Depth of Water at Point 1 given Discharge of Two Wells under Consideration Calculator

✖Depth of water 2 means the depth of the water in 2nd well.ⓘ Depth of Water 2 [h₂]			+10% -10%
✖Discharge is the flow rate of water that is extracted from or injected into a well.ⓘ Discharge [Q]			+10% -10%
✖Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used.ⓘ Radial Distance at Observation Well 2 [r₂]			+10% -10%
✖Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used.ⓘ Radial Distance at Observation Well 1 [r₁]			+10% -10%
✖Coefficient of Permeability in Well Hydraulics of soil in well hydraulics describes how easily a liquid will move through the soil.ⓘ Coefficient of Permeability in Well Hydraulics [K_WH]			+10% -10%

✖Depth of Water 1 is the depth of water in the 1st considered well.ⓘ Depth of Water at Point 1 given Discharge of Two Wells under Consideration [h₁]

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Depth of Water at Point 1 given Discharge of Two Wells under Consideration Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
h₁ = sqrt(h₂^2-(Q*log((r₂/r₁),e))/(pi*K_WH))
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 1 - (Measured in Meter) - Depth of Water 1 is the depth of water in the 1st considered well.
Depth of Water 2 - (Measured in Meter) - Depth of water 2 means the depth of the water in 2nd well.
Discharge - (Measured in Cubic Meter per Second) - Discharge is the flow rate of water that is extracted from or injected into a well.
Radial Distance at Observation Well 2 - (Measured in Meter) - Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used.
Radial Distance at Observation Well 1 - (Measured in Meter) - Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used.
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

Depth of Water 2: 17.8644 Meter --> 17.8644 Meter No Conversion Required
Discharge: 1.01 Cubic Meter per Second --> 1.01 Cubic Meter per Second No Conversion Required
Radial Distance at Observation Well 2: 10 Meter --> 10 Meter No Conversion Required
Radial Distance at Observation Well 1: 1.07 Meter --> 1.07 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

h₁ = sqrt(h₂^2-(Q*log((r₂/r₁),e))/(pi*K_WH)) --> sqrt(17.8644^2-(1.01*log((10/1.07),e))/(pi*0.1))

Evaluating ... ...

h₁ = 17.8240930388535

STEP 3: Convert Result to Output's Unit

17.8240930388535 Meter --> No Conversion Required

FINAL ANSWER

17.8240930388535 ≈ 17.82409 Meter <-- Depth of Water 1

(Calculation completed in 00.004 seconds)

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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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< Depth of Water in Well Calculators

Depth of Water at Point 1 given Discharge of Two Wells under Consideration

LaTeX 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

LaTeX 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

LaTeX Go Depth of Water in Well given Discharge = 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

LaTeX 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 1 given Discharge of Two Wells under Consideration Formula

LaTeX Go

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 at Point 1 given Discharge of Two Wells under Consideration?

Depth of Water at Point 1 given Discharge of Two Wells under Consideration calculator uses 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)) to calculate the Depth of Water 1, The Depth of Water at Point 1 given Discharge of Two Wells under Consideration formula is defined as the calculation of the value of depth of water at point 1 when we have prior information of discharge of two wells under consideration. Depth of Water 1 is denoted by h₁ symbol.

How to calculate Depth of Water at Point 1 given Discharge of Two Wells under Consideration using this online calculator? To use this online calculator for Depth of Water at Point 1 given Discharge of Two Wells under Consideration, enter Depth of Water 2 (h₂), Discharge (Q), Radial Distance at Observation Well 2 (r₂), Radial Distance at Observation Well 1 (r₁) & Coefficient of Permeability in Well Hydraulics (K_WH) and hit the calculate button. Here is how the Depth of Water at Point 1 given Discharge of Two Wells under Consideration calculation can be explained with given input values -> 17.82409 = sqrt(17.8644^2-(1.01*log((10/1.07),e))/(pi*0.1)).

FAQ

What is Depth of Water at Point 1 given Discharge of Two Wells under Consideration?

The Depth of Water at Point 1 given Discharge of Two Wells under Consideration formula is defined as the calculation of the value of depth of water at point 1 when we have prior information of discharge of two wells under consideration and is represented as h₁ = sqrt(h₂^2-(Q*log((r₂/r₁),e))/(pi*K_WH)) or 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 2 means the depth of the water in 2nd well, Discharge is the flow rate of water that is extracted from or injected into a well, Radial Distance at Observation Well 2 is the value of radial distance from well 2 when we have prior information of other parameters used, Radial Distance at Observation Well 1 is the value of radial distance from well 1 when we have prior information of other parameters used & 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 at Point 1 given Discharge of Two Wells under Consideration?

The Depth of Water at Point 1 given Discharge of Two Wells under Consideration formula is defined as the calculation of the value of depth of water at point 1 when we have prior information of discharge of two wells under consideration is calculated using 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)). To calculate Depth of Water at Point 1 given Discharge of Two Wells under Consideration, you need Depth of Water 2 (h₂), Discharge (Q), Radial Distance at Observation Well 2 (r₂), Radial Distance at Observation Well 1 (r₁) & Coefficient of Permeability in Well Hydraulics (K_WH). With our tool, you need to enter the respective value for Depth of Water 2, Discharge, Radial Distance at Observation Well 2, Radial Distance at Observation Well 1 & 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 1?

In this formula, Depth of Water 1 uses Depth of Water 2, Discharge, Radial Distance at Observation Well 2, Radial Distance at Observation Well 1 & 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 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))

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