permeability in Well Hydraulics of soil in well hydraulics describes how easily a liquid will move through the soil.
STEP 1: Convert Input(s) to Base Unit
Thickness of Unconfined Aquifer: 5 Meter --> 5 Meter No Conversion Required
Discharge: 1.01 Cubic Meter per Second --> 1.01 Cubic Meter per Second No Conversion Required
Radius of Influence: 8.6 Meter --> 8.6 Meter No Conversion Required
Radius of well: 7.5 Meter --> 7.5 Meter No Conversion Required
Coefficient of Permeability in Well Hydraulics: 10 Centimeter per Second --> 0.1 Meter per Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
hw = sqrt(H^2-(Q*log((Rw/r),e))/(pi*KWH)) --> sqrt(5^2-(1.01*log((8.6/7.5),e))/(pi*0.1))
Evaluating ... ...
hw = 1.228500482931
STEP 3: Convert Result to Output's Unit
1.228500482931 Meter --> No Conversion Required
FINAL ANSWER
1.228500482931 1.2285 Meter <-- Depth of Water
(Calculation completed in 00.004 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
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Meerut Institute of Engineering and Technology (MIET), Meerut
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6 Depth ot Water in Well Calculators

Depth of Water at Point 1 given Discharge of Two Wells under Consideration
Go Depth of Water 1 = sqrt(Depth of Water 2^2-(Discharge*log((Radial Distance at Observation Well 2/Radial Distance at Observation Well 1),e))/(pi*Coefficient of Permeability in Well Hydraulics))
Depth of Water at Point 2 given Discharge of Two Wells under Consideration
Go Depth of Water 2 = sqrt(Depth of Water 1^2+(Discharge*log((Radial Distance at Observation Well 2/Radial Distance at Observation Well 1),e))/(pi*Coefficient of Permeability in Well Hydraulics))
Depth of Water in Well given Discharge in Unconfined Aquifer
Go Depth of Water = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of well),e))/(pi*Coefficient of Permeability in Well Hydraulics))
Depth of Water at Point 1 given Discharge from Two Wells with Base 10
Go Depth of Water 1 = sqrt(Depth of Water 2^2-(Discharge*log((Radial Distance at Observation Well 2/Radial Distance at Observation Well 1),10))/(1.36*Coefficient of Permeability in Well Hydraulics))
Depth of Water at Point 2 given Discharge from Two Wells with Base 10
Go Depth of Water 2 = sqrt(Depth of Water 1^2+(Discharge*log((Radial Distance at Observation Well 2/Radial Distance at Observation Well 1),10))/(1.36*Coefficient of Permeability in Well Hydraulics))
Depth of Water in Well given Drawdown Value measured at Well
Go Depth of Water = Thickness of Unconfined Aquifer-Total Drawdown in Well

Depth of Water in Well given Discharge in Unconfined Aquifer Formula

Depth of Water = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of well),e))/(pi*Coefficient of Permeability in Well Hydraulics))
hw = sqrt(H^2-(Q*log((Rw/r),e))/(pi*KWH))

What is aquifer ?

An aquifer is an underground layer of water-bearing permeable rock, rock fractures or unconsolidated materials (gravel, sand, or silt). Groundwater can be extracted using a water well.

How to Calculate Depth of Water in Well given Discharge in Unconfined Aquifer?

Depth of Water in Well given Discharge in Unconfined Aquifer calculator uses Depth of Water = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of well),e))/(pi*Coefficient of Permeability in Well Hydraulics)) to calculate the Depth of Water, Depth of Water in Well given Discharge in Unconfined Aquifer calculates value of depth of water when we have prior information of other parameters used. Depth of Water is denoted by hw symbol.

How to calculate Depth of Water in Well given Discharge in Unconfined Aquifer using this online calculator? To use this online calculator for Depth of Water in Well given Discharge in Unconfined Aquifer, enter Thickness of Unconfined Aquifer (H), Discharge (Q), Radius of Influence (Rw), Radius of well (r) & Coefficient of Permeability in Well Hydraulics (KWH) and hit the calculate button. Here is how the Depth of Water in Well given Discharge in Unconfined Aquifer calculation can be explained with given input values -> 3.71816 = sqrt(5^2-(1.01*log((8.6/7.5),e))/(pi*0.1)).

FAQ

What is Depth of Water in Well given Discharge in Unconfined Aquifer?
Depth of Water in Well given Discharge in Unconfined Aquifer calculates value of depth of water when we have prior information of other parameters used and is represented as hw = sqrt(H^2-(Q*log((Rw/r),e))/(pi*KWH)) or Depth of Water = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of well),e))/(pi*Coefficient of Permeability in Well Hydraulics)). Thickness of Unconfined Aquifer is measured from impermeable layer to the initial level of water table, 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 is defined as the distance from center of well to its outer boundary & Coefficient of Permeability in Well Hydraulics of soil in well hydraulics describes how easily a liquid will move through the soil.
How to calculate Depth of Water in Well given Discharge in Unconfined Aquifer?
Depth of Water in Well given Discharge in Unconfined Aquifer calculates value of depth of water when we have prior information of other parameters used is calculated using Depth of Water = sqrt(Thickness of Unconfined Aquifer^2-(Discharge*log((Radius of Influence/Radius of well),e))/(pi*Coefficient of Permeability in Well Hydraulics)). To calculate Depth of Water in Well given Discharge in Unconfined Aquifer, you need Thickness of Unconfined Aquifer (H), Discharge (Q), Radius of Influence (Rw), Radius of well (r) & Coefficient of Permeability in Well Hydraulics (KWH). With our tool, you need to enter the respective value for Thickness of Unconfined Aquifer, Discharge, Radius of Influence, Radius of well & Coefficient of Permeability in Well Hydraulics 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 Depth of Water?
In this formula, Depth of Water uses Thickness of Unconfined Aquifer, Discharge, Radius of Influence, Radius of well & Coefficient of Permeability in Well Hydraulics. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Depth of Water = Thickness of Unconfined Aquifer-Total Drawdown in Well
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