Equation for Drawdown 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%
✖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.ⓘ Transmissivity [T]			+10% -10%
✖Time Period (pumping has been in Progress) or Time can be defined as the ongoing and continuous sequence of events that occur in succession, from the past through the present to the future.ⓘ Time Period [t]			+10% -10%
✖Distance from Pumping Well to the point where drawdown occurs.ⓘ Distance from Pumping Well [r]			+10% -10%
✖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.ⓘ Storage Coefficient [S]			+10% -10%

✖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.ⓘ Equation for Drawdown [s_t]

⎘ Copy

👎

Formula

✖

Equation for Drawdown

Formula

`"s"_{"t"} = ("Q"/(4*pi*"T"))*ln((2.2*"T"*"t")/("r"^2*"S"))`

Example

`"-0.001136m"=("3.0m³/s"/(4*pi*"11m²/s"))*ln((2.2*"11m²/s"*"30s")/(("3m")^2*"85"))`

Calculator

LaTeX

Reset

👍

Download Engineering Hydrology Formula PDF PDF Image

Equation for Drawdown Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient))
s_t = (Q/(4*pi*T))*ln((2.2*T*t)/(r^2*S))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Total Drawdown - (Measured in Meter) - 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.
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.
Transmissivity - (Measured in Square Meter per Second) - 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.
Time Period - (Measured in Second) - Time Period (pumping has been in Progress) or Time can be defined as the ongoing and continuous sequence of events that occur in succession, from the past through the present to the future.
Distance from Pumping Well - (Measured in Meter) - Distance from Pumping Well to the point where drawdown occurs.
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.

STEP 1: Convert Input(s) to Base Unit

Discharge: 3 Cubic Meter per Second --> 3 Cubic Meter per Second No Conversion Required
Transmissivity: 11 Square Meter per Second --> 11 Square Meter per Second No Conversion Required
Time Period: 30 Second --> 30 Second No Conversion Required
Distance from Pumping Well: 3 Meter --> 3 Meter No Conversion Required
Storage Coefficient: 85 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

s_t = (Q/(4*pi*T))*ln((2.2*T*t)/(r^2*S)) --> (3/(4*pi*11))*ln((2.2*11*30)/(3^2*85))

Evaluating ... ...

s_t = -0.00113562446528982

STEP 3: Convert Result to Output's Unit

-0.00113562446528982 Meter --> No Conversion Required

FINAL ANSWER

-0.00113562446528982 ≈ -0.001136 Meter <-- Total Drawdown

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Engineering Hydrology » Groundwater Hydrology » Unsteady Flow in a Confined Aquifer » Equation for Drawdown

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has verified this Calculator and 900+ more calculators!

< 11 Unsteady Flow in a Confined Aquifer Calculators

Equation for Drawdown

Go Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient))

Drawdown at Time Interval 't1'

Go Drawdown at time interval t1 = Drawdown at time interval t2-((Discharge/(4*pi*Transmissivity))*ln(Time of Drawdown (t2)/Time of Drawdown (t1)))

Drawdown at Time Interval 't2'

Go Drawdown at time interval t2 = ((Discharge/(4*pi*Transmissivity))*ln(Time of Drawdown (t2)/Time of Drawdown (t1)))+Drawdown at time interval t1

Equation for Well Function series to number of 4 digits

Go Well Function of u = -0.577216-ln(Well Parameter)+Well Parameter-(Well Parameter^2/2.2!)+(Well Parameter^3/3.3!)

Equation for Well Parameter

Go Well Parameter = (Distance from Pumping Well^2*Storage Coefficient)/(4*Transmissivity*Time Period)

Distance from Pumping Well given Storage Coefficient

Go Distance from Pumping Well = sqrt((2.25*Transmissivity*Starting Time/Storage Coefficient))

Initial Time given Pumping Well along with Storage Coefficient

Go Starting Time = (Storage Coefficient*Distance from Pumping Well^2)/(2.25*Transmissivity)

Transmissivity about given storage coefficient

Go Transmissivity = (Storage Coefficient*Distance from Pumping Well^2)/(2.25*Starting Time)

Equation for Storage Coefficient

Go Storage Coefficient = 2.25*Transmissivity*Starting Time/Distance from Pumping Well^2

Initial Constant Piezometric Head given drawdown

Go Initial constant Piezometric Head = Possible Drawdown in Confined Aquifer+Drawdown at time t

Drawdown given Piezometric Head

Go Possible Drawdown in Confined Aquifer = Initial constant Piezometric Head-Drawdown at time t

Equation for Drawdown Formula

Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient))
s_t = (Q/(4*pi*T))*ln((2.2*T*t)/(r^2*S))

What is Discharge In Hydrology?

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 in addition to the water itself.

How to Calculate Equation for Drawdown?

Equation for Drawdown calculator uses Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient)) to calculate the Total Drawdown, The Equation for Drawdown 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 calculate Equation for Drawdown using this online calculator? To use this online calculator for Equation for Drawdown, enter Discharge (Q), Transmissivity (T), Time Period (t), Distance from Pumping Well (r) & Storage Coefficient (S) and hit the calculate button. Here is how the Equation for Drawdown calculation can be explained with given input values -> -0.001136 = (3/(4*pi*11))*ln((2.2*11*30)/(3^2*85)).

FAQ

What is Equation for Drawdown?

The Equation for Drawdown 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 and is represented as s_t = (Q/(4*pi*T))*ln((2.2*T*t)/(r^2*S)) or Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient)). 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, 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, Time Period (pumping has been in Progress) or Time can be defined as the ongoing and continuous sequence of events that occur in succession, from the past through the present to the future, Distance from Pumping Well to the point where drawdown occurs & 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.

How to calculate Equation for Drawdown?

The Equation for Drawdown 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 is calculated using Total Drawdown = (Discharge/(4*pi*Transmissivity))*ln((2.2*Transmissivity*Time Period)/(Distance from Pumping Well^2*Storage Coefficient)). To calculate Equation for Drawdown, you need Discharge (Q), Transmissivity (T), Time Period (t), Distance from Pumping Well (r) & Storage Coefficient (S). With our tool, you need to enter the respective value for Discharge, Transmissivity, Time Period, Distance from Pumping Well & Storage Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search