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Discharge in Unconfined Aquifer Formula

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GoRate of Flow given Flow Velocity Formula

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GoDischarge in Unconfined Aquifer with Base 10 Formula

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Discharge is the flow rate of water that is extracted from or injected into a well. Check FAQs

Q = \frac{π \cdot K WH \cdot (H^{2} - {h w}^{2})}{\log ((\frac{R w}{r}), e)}

Q - Discharge?K_WH - Coefficient of Permeability in Well Hydraulics?H - Thickness of Unconfined Aquifer?h_w - Depth of Water?R_w - Radius of Influence?r - Radius of Well?π - Archimedes' constant?

Discharge in Unconfined Aquifer Example

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Here is how the Discharge in Unconfined Aquifer equation looks like with Values.

Here is how the Discharge in Unconfined Aquifer equation looks like with Units.

Here is how the Discharge in Unconfined Aquifer equation looks like.

0.8189 = \frac{3.1416 \cdot 10 \cdot (5^{2} - {2.44}^{2})}{\log ((\frac{8.6}{7.5}), e)}

0.8189m³/s = \frac{3.1416 \cdot 10cm/s \cdot ({5m}^{2} - {2.44m}^{2})}{\log ((\frac{8.6m}{7.5m}), e)}

0.8189 = \frac{3.1416 \cdot 10 \cdot (5^{2} - {2.44}^{2})}{\log ((\frac{8.6}{7.5}), e)}

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Discharge in Unconfined Aquifer Solution

Follow our step by step solution on how to calculate Discharge in Unconfined Aquifer?

FIRST Step Consider the formula

Q = \frac{π \cdot K WH \cdot (H^{2} - {h w}^{2})}{\log ((\frac{R w}{r}), e)}

Next Step Substitute values of Variables

∴

Q = \frac{π \cdot 10cm/s \cdot ({5m}^{2} - {2.44m}^{2})}{\log ((\frac{8.6m}{7.5m}), e)}

Next Step Substitute values of Constants

∴

Q = \frac{3.1416 \cdot 10cm/s \cdot ({5m}^{2} - {2.44m}^{2})}{\log ((\frac{8.6m}{7.5m}), e)}

Next Step Convert Units

∴

Q = \frac{3.1416 \cdot 0.1m/s \cdot ({5m}^{2} - {2.44m}^{2})}{\log ((\frac{8.6m}{7.5m}), e)}

Next Step Prepare to Evaluate

∴

Q = \frac{3.1416 \cdot 0.1 \cdot (5^{2} - {2.44}^{2})}{\log ((\frac{8.6}{7.5}), e)}

Next Step Evaluate

∴

Q = 0.818911020627159m³/s

LAST Step Rounding Answer

∴

Q = 0.8189m³/s

Discharge in Unconfined Aquifer Formula Elements

Variables

Constants

Functions

Discharge

Discharge is the flow rate of water that is extracted from or injected into a well.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Discharge

Open Variable

Coefficient of Permeability in Well Hydraulics

Coefficient of Permeability in Well Hydraulics of soil in well hydraulics describes how easily a liquid will move through the soil.

Symbol: K_WH

Measurement: SpeedUnit: cm/s

Note: Value should be greater than 0.

Formulas to find Coefficient of Permeability in Well Hydraulics

Open Variable

Thickness of Unconfined Aquifer

Thickness of Unconfined Aquifer is measured from impermeable layer to the initial level of water table.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Thickness of Unconfined Aquifer

Open Variable

Depth of Water

Depth of Water is the depth in the well measured above the impermeable layer.

Symbol: h_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Water

Open Variable

Radius of Influence

Radius of Influence measured from the center of the well to the point where drawdown curve meets the original water table.

Symbol: R_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Influence

Open Variable

Radius of Well

Radius of Well is defined as the distance from center of well to its outer boundary.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Well

Open Variable

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

log

Logarithmic function is an inverse function to exponentiation.

Syntax: log(Base, Number)

Other Formulas to find Discharge

Go Rate of Flow given Flow Velocity

Q = (V wh' \cdot A sec)

Go Discharge in Unconfined Aquifer with Base 10

Q = \frac{1.36 \cdot K WH \cdot ({b w}^{2} - {h w}^{2})}{\log ((\frac{R w}{r}), 10)}

Go Discharge when Two Observation Well is Taken

Q = \frac{π \cdot K WH \cdot ({h 2}^{2} - {h 1}^{2})}{\log ((\frac{r 2}{r 1}), e)}

Go Discharge from Two Wells with Base 10

Q = \frac{1.36 \cdot K WH \cdot ({h 2}^{2} - {h 1}^{2})}{\log ((\frac{r 2}{r1'}), 10)}

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How to Evaluate Discharge in Unconfined Aquifer?

Discharge in Unconfined Aquifer evaluator uses Discharge = (pi*Coefficient of Permeability in Well Hydraulics*(Thickness of Unconfined Aquifer^2-Depth of Water^2))/(log((Radius of Influence/Radius of Well),e)) to evaluate the Discharge, The Discharge in Unconfined Aquifer is defined as the value of discharge in unconfined aquifer when we have prior information of other parameters used. Discharge is denoted by Q symbol.

How to evaluate Discharge in Unconfined Aquifer using this online evaluator? To use this online evaluator for Discharge in Unconfined Aquifer, enter Coefficient of Permeability in Well Hydraulics (K_WH), Thickness of Unconfined Aquifer (H), Depth of Water (h_w), Radius of Influence (R_w) & Radius of Well (r) and hit the calculate button.

FAQs on Discharge in Unconfined Aquifer

What is the formula to find Discharge in Unconfined Aquifer?

The formula of Discharge in Unconfined Aquifer is expressed as Discharge = (pi*Coefficient of Permeability in Well Hydraulics*(Thickness of Unconfined Aquifer^2-Depth of Water^2))/(log((Radius of Influence/Radius of Well),e)). Here is an example- 0.818911 = (pi*0.1*(5^2-2.44^2))/(log((8.6/7.5),e)).

How to calculate Discharge in Unconfined Aquifer?

With Coefficient of Permeability in Well Hydraulics (K_WH), Thickness of Unconfined Aquifer (H), Depth of Water (h_w), Radius of Influence (R_w) & Radius of Well (r) we can find Discharge in Unconfined Aquifer using the formula - Discharge = (pi*Coefficient of Permeability in Well Hydraulics*(Thickness of Unconfined Aquifer^2-Depth of Water^2))/(log((Radius of Influence/Radius of Well),e)). This formula also uses Archimedes' constant and Logarithmic Inverse (log) function(s).

What are the other ways to Calculate Discharge?

Here are the different ways to Calculate Discharge-

Discharge=(Velocity of Flow*Area of Cross Section)
Discharge=(1.36*Coefficient of Permeability in Well Hydraulics*(Aquifer Thickness^2-Depth of Water^2))/(log((Radius of Influence/Radius of Well),10))
Discharge=(pi*Coefficient of Permeability in Well Hydraulics*(Depth of Water 2^2-Depth of Water 1^2))/(log((Radial Distance at Observation Well 2/Radial Distance at Observation Well 1),e))

Can the Discharge in Unconfined Aquifer be negative?

Yes, the Discharge in Unconfined Aquifer, measured in Volumetric Flow Rate can be negative.

Which unit is used to measure Discharge in Unconfined Aquifer?

Discharge in Unconfined Aquifer is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Discharge in Unconfined Aquifer can be measured.

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