Equation for head for unconfined aquifer on horizontal impervious base Solution

STEP 0: Pre-Calculation Summary
Formula Used
Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between upstream and downstream^2)/Coefficient of Permeability))/Length between upstream and downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2)
h = sqrt(((-R*x^2)/K)-(((ho^2-h1^2-((R*Lstream^2)/K))/Lstream)*x)+ho^2)
This formula uses 1 Functions, 7 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Water Table Profile - (Measured in Meter) - Water table profile is the depth of water table below aquifer.
Natural Recharge - (Measured in Cubic Meter per Second) - Natural Recharge is the replenishment of infiltrating groundwater.
Flow in 'x' Direction - (Measured in Cubic Meter per Second) - Flow in 'x' Direction from One-Dimensional Dupit Flow with Recharge Representation.
Coefficient of Permeability - (Measured in Meter per Second) - The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.
Piezometric Head at Upstream End - (Measured in Meter) - Piezometric Head at Upstream End is defined as a specific measurement of liquid pressure above a vertical datum.
Piezometric Head at Downstream End - (Measured in Meter) - Piezometric Head at Downstream End is defined as a specific measurement of liquid pressure above a vertical datum.
Length between upstream and downstream - (Measured in Meter) - Length between upstream and downstream water bodies on a horizontal base with a difference in surface elevations.
STEP 1: Convert Input(s) to Base Unit
Natural Recharge: 16 Cubic Meter per Second --> 16 Cubic Meter per Second No Conversion Required
Flow in 'x' Direction: 2 Cubic Meter per Second --> 2 Cubic Meter per Second No Conversion Required
Coefficient of Permeability: 9 Centimeter per Second --> 0.09 Meter per Second (Check conversion here)
Piezometric Head at Upstream End: 12 Meter --> 12 Meter No Conversion Required
Piezometric Head at Downstream End: 5 Meter --> 5 Meter No Conversion Required
Length between upstream and downstream: 4.09 Meter --> 4.09 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = sqrt(((-R*x^2)/K)-(((ho^2-h1^2-((R*Lstream^2)/K))/Lstream)*x)+ho^2) --> sqrt(((-16*2^2)/0.09)-(((12^2-5^2-((16*4.09^2)/0.09))/4.09)*2)+12^2)
Evaluating ... ...
h = 28.790977789312
STEP 3: Convert Result to Output's Unit
28.790977789312 Meter --> No Conversion Required
FINAL ANSWER
28.790977789312 28.79098 Meter <-- Water Table Profile
(Calculation completed in 00.004 seconds)

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 Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
Chandana P Dev has verified this Calculator and 1700+ more calculators!

8 One Dimensional Dupit's flow with Recharge Calculators

Equation for head for unconfined aquifer on horizontal impervious base
Go Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between upstream and downstream^2)/Coefficient of Permeability))/Length between upstream and downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2)
Discharge per Unit Width of Aquifer at any Location x
Go Discharge of Aquifer at any Location x = Natural Recharge*(Flow in 'x' Direction-(Length between upstream and downstream/2))+(Coefficient of Permeability/2*Length between upstream and downstream)*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)
Discharge at downstream water body of catchment
Go Discharge at Downstream Side = ((Natural Recharge*Length between upstream and downstream)/2)+((Coefficient of Permeability/(2*Length between upstream and downstream))*(Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2))
Equation for Water Divide
Go Water Divide = (Length between upstream and downstream/2)-(Coefficient of Permeability/Natural Recharge)*((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2)/2*Length between upstream and downstream)
Coefficient of Aquifer Permeability given water table profile
Go Coefficient of Permeability = ((Natural Recharge/Water Table Profile^2)*(Length between tile drain-Flow in 'x' Direction)*Flow in 'x' Direction)
Coefficient of aquifer permeability when discharge per unit width of aquifer
Go Coefficient of Permeability = (Discharge*2*Length between upstream and downstream)/((Piezometric Head at Upstream End^2)-(Piezometric Head at Downstream End^2))
Coefficient of Aquifer Permeability given Maximum Height of Water Table
Go Coefficient of Permeability = (Natural Recharge*Length between tile drain^2)/(2*Maximum Height of Water Table)^2
Discharge entering drain per unit length of drain
Go Discharge per unit length of the drain = 2*(Natural Recharge*(Length between tile drain/2))

Equation for head for unconfined aquifer on horizontal impervious base Formula

Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between upstream and downstream^2)/Coefficient of Permeability))/Length between upstream and downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2)
h = sqrt(((-R*x^2)/K)-(((ho^2-h1^2-((R*Lstream^2)/K))/Lstream)*x)+ho^2)

What is Aquifer in Hydrology?

Aquifer, in hydrology, rock layer that contains water and releases it in appreciable amounts. The rock contains water-filled pore spaces, and, when the spaces are connected, the water is able to flow through the matrix of the rock. An aquifer also may be called a water-bearing stratum, lens, or zone.

How to Calculate Equation for head for unconfined aquifer on horizontal impervious base?

Equation for head for unconfined aquifer on horizontal impervious base calculator uses Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between upstream and downstream^2)/Coefficient of Permeability))/Length between upstream and downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2) to calculate the Water Table Profile, The Equation for head for unconfined aquifer on horizontal impervious base is defined as a specific measurement of liquid pressure above a vertical datum. Water Table Profile is denoted by h symbol.

How to calculate Equation for head for unconfined aquifer on horizontal impervious base using this online calculator? To use this online calculator for Equation for head for unconfined aquifer on horizontal impervious base, enter Natural Recharge (R), Flow in 'x' Direction (x), Coefficient of Permeability (K), Piezometric Head at Upstream End (ho), Piezometric Head at Downstream End (h1) & Length between upstream and downstream (Lstream) and hit the calculate button. Here is how the Equation for head for unconfined aquifer on horizontal impervious base calculation can be explained with given input values -> 28.79098 = sqrt(((-16*2^2)/0.09)-(((12^2-5^2-((16*4.09^2)/0.09))/4.09)*2)+12^2).

FAQ

What is Equation for head for unconfined aquifer on horizontal impervious base?
The Equation for head for unconfined aquifer on horizontal impervious base is defined as a specific measurement of liquid pressure above a vertical datum and is represented as h = sqrt(((-R*x^2)/K)-(((ho^2-h1^2-((R*Lstream^2)/K))/Lstream)*x)+ho^2) or Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between upstream and downstream^2)/Coefficient of Permeability))/Length between upstream and downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2). Natural Recharge is the replenishment of infiltrating groundwater, Flow in 'x' Direction from One-Dimensional Dupit Flow with Recharge Representation, The Coefficient of Permeability of soil describes how easily a liquid will move through the soil, Piezometric Head at Upstream End is defined as a specific measurement of liquid pressure above a vertical datum, Piezometric Head at Downstream End is defined as a specific measurement of liquid pressure above a vertical datum & Length between upstream and downstream water bodies on a horizontal base with a difference in surface elevations.
How to calculate Equation for head for unconfined aquifer on horizontal impervious base?
The Equation for head for unconfined aquifer on horizontal impervious base is defined as a specific measurement of liquid pressure above a vertical datum is calculated using Water Table Profile = sqrt(((-Natural Recharge*Flow in 'x' Direction^2)/Coefficient of Permeability)-(((Piezometric Head at Upstream End^2-Piezometric Head at Downstream End^2-((Natural Recharge*Length between upstream and downstream^2)/Coefficient of Permeability))/Length between upstream and downstream)*Flow in 'x' Direction)+Piezometric Head at Upstream End^2). To calculate Equation for head for unconfined aquifer on horizontal impervious base, you need Natural Recharge (R), Flow in 'x' Direction (x), Coefficient of Permeability (K), Piezometric Head at Upstream End (ho), Piezometric Head at Downstream End (h1) & Length between upstream and downstream (Lstream). With our tool, you need to enter the respective value for Natural Recharge, Flow in 'x' Direction, Coefficient of Permeability, Piezometric Head at Upstream End, Piezometric Head at Downstream End & Length between upstream and downstream and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!