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Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Formula

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The Water Table Profile refers to the depth of water table below aquifer. Check FAQs

h = \sqrt{(\frac{- R \cdot x^{2}}{K}) - ((\frac{{h o}^{2} - {h 1}^{2} - (\frac{R \cdot {L stream}^{2}}{K})}{L stream}) \cdot x) + {h o}^{2}}

h - Water Table Profile?R - Natural Recharge?x - Flow in 'x' Direction?K - Coefficient of Permeability?h_o - Piezometric Head at Upstream End?h₁ - Piezometric Head at Downstream End?L_stream - Length between Upstream and Downstream?

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Example

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Here is how the Equation of Head for Unconfined Aquifer on Horizontal Impervious Base equation looks like with Values.

Here is how the Equation of Head for Unconfined Aquifer on Horizontal Impervious Base equation looks like with Units.

Here is how the Equation of Head for Unconfined Aquifer on Horizontal Impervious Base equation looks like.

28.791 = \sqrt{(\frac{- 16 \cdot 2^{2}}{9}) - ((\frac{12^{2} - 5^{2} - (\frac{16 \cdot {4.09}^{2}}{9})}{4.09}) \cdot 2) + 12^{2}}

28.791m = \sqrt{(\frac{- 16m³/s \cdot {2m³/s}^{2}}{9cm/s}) - ((\frac{{12m}^{2} - {5m}^{2} - (\frac{16m³/s \cdot {4.09m}^{2}}{9cm/s})}{4.09m}) \cdot 2m³/s) + {12m}^{2}}

28.791 = \sqrt{(\frac{- 16 \cdot 2^{2}}{9}) - ((\frac{12^{2} - 5^{2} - (\frac{16 \cdot {4.09}^{2}}{9})}{4.09}) \cdot 2) + 12^{2}}

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Home » Engineering » Civil » Engineering Hydrology » Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Solution

Follow our step by step solution on how to calculate Equation of Head for Unconfined Aquifer on Horizontal Impervious Base?

FIRST Step Consider the formula

h = \sqrt{(\frac{- R \cdot x^{2}}{K}) - ((\frac{{h o}^{2} - {h 1}^{2} - (\frac{R \cdot {L stream}^{2}}{K})}{L stream}) \cdot x) + {h o}^{2}}

Next Step Substitute values of Variables

∴

h = \sqrt{(\frac{- 16m³/s \cdot {2m³/s}^{2}}{9cm/s}) - ((\frac{{12m}^{2} - {5m}^{2} - (\frac{16m³/s \cdot {4.09m}^{2}}{9cm/s})}{4.09m}) \cdot 2m³/s) + {12m}^{2}}

Next Step Convert Units

∴

h = \sqrt{(\frac{- 16m³/s \cdot {2m³/s}^{2}}{0.09m/s}) - ((\frac{{12m}^{2} - {5m}^{2} - (\frac{16m³/s \cdot {4.09m}^{2}}{0.09m/s})}{4.09m}) \cdot 2m³/s) + {12m}^{2}}

Next Step Prepare to Evaluate

∴

h = \sqrt{(\frac{- 16 \cdot 2^{2}}{0.09}) - ((\frac{12^{2} - 5^{2} - (\frac{16 \cdot {4.09}^{2}}{0.09})}{4.09}) \cdot 2) + 12^{2}}

Next Step Evaluate

∴

h = 28.790977789312m

LAST Step Rounding Answer

∴

h = 28.791m

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Formula Elements

Variables

Functions

Water Table Profile

The Water Table Profile refers to the depth of water table below aquifer.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Natural Recharge

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.

Symbol: R

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Flow in 'x' Direction

The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation.

Symbol: x

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Coefficient of Permeability

The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.

Symbol: K

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Piezometric Head at Upstream End

The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum.

Symbol: h_o

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Piezometric Head at Downstream End

The Piezometric Head at Downstream End refers to the specific measurement of liquid pressure above a vertical datum.

Symbol: h₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Length between Upstream and Downstream

The Length between Upstream and Downstream refers to the horizontal base with a difference in surface elevations.

Symbol: L_stream

Measurement: LengthUnit: m

Note: Value should be greater than 0.

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.

Syntax: sqrt(Number)

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Formula and 2000+ more formulas!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

Other formulas in One Dimensional Dupit's Flow with Recharge category

Go Equation for Water Divide

a = (\frac{L stream}{2}) - (\frac{K}{R}) \cdot (\frac{{h o}^{2} - {h 1}^{2}}{2} \cdot L stream)

Go Discharge per Unit Width of Aquifer at any Location x

q x = R \cdot (x - (\frac{L stream}{2})) + (\frac{K}{2} \cdot L stream) \cdot ({h o}^{2} - {h 1}^{2})

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

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base evaluator 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 evaluate 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 evaluate Equation of Head for Unconfined Aquifer on Horizontal Impervious Base using this online evaluator? To use this online evaluator 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.

FAQs on Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

What is the formula to find Equation of Head for Unconfined Aquifer on Horizontal Impervious Base?

The formula of Equation of Head for Unconfined Aquifer on Horizontal Impervious Base is expressed as 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). Here is an example- 28.79098 = sqrt(((-16*2^2)/0.09)-(((12^2-5^2-((16*4.09^2)/0.09))/4.09)*2)+12^2).

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

With 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) we can find Equation of Head for Unconfined Aquifer on Horizontal Impervious Base using the formula - 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). This formula also uses Square Root (sqrt) function(s).

Can the Equation of Head for Unconfined Aquifer on Horizontal Impervious Base be negative?

No, the Equation of Head for Unconfined Aquifer on Horizontal Impervious Base, measured in Length cannot be negative.

Which unit is used to measure Equation of Head for Unconfined Aquifer on Horizontal Impervious Base?

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Equation of Head for Unconfined Aquifer on Horizontal Impervious Base can be measured.

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Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Formula

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Example

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Solution

Equation of Head for Unconfined Aquifer on Horizontal Impervious Base Formula Elements

Credits

Other formulas in One Dimensional Dupit's Flow with Recharge category

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

FAQs on Equation of Head for Unconfined Aquifer on Horizontal Impervious Base

Variable Name