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Change in Drawdown given Discharge Formula

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The Change in Drawdown refers to the maximum lowering of the groundwater table caused by pumping or artesian flow. Check FAQs

s = Q \cdot \frac{\ln (\frac{r 2}{r 1})}{2} \cdot π \cdot T

s - Change in Drawdown?Q - Discharge?r₂ - Radial Distance at Observation Well 2?r₁ - Radial Distance at Observation Well 1?T - Transmissivity of an Unconfined Aquifer?π - Archimedes' constant?

Change in Drawdown given Discharge Example

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Here is how the Change in Drawdown given Discharge equation looks like with Values.

Here is how the Change in Drawdown given Discharge equation looks like with Units.

Here is how the Change in Drawdown given Discharge equation looks like.

0.995 = 1.3 \cdot \frac{\ln (\frac{10}{5})}{2} \cdot 3.1416 \cdot 0.703

0.995m = 1.3m³/s \cdot \frac{\ln (\frac{10m}{5m})}{2} \cdot 3.1416 \cdot 0.703m²/s

0.995 = 1.3 \cdot \frac{\ln (\frac{10}{5})}{2} \cdot 3.1416 \cdot 0.703

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Change in Drawdown given Discharge Solution

Follow our step by step solution on how to calculate Change in Drawdown given Discharge?

FIRST Step Consider the formula

s = Q \cdot \frac{\ln (\frac{r 2}{r 1})}{2} \cdot π \cdot T

Next Step Substitute values of Variables

∴

s = 1.3m³/s \cdot \frac{\ln (\frac{10m}{5m})}{2} \cdot π \cdot 0.703m²/s

Next Step Substitute values of Constants

∴

s = 1.3m³/s \cdot \frac{\ln (\frac{10m}{5m})}{2} \cdot 3.1416 \cdot 0.703m²/s

Next Step Prepare to Evaluate

∴

s = 1.3 \cdot \frac{\ln (\frac{10}{5})}{2} \cdot 3.1416 \cdot 0.703

Next Step Evaluate

∴

s = 0.995047963964231m

LAST Step Rounding Answer

∴

s = 0.995m

Change in Drawdown given Discharge Formula Elements

Variables

Constants

Functions

Change in Drawdown

The Change in Drawdown refers to the maximum lowering of the groundwater table caused by pumping or artesian flow.

Symbol: s

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Change in Drawdown

Discharge

The Discharge refers to the volumetric flow rate of water that is transported through a given cross-sectional area. It includes any suspended solids, dissolved chemicals, or biologic material.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge

Radial Distance at Observation Well 2

The Radial Distance at Observation Well 2 refers to the refers to the horizontal distance from the center of a pumping well to the observation well.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radial Distance at Observation Well 2

Radial Distance at Observation Well 1

The Radial Distance at Observation Well 1 refers to the refers to the horizontal distance from the center of a pumping well to the observation well.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radial Distance at Observation Well 1

Transmissivity of an Unconfined Aquifer

The Transmissivity of an Unconfined Aquifer refers to the ability of the aquifer to transmit groundwater throughout its entire saturated thickness.

Symbol: T

Measurement: Kinematic ViscosityUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Transmissivity of an Unconfined Aquifer

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

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Unconfined Flow by Dupit's Assumption category

Go Mass Flux Entering Element

M x1 = ρ water \cdot V x \cdot H w \cdot Δy

Go Discharge per Unit Width of Aquifer considering Permeability

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

Go Water Table Profile Neglecting Depths of Water in Drains

h = \sqrt{(\frac{R}{K}) \cdot (L - x) \cdot x}

Go Maximum Height of Water Table

h m = (\frac{L}{2}) \cdot \sqrt{\frac{R}{K}}

How to Evaluate Change in Drawdown given Discharge?

Change in Drawdown given Discharge evaluator uses Change in Drawdown = Discharge*ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1)/2*pi*Transmissivity of an Unconfined Aquifer to evaluate the Change in Drawdown, The Change in Drawdown given Discharge formula is defined as the concept which quantifies how much the water level (drawdown) in an aquifer or well changes in response to a specific rate of water extraction (discharge). It is often used in the analysis of aquifer performance and is essential for sustainable groundwater management. Change in Drawdown is denoted by s symbol.

How to evaluate Change in Drawdown given Discharge using this online evaluator? To use this online evaluator for Change in Drawdown given Discharge, enter Discharge (Q), Radial Distance at Observation Well 2 (r₂), Radial Distance at Observation Well 1 (r₁) & Transmissivity of an Unconfined Aquifer (T) and hit the calculate button.

FAQs on Change in Drawdown given Discharge

What is the formula to find Change in Drawdown given Discharge?

The formula of Change in Drawdown given Discharge is expressed as Change in Drawdown = Discharge*ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1)/2*pi*Transmissivity of an Unconfined Aquifer. Here is an example- 0.995048 = 1.3*ln(10/5)/2*pi*0.703.

How to calculate Change in Drawdown given Discharge?

With Discharge (Q), Radial Distance at Observation Well 2 (r₂), Radial Distance at Observation Well 1 (r₁) & Transmissivity of an Unconfined Aquifer (T) we can find Change in Drawdown given Discharge using the formula - Change in Drawdown = Discharge*ln(Radial Distance at Observation Well 2/Radial Distance at Observation Well 1)/2*pi*Transmissivity of an Unconfined Aquifer. This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

Can the Change in Drawdown given Discharge be negative?

Yes, the Change in Drawdown given Discharge, measured in Length can be negative.

Which unit is used to measure Change in Drawdown given Discharge?

Change in Drawdown given Discharge is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Change in Drawdown given Discharge can be measured.

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Change in Drawdown given Discharge Formula

Change in Drawdown given Discharge Example

Change in Drawdown given Discharge Solution

Change in Drawdown given Discharge Formula Elements

Other formulas in Unconfined Flow by Dupit's Assumption category

How to Evaluate Change in Drawdown given Discharge?

FAQs on Change in Drawdown given Discharge

Variable Name