Equation for Residual Drawdown for small values of Distance and large values of Time Calculator

✖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.ⓘ Discharge [Q]			+10% -10%
✖Transmissibility is most simply defined as the effective hydraulic conductivity of an aquifer or other water-bearing unit multiplied by the thickness of that unit.ⓘ Transmissibility [T]			+10% -10%
✖The time from start of pump is the pumping started at the instant when the groundwater started to flow into the cone of depression.ⓘ Time from start of pump [t]			+10% -10%
✖Time since Stoppage of Pumping ( start of recovery).ⓘ Time since Stoppage of Pumping [t']			+10% -10%

✖Residual Drawdown is the change in groundwater level due to an applied stress after the cessation of the pumping.ⓘ Equation for Residual Drawdown for small values of Distance and large values of Time [s']

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Formula

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Equation for Residual Drawdown for small values of Distance and large values of Time

Formula

`"s'" = (2.302*"Q"/4*pi*"T")*log10("t"/"t'")`

Example

`"13.26915"=(2.302*"3.0m³/s"/4*pi*"3.5m²/s")*log10("50min"/"10min")`

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Equation for Residual Drawdown for small values of Distance and large values of Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Residual Drawdown = (2.302*Discharge/4*pi*Transmissibility)*log10(Time from start of pump/Time since Stoppage of Pumping)
s' = (2.302*Q/4*pi*T)*log10(t/t')
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)

Variables Used

Residual Drawdown - Residual Drawdown is the change in groundwater level due to an applied stress after the cessation of the pumping.
Discharge - (Measured in Cubic Meter per Second) - 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.
Transmissibility - (Measured in Square Meter per Second) - Transmissibility is most simply defined as the effective hydraulic conductivity of an aquifer or other water-bearing unit multiplied by the thickness of that unit.
Time from start of pump - (Measured in Second) - The time from start of pump is the pumping started at the instant when the groundwater started to flow into the cone of depression.
Time since Stoppage of Pumping - (Measured in Second) - Time since Stoppage of Pumping ( start of recovery).

STEP 1: Convert Input(s) to Base Unit

Discharge: 3 Cubic Meter per Second --> 3 Cubic Meter per Second No Conversion Required
Transmissibility: 3.5 Square Meter per Second --> 3.5 Square Meter per Second No Conversion Required
Time from start of pump: 50 Minute --> 3000 Second (Check conversion here)
Time since Stoppage of Pumping: 10 Minute --> 600 Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

s' = (2.302*Q/4*pi*T)*log10(t/t') --> (2.302*3/4*pi*3.5)*log10(3000/600)

Evaluating ... ...

s' = 13.2691480127725

STEP 3: Convert Result to Output's Unit

13.2691480127725 --> No Conversion Required

FINAL ANSWER

13.2691480127725 ≈ 13.26915 <-- Residual Drawdown

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Engineering Hydrology » Groundwater Hydrology » Recovery of Piezometric Head » Equation for Residual Drawdown for small values of Distance and large values of Time

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Equation for Residual Drawdown for small values of Distance and large values of Time

Go Residual Drawdown = (2.302*Discharge/4*pi*Transmissibility)*log10(Time from start of pump/Time since Stoppage of Pumping)

Equation for Residual Drawdown

Go Residual Drawdown = (Discharge/4*pi*Transmissibility)*(Well Function of u-Well Function after the Cessation of Pumping)

Transmissibility about straight-line slope

Go Transmissibility = 2.302*Discharge/(4*pi*Slope)

Equation for Slope of Line

Go Slope = 2.302*Discharge/(4*pi*Transmissibility)

Discharge about straight-line slope

Go Discharge = 4*pi*Transmissibility*Slope/2.302

Equation for Residual Drawdown for small values of Distance and large values of Time Formula

Residual Drawdown = (2.302*Discharge/4*pi*Transmissibility)*log10(Time from start of pump/Time since Stoppage of Pumping)
s' = (2.302*Q/4*pi*T)*log10(t/t')

What is Transmissivity in hydrology?

Transmissivity describes the ability of the aquifer to transmit groundwater throughout its entire saturated thickness . Transmissivity is measured as the rate at which groundwater can flow through an aquifer section of unit width under a unit hydraulic gradient.

How to Calculate Equation for Residual Drawdown for small values of Distance and large values of Time?

Equation for Residual Drawdown for small values of Distance and large values of Time calculator uses Residual Drawdown = (2.302*Discharge/4*pi*Transmissibility)*log10(Time from start of pump/Time since Stoppage of Pumping) to calculate the Residual Drawdown, The Equation for Residual Drawdown for small values of Distance and large values of Time is defined as the change in groundwater level due to an applied stress after the cessation of Pumping. Residual Drawdown is denoted by s' symbol.

How to calculate Equation for Residual Drawdown for small values of Distance and large values of Time using this online calculator? To use this online calculator for Equation for Residual Drawdown for small values of Distance and large values of Time, enter Discharge (Q), Transmissibility (T), Time from start of pump (t) & Time since Stoppage of Pumping (t') and hit the calculate button. Here is how the Equation for Residual Drawdown for small values of Distance and large values of Time calculation can be explained with given input values -> 13.26915 = (2.302*3/4*pi*3.5)*log10(3000/600).

FAQ

What is Equation for Residual Drawdown for small values of Distance and large values of Time?

The Equation for Residual Drawdown for small values of Distance and large values of Time is defined as the change in groundwater level due to an applied stress after the cessation of Pumping and is represented as s' = (2.302*Q/4*pi*T)*log10(t/t') or Residual Drawdown = (2.302*Discharge/4*pi*Transmissibility)*log10(Time from start of pump/Time since Stoppage of Pumping). 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, Transmissibility is most simply defined as the effective hydraulic conductivity of an aquifer or other water-bearing unit multiplied by the thickness of that unit, The time from start of pump is the pumping started at the instant when the groundwater started to flow into the cone of depression & Time since Stoppage of Pumping ( start of recovery).

How to calculate Equation for Residual Drawdown for small values of Distance and large values of Time?

The Equation for Residual Drawdown for small values of Distance and large values of Time is defined as the change in groundwater level due to an applied stress after the cessation of Pumping is calculated using Residual Drawdown = (2.302*Discharge/4*pi*Transmissibility)*log10(Time from start of pump/Time since Stoppage of Pumping). To calculate Equation for Residual Drawdown for small values of Distance and large values of Time, you need Discharge (Q), Transmissibility (T), Time from start of pump (t) & Time since Stoppage of Pumping (t'). With our tool, you need to enter the respective value for Discharge, Transmissibility, Time from start of pump & Time since Stoppage of Pumping and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Residual Drawdown?

In this formula, Residual Drawdown uses Discharge, Transmissibility, Time from start of pump & Time since Stoppage of Pumping. We can use 1 other way(s) to calculate the same, which is/are as follows -

Residual Drawdown = (Discharge/4*pi*Transmissibility)*(Well Function of u-Well Function after the Cessation of Pumping)

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