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Specific Capacity under Unsteady Drawdown Conditions Formula

GoSpecific Capacity and Discharge into Well Relationship Formula

GoSpecific capacity per unit well area of aquifer Formula

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The Specific Capacity is referred as amount of water furnished under a standard unit head. Check FAQs

K s = \frac{1}{(\frac{1}{4} \cdot π \cdot T) \cdot (\ln (2.25 \cdot T \cdot \frac{t}{{R w}^{2}} \cdot S)) + C 2 \cdot Q f}

K_s - Specific Capacity?T - Transmissivity?t - Time from start of pump?R_w - Radius of the Pumping Well?S - Storage Coefficient?C₂ - Well Constant C2?Q_f - Flow Discharge?π - Archimedes' constant?

Specific Capacity under Unsteady Drawdown Conditions Example

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Here is how the Specific Capacity under Unsteady Drawdown Conditions equation looks like with Values.

Here is how the Specific Capacity under Unsteady Drawdown Conditions equation looks like with Units.

Here is how the Specific Capacity under Unsteady Drawdown Conditions equation looks like.

0.0145 = \frac{1}{(\frac{1}{4} \cdot 3.1416 \cdot 11) \cdot (\ln (2.25 \cdot 11 \cdot \frac{50}{6^{2}} \cdot 1.2)) + 0.05 \cdot 30}

0.0145 = \frac{1}{(\frac{1}{4} \cdot 3.1416 \cdot 11m²/s) \cdot (\ln (2.25 \cdot 11m²/s \cdot \frac{50min}{{6m}^{2}} \cdot 1.2)) + 0.05 \cdot 30m³/s}

0.0145 = \frac{1}{(\frac{1}{4} \cdot 3.1416 \cdot 11) \cdot (\ln (2.25 \cdot 11 \cdot \frac{50}{6^{2}} \cdot 1.2)) + 0.05 \cdot 30}

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Specific Capacity under Unsteady Drawdown Conditions Solution

Follow our step by step solution on how to calculate Specific Capacity under Unsteady Drawdown Conditions?

FIRST Step Consider the formula

K s = \frac{1}{(\frac{1}{4} \cdot π \cdot T) \cdot (\ln (2.25 \cdot T \cdot \frac{t}{{R w}^{2}} \cdot S)) + C 2 \cdot Q f}

Next Step Substitute values of Variables

∴

K s = \frac{1}{(\frac{1}{4} \cdot π \cdot 11m²/s) \cdot (\ln (2.25 \cdot 11m²/s \cdot \frac{50min}{{6m}^{2}} \cdot 1.2)) + 0.05 \cdot 30m³/s}

Next Step Substitute values of Constants

∴

K s = \frac{1}{(\frac{1}{4} \cdot 3.1416 \cdot 11m²/s) \cdot (\ln (2.25 \cdot 11m²/s \cdot \frac{50min}{{6m}^{2}} \cdot 1.2)) + 0.05 \cdot 30m³/s}

Next Step Convert Units

∴

K s = \frac{1}{(\frac{1}{4} \cdot 3.1416 \cdot 11m²/s) \cdot (\ln (2.25 \cdot 11m²/s \cdot \frac{3000s}{{6m}^{2}} \cdot 1.2)) + 0.05 \cdot 30m³/s}

Next Step Prepare to Evaluate

∴

K s = \frac{1}{(\frac{1}{4} \cdot 3.1416 \cdot 11) \cdot (\ln (2.25 \cdot 11 \cdot \frac{3000}{6^{2}} \cdot 1.2)) + 0.05 \cdot 30}

Next Step Evaluate

∴

K s = 0.0144910574614259

LAST Step Rounding Answer

∴

K s = 0.0145

Specific Capacity under Unsteady Drawdown Conditions Formula Elements

Variables

Constants

Functions

Specific Capacity

The Specific Capacity is referred as amount of water furnished under a standard unit head.

Symbol: K_s

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Capacity

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 from start of pump

The time from start of pump is the pumping started at the instant when the groundwater started to flow into the cone of depression.

Symbol: t

Measurement: TimeUnit: min

Note: Value can be positive or negative.

Formulas to find Time from start of pump

Radius of the Pumping Well

The Radius of the Pumping Well refers to the physical radius of the well itself, typically measured from the center of the well to its outer edge.

Symbol: R_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Radius of the 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

Well Constant C2

The Well Constant C2 refers to the coefficient used in the equation for total drawdown in a well, representing the well losses due to turbulent flow and other factors within the well structure.

Symbol: C₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Well Constant C2

Flow Discharge

The Flow Discharge refers to the volume of water passing through a particular cross-section of a river or stream per unit of time. It is typically measured in (m³/s) or cubic feet per second (cfs).

Symbol: Q_f

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Flow Discharge

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 to find Specific Capacity

Go Specific Capacity and Discharge into Well Relationship

K s = \frac{Q f}{s w}

Go Specific capacity per unit well area of aquifer

K s = \frac{K o}{A}

How to Evaluate Specific Capacity under Unsteady Drawdown Conditions?

Specific Capacity under Unsteady Drawdown Conditions evaluator uses Specific Capacity = 1/((1/4*pi*Transmissivity)*(ln(2.25*Transmissivity*Time from start of pump/(Radius of the Pumping Well^2)*Storage Coefficient))+Well Constant C2*Flow Discharge) to evaluate the Specific Capacity, The Specific Capacity under Unsteady Drawdown Conditions is defined as the discharge per unit drawdown at the well. Specific Capacity is denoted by K_s symbol.

How to evaluate Specific Capacity under Unsteady Drawdown Conditions using this online evaluator? To use this online evaluator for Specific Capacity under Unsteady Drawdown Conditions, enter Transmissivity (T), Time from start of pump (t), Radius of the Pumping Well (R_w), Storage Coefficient (S), Well Constant C2 (C₂) & Flow Discharge (Q_f) and hit the calculate button.

FAQs on Specific Capacity under Unsteady Drawdown Conditions

What is the formula to find Specific Capacity under Unsteady Drawdown Conditions?

The formula of Specific Capacity under Unsteady Drawdown Conditions is expressed as Specific Capacity = 1/((1/4*pi*Transmissivity)*(ln(2.25*Transmissivity*Time from start of pump/(Radius of the Pumping Well^2)*Storage Coefficient))+Well Constant C2*Flow Discharge). Here is an example- 0.014491 = 1/((1/4*pi*11)*(ln(2.25*11*3000/(6^2)*1.2))+0.05*30).

How to calculate Specific Capacity under Unsteady Drawdown Conditions?

With Transmissivity (T), Time from start of pump (t), Radius of the Pumping Well (R_w), Storage Coefficient (S), Well Constant C2 (C₂) & Flow Discharge (Q_f) we can find Specific Capacity under Unsteady Drawdown Conditions using the formula - Specific Capacity = 1/((1/4*pi*Transmissivity)*(ln(2.25*Transmissivity*Time from start of pump/(Radius of the Pumping Well^2)*Storage Coefficient))+Well Constant C2*Flow Discharge). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Specific Capacity?

Here are the different ways to Calculate Specific Capacity-

Specific Capacity=Flow Discharge/Total drawdown at the well
Specific Capacity=Proportionality Constant/Area of the Well

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: Unit

Specific Capacity under Unsteady Drawdown Conditions Formula

​GoSpecific Capacity and Discharge into Well Relationship Formula

​GoSpecific capacity per unit well area of aquifer Formula

Specific Capacity under Unsteady Drawdown Conditions Example

Specific Capacity under Unsteady Drawdown Conditions Solution

Specific Capacity under Unsteady Drawdown Conditions Formula Elements

Other Formulas to find Specific Capacity

How to Evaluate Specific Capacity under Unsteady Drawdown Conditions?

FAQs on Specific Capacity under Unsteady Drawdown Conditions

Variable Name

GoSpecific Capacity and Discharge into Well Relationship Formula

GoSpecific capacity per unit well area of aquifer Formula