✖The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table.ⓘ Natural Recharge [R]			+10% -10%
✖The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation.ⓘ Flow in 'x' Direction [x]			+10% -10%
✖The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.ⓘ Coefficient of Permeability [K]			+10% -10%
✖The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum.ⓘ Piezometric Head at Upstream End [h_o]			+10% -10%
✖The Piezometric Head at Downstream End refers to the specific measurement of liquid pressure above a vertical datum.ⓘ Piezometric Head at Downstream End [h₁]			+10% -10%
✖The Length between Upstream and Downstream refers to the horizontal base with a difference in surface elevations.ⓘ Length between Upstream and Downstream [L_stream]			+10% -10%

✖The Water Table Profile refers to the depth of water table below aquifer.ⓘ Equation of Head for Unconfined Aquifer on Horizontal Impervious Base [h]

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Formula

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Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

Formula

`"h" = sqrt(((-"R"*"x"^2)/"K")-((("h"_{"o"}^2-"h"_{"1"}^2-(("R"*"L"_{"stream"}^2)/"K"))/"L"_{"stream"})*"x")+"h"_{"o"}^2)`

Example

`"28.79098m"=sqrt(((-"16m³/s"*("2.0m³/s")^2)/"9cm/s")-(((("12m")^2-("5m")^2-(("16m³/s"*("4.09m")^2)/"9cm/s"))/"4.09m")*"2.0m³/s")+("12m")^2)`

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Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Solution

STEP 0: Pre-Calculation Summary

Formula Used

Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between Upstream and Downstream^2)/Coefficient of Permeability))/Length between Upstream and Downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2)
h = sqrt(((-R*x^2)/K)-(((h_o^2-h₁^2-((R*L_stream^2)/K))/L_stream)*x)+h_o^2)
This formula uses 1 Functions, 7 Variables

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)

Variables Used

Water Table Profile - (Measured in Meter) - The Water Table Profile refers to the depth of water table below aquifer.
Natural Recharge - (Measured in Cubic Meter per Second) - The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table.
Flow in 'x' Direction - (Measured in Cubic Meter per Second) - The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation.
Coefficient of Permeability - (Measured in Meter per Second) - The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.
Piezometric Head at Upstream End - (Measured in Meter) - The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum.
Piezometric Head at Downstream End - (Measured in Meter) - The Piezometric Head at Downstream End refers to the specific measurement of liquid pressure above a vertical datum.
Length between Upstream and Downstream - (Measured in Meter) - The Length between Upstream and Downstream refers to the horizontal base with a difference in surface elevations.

STEP 1: Convert Input(s) to Base Unit

Natural Recharge: 16 Cubic Meter per Second --> 16 Cubic Meter per Second No Conversion Required
Flow in 'x' Direction: 2 Cubic Meter per Second --> 2 Cubic Meter per Second No Conversion Required
Coefficient of Permeability: 9 Centimeter per Second --> 0.09 Meter per Second (Check conversion here)
Piezometric Head at Upstream End: 12 Meter --> 12 Meter No Conversion Required
Piezometric Head at Downstream End: 5 Meter --> 5 Meter No Conversion Required
Length between Upstream and Downstream: 4.09 Meter --> 4.09 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(((-R*x^2)/K)-(((h_o^2-h₁^2-((R*L_stream^2)/K))/L_stream)*x)+h_o^2) --> sqrt(((-16*2^2)/0.09)-(((12^2-5^2-((16*4.09^2)/0.09))/4.09)*2)+12^2)

Evaluating ... ...

h = 28.790977789312

STEP 3: Convert Result to Output's Unit

28.790977789312 Meter --> No Conversion Required

FINAL ANSWER

28.790977789312 ≈ 28.79098 Meter <-- Water Table Profile

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Engineering Hydrology » Groundwater Hydrology » Unconfined Flow » Unconfined Flow by Dupit's Assumption » One Dimensional Dupit's Flow with Recharge » Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

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< 8 One Dimensional Dupit's Flow with Recharge Calculators

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

Go Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between Upstream and Downstream^2)/Coefficient of Permeability))/Length between Upstream and Downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2)

Discharge per Unit Width of Aquifer at any Location x

Go Discharge of Aquifer at any Location x = Natural Recharge*(Flow in 'x' Direction-(Length between Upstream and Downstream/2))+(Coefficient of Permeability/2*Length between Upstream and Downstream)*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)

Discharge at Downstream Water Body of Catchment

Go Discharge at Downstream Side = ((Natural Recharge*Length between Upstream and Downstream)/2)+((Coefficient of Permeability/(2*Length between Upstream and Downstream))*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2))

Equation for Water Divide

Go Water Divide = (Length between Upstream and Downstream/2)-(Coefficient of Permeability/Natural Recharge)*((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)/2*Length between Upstream and Downstream)

Coefficient of Aquifer Permeability given Water Table Profile

Go Coefficient of Permeability = ((Natural Recharge/Water Table Profile^2)*(Length between Tile Drain-Flow in 'x' Direction)*Flow in 'x' Direction)

Coefficient of Aquifer Permeability considering Discharge per Unit Width of Aquifer

Go Coefficient of Permeability = (Discharge*2*Length between Upstream and Downstream)/((Piezometric Head at Upstream End^2)-(Piezometric Head at Downstream End^2))

Coefficient of Aquifer Permeability given Maximum Height of Water Table

Go Coefficient of Permeability = (Natural Recharge*Length between Tile Drain^2)/(2*Maximum Height of Water Table)^2

Discharge Entering Drain per Unit Length of Drain

Go Discharge per unit Length of the Drain = 2*(Natural Recharge*(Length between Tile Drain/2))

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Formula

What is Aquifer in Hydrology?

Aquifer, in hydrology, rock layer that contains water and releases it in appreciable amounts. The rock contains water-filled pore spaces, and, when the spaces are connected, the water is able to flow through the matrix of the rock. An aquifer also may be called a water-bearing stratum, lens, or zone.

How to Calculate Equation of Head for Unconfined Aquifer on Horizontal Impervious Base?

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base calculator uses Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between Upstream and Downstream^2)/Coefficient of Permeability))/Length between Upstream and Downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2) to calculate the Water Table Profile, The Equation of Head for Unconfined Aquifer on Horizontal Impervious Base formula is defined as a specific measurement of liquid pressure above a vertical datum. Water Table Profile is denoted by h symbol.

How to calculate Equation of Head for Unconfined Aquifer on Horizontal Impervious Base using this online calculator? To use this online calculator for Equation of Head for Unconfined Aquifer on Horizontal Impervious Base, enter Natural Recharge (R), Flow in 'x' Direction (x), Coefficient of Permeability (K), Piezometric Head at Upstream End (h_o), Piezometric Head at Downstream End (h₁) & Length between Upstream and Downstream (L_stream) and hit the calculate button. Here is how the Equation of Head for Unconfined Aquifer on Horizontal Impervious Base calculation can be explained with given input values -> 28.79098 = sqrt(((-16*2^2)/0.09)-(((12^2-5^2-((16*4.09^2)/0.09))/4.09)*2)+12^2).

FAQ

What is Equation of Head for Unconfined Aquifer on Horizontal Impervious Base?

The Equation of Head for Unconfined Aquifer on Horizontal Impervious Base formula is defined as a specific measurement of liquid pressure above a vertical datum and is represented as h = sqrt(((-R*x^2)/K)-(((h_o^2-h₁^2-((R*L_stream^2)/K))/L_stream)*x)+h_o^2) or Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between Upstream and Downstream^2)/Coefficient of Permeability))/Length between Upstream and Downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2). The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table, The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation, The Coefficient of Permeability of soil describes how easily a liquid will move through the soil, The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum, The Piezometric Head at Downstream End refers to the specific measurement of liquid pressure above a vertical datum & The Length between Upstream and Downstream refers to the horizontal base with a difference in surface elevations.

How to calculate Equation of Head for Unconfined Aquifer on Horizontal Impervious Base?

The Equation of Head for Unconfined Aquifer on Horizontal Impervious Base formula is defined as a specific measurement of liquid pressure above a vertical datum is calculated using Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between Upstream and Downstream^2)/Coefficient of Permeability))/Length between Upstream and Downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2). To calculate Equation of Head for Unconfined Aquifer on Horizontal Impervious Base, you need Natural Recharge (R), Flow in 'x' Direction (x), Coefficient of Permeability (K), Piezometric Head at Upstream End (h_o), Piezometric Head at Downstream End (h₁) & Length between Upstream and Downstream (L_stream). With our tool, you need to enter the respective value for Natural Recharge, Flow in 'x' Direction, Coefficient of Permeability, Piezometric Head at Upstream End, Piezometric Head at Downstream End & Length between Upstream and Downstream 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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