Discharge per Unit Width of Aquifer at any Location x Calculator

✖Natural Recharge is the replenishment of infiltrating groundwater.ⓘ Natural Recharge [R]			+10% -10%
✖Flow in 'x' Direction from One-Dimensional Dupit Flow with Recharge Representation.ⓘ Flow in 'x' Direction [x]			+10% -10%
✖Length between upstream and downstream water bodies on a horizontal base with a difference in surface elevations.ⓘ Length between upstream and downstream [L_stream]			+10% -10%
✖The Coefficient of Permeability of soil describes how easily a liquid will move through the soil.ⓘ Coefficient of Permeability [K]			+10% -10%
✖Piezometric Head at Upstream End is defined as a specific measurement of liquid pressure above a vertical datum.ⓘ Piezometric Head at Upstream End [h_o]			+10% -10%
✖Piezometric Head at Downstream End is defined as a specific measurement of liquid pressure above a vertical datum.ⓘ Piezometric Head at Downstream End [h₁]			+10% -10%

✖Discharge of Aquifer at any Location x, discharge is the volumetric flow rate of water that is transported through a given cross-sectional area.ⓘ Discharge per Unit Width of Aquifer at any Location x [q_x]

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Formula

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Discharge per Unit Width of Aquifer at any Location x

Formula

`"q"_{"x"} = "R"*("x"-("L"_{"stream"}/2))+("K"/2*"L"_{"stream"})*("h"_{"o"}^2-"h"_{"1"}^2)`

Example

`"21.18195m³/s"="16m³/s"*("2.0m³/s"-("4.09m"/2))+("9cm/s"/2*"4.09m")*(("12m")^2-("5m")^2)`

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Discharge per Unit Width of Aquifer at any Location x Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
q_x = R*(x-(L_stream/2))+(K/2*L_stream)*(h_o^2-h₁^2)
This formula uses 7 Variables

Variables Used

Discharge of Aquifer at any Location x - (Measured in Cubic Meter per Second) - Discharge of Aquifer at any Location x, discharge is the volumetric flow rate of water that is transported through a given cross-sectional area.
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.
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.
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.

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
Length between upstream and downstream: 4.09 Meter --> 4.09 Meter 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_x = R*(x-(L_stream/2))+(K/2*L_stream)*(h_o^2-h₁^2) --> 16*(2-(4.09/2))+(0.09/2*4.09)*(12^2-5^2)

Evaluating ... ...

q_x = 21.18195

STEP 3: Convert Result to Output's Unit

21.18195 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

21.18195 Cubic Meter per Second <-- Discharge of Aquifer at any Location x

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Engineering Hydrology » Groundwater Hydrology » Unconfined Flow by Dupit's Assumption » One Dimensional Dupit's flow with Recharge » Discharge per Unit Width of Aquifer at any Location x

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Coorg Institute of Technology (CIT), Coorg

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< 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))

Discharge per Unit Width of Aquifer at any Location x Formula

What is Recharge?

Recharge is the primary method through which water enters an aquifer. This process usually occurs in the vadose zone below plant roots and, is often expressed as a flux to the water table surface. Groundwater recharge also encompasses water moving away from the water table farther into the saturated zone.

How to Calculate Discharge per Unit Width of Aquifer at any Location x?

Discharge per Unit Width of Aquifer at any Location x calculator uses 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) to calculate the Discharge of Aquifer at any Location x, The Discharge per Unit Width of Aquifer at any Location x is defined as the volumetric flow rate of water that is transported through a given cross-sectional area. Discharge of Aquifer at any Location x is denoted by q_x symbol.

How to calculate Discharge per Unit Width of Aquifer at any Location x using this online calculator? To use this online calculator for Discharge per Unit Width of Aquifer at any Location x, enter Natural Recharge (R), Flow in 'x' Direction (x), Length between upstream and downstream (L_stream), Coefficient of Permeability (K), Piezometric Head at Upstream End (h_o) & Piezometric Head at Downstream End (h₁) and hit the calculate button. Here is how the Discharge per Unit Width of Aquifer at any Location x calculation can be explained with given input values -> 21.18195 = 16*(2-(4.09/2))+(0.09/2*4.09)*(12^2-5^2).

FAQ

What is Discharge per Unit Width of Aquifer at any Location x?

The Discharge per Unit Width of Aquifer at any Location x is defined as the volumetric flow rate of water that is transported through a given cross-sectional area and is represented as q_x = R*(x-(L_stream/2))+(K/2*L_stream)*(h_o^2-h₁^2) or 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). Natural Recharge is the replenishment of infiltrating groundwater, Flow in 'x' Direction from One-Dimensional Dupit Flow with Recharge Representation, Length between upstream and downstream water bodies on a horizontal base with a difference in surface elevations, 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.

How to calculate Discharge per Unit Width of Aquifer at any Location x?

The Discharge per Unit Width of Aquifer at any Location x is defined as the volumetric flow rate of water that is transported through a given cross-sectional area is calculated using 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). To calculate Discharge per Unit Width of Aquifer at any Location x, you need Natural Recharge (R), Flow in 'x' Direction (x), Length between upstream and downstream (L_stream), Coefficient of Permeability (K), Piezometric Head at Upstream End (h_o) & Piezometric Head at Downstream End (h₁). With our tool, you need to enter the respective value for Natural Recharge, Flow in 'x' Direction, Length between upstream and downstream, Coefficient of Permeability, Piezometric Head at Upstream End & Piezometric Head at Downstream End and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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