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Drawdown Formula

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Total Drawdown is the reduction in hydraulic head observed at a well in an aquifer, typically due to pumping a well as part of an aquifer test or well test. Check FAQs

s t = (\frac{Q}{4 \cdot π \cdot T}) \cdot \ln (\frac{2.2 \cdot T \cdot t}{r^{2} \cdot S})

s_t - Total Drawdown?Q - Discharge?T - Transmissivity?t - Time Period?r - Distance from Pumping Well?S - Storage Coefficient?π - Archimedes' constant?

Drawdown Example

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Here is how the Drawdown equation looks like with Values.

Here is how the Drawdown equation looks like with Units.

Here is how the Drawdown equation looks like.

0.0307 = (\frac{3}{4 \cdot 3.1416 \cdot 11}) \cdot \ln (\frac{2.2 \cdot 11 \cdot 130}{3^{2} \cdot 85})

0.0307m = (\frac{3m³/s}{4 \cdot 3.1416 \cdot 11m²/s}) \cdot \ln (\frac{2.2 \cdot 11m²/s \cdot 130s}{{3m}^{2} \cdot 85})

0.0307 = (\frac{3}{4 \cdot 3.1416 \cdot 11}) \cdot \ln (\frac{2.2 \cdot 11 \cdot 130}{3^{2} \cdot 85})

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Drawdown Solution

Follow our step by step solution on how to calculate Drawdown?

FIRST Step Consider the formula

s t = (\frac{Q}{4 \cdot π \cdot T}) \cdot \ln (\frac{2.2 \cdot T \cdot t}{r^{2} \cdot S})

Next Step Substitute values of Variables

∴

s t = (\frac{3m³/s}{4 \cdot π \cdot 11m²/s}) \cdot \ln (\frac{2.2 \cdot 11m²/s \cdot 130s}{{3m}^{2} \cdot 85})

Next Step Substitute values of Constants

∴

s t = (\frac{3m³/s}{4 \cdot 3.1416 \cdot 11m²/s}) \cdot \ln (\frac{2.2 \cdot 11m²/s \cdot 130s}{{3m}^{2} \cdot 85})

Next Step Prepare to Evaluate

∴

s t = (\frac{3}{4 \cdot 3.1416 \cdot 11}) \cdot \ln (\frac{2.2 \cdot 11 \cdot 130}{3^{2} \cdot 85})

Next Step Evaluate

∴

s t = 0.0306882109079858m

LAST Step Rounding Answer

∴

s t = 0.0307m

Drawdown Formula Elements

Variables

Constants

Functions

Total Drawdown

Total Drawdown is the reduction in hydraulic head observed at a well in an aquifer, typically due to pumping a well as part of an aquifer test or well test.

Symbol: s_t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Total Drawdown

Discharge

Discharge is 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

Transmissivity

Transmissivity is the rate at which groundwater flows horizontally through an aquifer or the degree to which a medium allows something, in particular electromagnetic radiation, to pass through it.

Symbol: T

Measurement: Kinematic ViscosityUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Transmissivity

Time Period

Time Period is the duration over which groundwater observations, measurements, or modeling simulations are conducted. It can vary from short-term periods to long-term periods.

Symbol: t

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Period

Distance from Pumping Well

Distance from Pumping Well is the horizontal distance between a specific point in an aquifer and the location of a pumping well. It influences the behavior of groundwater flow.

Symbol: r

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from Pumping Well

Storage Coefficient

Storage Coefficient is the volume of water released from storage per unit decline in hydraulic head in the aquifer, per unit area of the aquifer.

Symbol: S

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Storage Coefficient

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 Unsteady Flow in a Confined Aquifer category

Go Drawdown at Time Interval 't1'

s 1 = s 2 - ((\frac{Q}{4 \cdot π \cdot T}) \cdot \ln (\frac{t 2}{t 1}))

Go Drawdown at Time Interval 't2'

s 2 = ((\frac{Q}{4 \cdot π \cdot T}) \cdot \ln (\frac{t 2}{t 1})) + s 1

Go Equation for Storage Coefficient

S = 2.25 \cdot T \cdot \frac{t 0}{r^{2}}

Go Transmissivity about given Storage Coefficient

T = \frac{S \cdot r^{2}}{2.25 \cdot t 0}

How to Evaluate Drawdown?

Drawdown evaluator uses Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient)) to evaluate the Total Drawdown, The Drawdown formula is defined as the change in groundwater level due to an applied stress, caused by events such as: Pumping from a well, pumping from a neighboring well. Time is derived on Semi-log sheet plotted against drawdown. Total Drawdown is denoted by s_t symbol.

How to evaluate Drawdown using this online evaluator? To use this online evaluator for Drawdown, enter Discharge (Q), Transmissivity (T), Time Period (t), Distance from Pumping Well (r) & Storage Coefficient (S) and hit the calculate button.

FAQs on Drawdown

What is the formula to find Drawdown?

The formula of Drawdown is expressed as Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient)). Here is an example- -0.001136 = (3/(4*pi*11))*ln((2.2*11*130)/(3^2*85)).

How to calculate Drawdown?

With Discharge (Q), Transmissivity (T), Time Period (t), Distance from Pumping Well (r) & Storage Coefficient (S) we can find Drawdown using the formula - Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient)). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

Can the Drawdown be negative?

Yes, the Drawdown, measured in Length can be negative.

Which unit is used to measure Drawdown?

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

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Drawdown Formula

Drawdown Example

Drawdown Solution

Drawdown Formula Elements

Other formulas in Unsteady Flow in a Confined Aquifer category

How to Evaluate Drawdown?

FAQs on Drawdown

Variable Name