Discharge at downstream water body of catchment Calculator

✖Natural Recharge is the replenishment of infiltrating groundwater.ⓘ Natural Recharge [R]			+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 at Downstream Side of the Water Body, Discharge increases downstream because of additional water from tributaries.ⓘ Discharge at downstream water body of catchment [q₁]

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Formula

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Discharge at downstream water body of catchment

Formula

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

Example

`"34.02929m³/s"=(("16m³/s"*"4.09m")/2)+(("9cm/s"/(2*"4.09m"))*(("12m")^2-("5m")^2))`

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Discharge at downstream water body of catchment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
q₁ = ((R*L_stream)/2)+((K/(2*L_stream))*(h_o^2-h₁^2))
This formula uses 6 Variables

Variables Used

Discharge at Downstream Side - (Measured in Cubic Meter per Second) - Discharge at Downstream Side of the Water Body, Discharge increases downstream because of additional water from tributaries.
Natural Recharge - (Measured in Cubic Meter per Second) - Natural Recharge is the replenishment of infiltrating groundwater.
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
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

q₁ = ((R*L_stream)/2)+((K/(2*L_stream))*(h_o^2-h₁^2)) --> ((16*4.09)/2)+((0.09/(2*4.09))*(12^2-5^2))

Evaluating ... ...

q₁ = 34.0292909535452

STEP 3: Convert Result to Output's Unit

34.0292909535452 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

34.0292909535452 ≈ 34.02929 Cubic Meter per Second <-- Discharge at Downstream Side

(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 at downstream water body of catchment

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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

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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 at downstream water body of catchment 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 at downstream water body of catchment?

Discharge at downstream water body of catchment calculator uses 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)) to calculate the Discharge at Downstream Side, The Discharge at downstream water body of catchment is defined as the volumetric flow rate of water that is transported through a given cross-sectional area at the Downstream Water Body. Discharge at Downstream Side is denoted by q₁ symbol.

How to calculate Discharge at downstream water body of catchment using this online calculator? To use this online calculator for Discharge at downstream water body of catchment, enter Natural Recharge (R), 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 at downstream water body of catchment calculation can be explained with given input values -> 34.02929 = ((16*4.09)/2)+((0.09/(2*4.09))*(12^2-5^2)).

FAQ

What is Discharge at downstream water body of catchment?

The Discharge at downstream water body of catchment is defined as the volumetric flow rate of water that is transported through a given cross-sectional area at the Downstream Water Body and is represented as q₁ = ((R*L_stream)/2)+((K/(2*L_stream))*(h_o^2-h₁^2)) or 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)). Natural Recharge is the replenishment of infiltrating groundwater, 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 at downstream water body of catchment?

The Discharge at downstream water body of catchment is defined as the volumetric flow rate of water that is transported through a given cross-sectional area at the Downstream Water Body is calculated using 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)). To calculate Discharge at downstream water body of catchment, you need Natural Recharge (R), 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, 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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