Discharge per Unit Width of Aquifer at any Location x Calculator

✖The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table.ⓘ Natural Recharge [R]			+10% -10%
✖The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation.ⓘ Flow in 'x' Direction [x]			+10% -10%
✖The Length between Upstream and Downstream refers to the 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%
✖The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum.ⓘ Piezometric Head at Upstream End [h_o]			+10% -10%
✖The Piezometric Head at Downstream End refers to the specific measurement of liquid pressure above a vertical datum.ⓘ Piezometric Head at Downstream End [h₁]			+10% -10%

✖The Discharge of Aquifer at any Location x refers to 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 \cdot (x - (\frac{L stream}{2})) + (\frac{K}{2} \cdot L stream) \cdot ({h o}^{2} - {h 1}^{2})

Example

21.18195 m³/s = 16 m³/s \cdot (2.0 m³/s - (\frac{4.09 m}{2})) + (\frac{9 cm/s}{2} \cdot 4.09 m) \cdot ({12 m}^{2} - {5 m}^{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) - The Discharge of Aquifer at any Location x refers to the volumetric flow rate of water that is transported through a given cross-sectional area.
Natural Recharge - (Measured in Cubic Meter per Second) - The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table.
Flow in 'x' Direction - (Measured in Cubic Meter per Second) - The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation.
Length between Upstream and Downstream - (Measured in Meter) - The Length between Upstream and Downstream refers to the 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) - The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum.
Piezometric Head at Downstream End - (Measured in Meter) - The Piezometric Head at Downstream End refers to the 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 » 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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< One Dimensional Dupit's Flow with Recharge Calculators

Equation of 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)

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). The Natural Recharge is a process by which groundwater is replenished naturally when precipitation infiltrates the ground, moving through the soil and rock layers until it reaches the water table, The Flow in 'x' Direction refers to the one-dimensional Dupit flow with recharge representation, The Length between Upstream and Downstream refers to the horizontal base with a difference in surface elevations, The Coefficient of Permeability of soil describes how easily a liquid will move through the soil, The Piezometric Head at Upstream End refers to the specific measurement of liquid pressure above a vertical datum & The Piezometric Head at Downstream End refers to the 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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