Head on Downstream Weir for Discharge through Free Weir Portion Calculator

✖Discharge through Free Portion is a measure of the quantity of fluid flow over unit time, representing the quantity in between the upstream and downstream portion.ⓘ Discharge through Free Portion [Q₁]			+10% -10%
✖Coefficient of Discharge is ratio of Actual discharge to theoretical discharge.ⓘ Coefficient of Discharge [C_d]			+10% -10%
✖Length of Weir Crest is the measurement or extent of Weir Crest from end to end.ⓘ Length of Weir Crest [L_w]			+10% -10%
✖The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Head on Upstream of Weirr pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.ⓘ Head on Upstream of Weir [H_Upstream]			+10% -10%

✖Head on Downstream of Weir pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.ⓘ Head on Downstream Weir for Discharge through Free Weir Portion [h₂]

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Formula

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Head on Downstream Weir for Discharge through Free Weir Portion

Formula

`"h"_{"2"} = -((3*"Q"_{"1"})/(2*"C"_{"d"}*"L"_{"w"}*sqrt(2*"g")))^(2/3)+"H"_{"Upstream"}`

Example

`"5.911192m"=-((3*"50.1m³/s")/(2*"0.66"*"3m"*sqrt(2*"9.8m/s²")))^(2/3)+"10.1m"`

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Head on Downstream Weir for Discharge through Free Weir Portion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Head on Downstream of Weir = -((3*Discharge through Free Portion)/(2*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)))^(2/3)+Head on Upstream of Weir
h₂ = -((3*Q₁)/(2*C_d*L_w*sqrt(2*g)))^(2/3)+H_Upstream
This formula uses 1 Functions, 6 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

Head on Downstream of Weir - (Measured in Meter) - Head on Downstream of Weir pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.
Discharge through Free Portion - (Measured in Cubic Meter per Second) - Discharge through Free Portion is a measure of the quantity of fluid flow over unit time, representing the quantity in between the upstream and downstream portion.
Coefficient of Discharge - Coefficient of Discharge is ratio of Actual discharge to theoretical discharge.
Length of Weir Crest - (Measured in Meter) - Length of Weir Crest is the measurement or extent of Weir Crest from end to end.
Acceleration due to Gravity - (Measured in Meter per Square Second) - The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Head on Upstream of Weir - (Measured in Meter) - Head on Upstream of Weirr pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.

STEP 1: Convert Input(s) to Base Unit

Discharge through Free Portion: 50.1 Cubic Meter per Second --> 50.1 Cubic Meter per Second No Conversion Required
Coefficient of Discharge: 0.66 --> No Conversion Required
Length of Weir Crest: 3 Meter --> 3 Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Head on Upstream of Weir: 10.1 Meter --> 10.1 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h₂ = -((3*Q₁)/(2*C_d*L_w*sqrt(2*g)))^(2/3)+H_Upstream --> -((3*50.1)/(2*0.66*3*sqrt(2*9.8)))^(2/3)+10.1

Evaluating ... ...

h₂ = 5.9111915015469

STEP 3: Convert Result to Output's Unit

5.9111915015469 Meter --> No Conversion Required

FINAL ANSWER

5.9111915015469 ≈ 5.911192 Meter <-- Head on Downstream of Weir

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Flow Over Notches and Weirs » Submerged Weirs » Head on Downstream Weir for Discharge through Free Weir Portion

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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National Institute of Technology Karnataka (NITK), Surathkal

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< 17 Submerged Weirs Calculators

Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir

Go Coefficient of Discharge = (3*Discharge through Free Portion)/(2*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)*(((Head on Upstream of Weir-Head on Downstream of Weir)+(Velocity over Submerged Weir^2/(2*Acceleration due to Gravity)))^(3/2)-(Velocity over Submerged Weir^2/(2*Acceleration due to Gravity))^(3/2)))

Length of Crest for Discharge through Free Weir

Go Length of Weir Crest = (3*Discharge through Free Portion)/(2*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*(((Head on Upstream of Weir-Head on Downstream of Weir)+(Velocity over Submerged Weir^2/(2*Acceleration due to Gravity)))^(3/2)-(Velocity over Submerged Weir^2/(2*Acceleration due to Gravity))^(3/2)))

Discharge through Free Weir if Velocity is Approached

Go Discharge through Free Portion = (2/3)*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)*(((Head on Upstream of Weir-Head on Downstream of Weir)+(Velocity over Submerged Weir^2/(2*Acceleration due to Gravity)))^(3/2)-(Velocity over Submerged Weir^2/(2*Acceleration due to Gravity))^(3/2))

Coefficient of Discharge if Velocity is Approached for Submerged Weir

Go Coefficient of Discharge = Discharge through Drowned Portion/(Length of Weir Crest*Head on Downstream of Weir*(sqrt(2*Acceleration due to Gravity*(Head on Upstream of Weir-Head on Downstream of Weir)+Velocity over Submerged Weir^2)))

Length of Crest for Discharge through Drowned Portion

Go Length of Weir Crest = Discharge through Drowned Portion/(Coefficient of Discharge*Head on Downstream of Weir*(sqrt(2*Acceleration due to Gravity*(Head on Upstream of Weir-Head on Downstream of Weir)+Velocity over Submerged Weir^2)))

Discharge through Submerged Weir if Velocity is Approached

Go Discharge through Drowned Portion = Coefficient of Discharge*Length of Weir Crest*Head on Downstream of Weir*(sqrt(2*Acceleration due to Gravity*(Head on Upstream of Weir-Head on Downstream of Weir)+Velocity over Submerged Weir^2))

Coefficient of Discharge given Discharge through Drowned Portion

Go Coefficient of Discharge = Discharge through Drowned Portion/((Length of Weir Crest*Head on Downstream of Weir)*sqrt(2*Acceleration due to Gravity*(Head on Upstream of Weir-Head on Downstream of Weir)))

Discharge through Drowned Portion

Go Discharge through Drowned Portion = Coefficient of Discharge*(Length of Weir Crest*Head on Downstream of Weir)*sqrt(2*Acceleration due to Gravity*(Head on Upstream of Weir-Head on Downstream of Weir))

Head on Upstream Weir for Discharge through Drowned Portion

Go Head on Upstream of Weir = (Discharge through Drowned Portion/(Coefficient of Discharge*Length of Weir Crest*Head on Downstream of Weir))^2*(1/(2*Acceleration due to Gravity))+Head on Downstream of Weir

Head on Downstream Weir for Discharge through Free Weir Portion

Go Head on Downstream of Weir = -((3*Discharge through Free Portion)/(2*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)))^(2/3)+Head on Upstream of Weir

Coefficient of Discharge given Discharge through Free Weir Portion

Go Coefficient of Discharge = (3*Discharge through Free Portion)/(2*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)*(Head on Upstream of Weir-Head on Downstream of Weir)^(3/2))

Head on Upstream Weir given Discharge through Free Weir Portion

Go Head on Upstream of Weir = ((3*Discharge through Free Portion)/(2*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)))^(2/3)+Head on Downstream of Weir

Length of Crest for Discharge through Free Weir Portion

Go Length of Weir Crest = (3*Discharge through Free Portion)/(2*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*(Head on Upstream of Weir-Head on Downstream of Weir)^(3/2))

Discharge through Free Weir Portion

Go Discharge through Free Portion = (2/3)*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)*(Head on Upstream of Weir-Head on Downstream of Weir)^(3/2)

Discharge through Free Weir Portion given Total Discharge over Submerged Weir

Go Discharge through Free Portion = Total Discharge of Submerged Weir-Discharge through Drowned Portion

Discharge through Drowned Portion given Total Discharge over Submerged Weir

Go Discharge through Drowned Portion = Total Discharge of Submerged Weir-Discharge through Free Portion

Total Discharge over Submerged Weir

Go Total Discharge of Submerged Weir = Discharge through Free Portion+Discharge through Drowned Portion

Head on Downstream Weir for Discharge through Free Weir Portion Formula

What is meant by Coefficient of discharge?

Coefficient of discharge is stated as the ratio between the actual flow discharge and theoretical flow discharge.

How to Calculate Head on Downstream Weir for Discharge through Free Weir Portion?

Head on Downstream Weir for Discharge through Free Weir Portion calculator uses Head on Downstream of Weir = -((3*Discharge through Free Portion)/(2*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)))^(2/3)+Head on Upstream of Weir to calculate the Head on Downstream of Weir, The Head on downstream weir for discharge through free weir portion is a measurement of head drop in the weir in a free weir portion. Head on Downstream of Weir is denoted by h₂ symbol.

How to calculate Head on Downstream Weir for Discharge through Free Weir Portion using this online calculator? To use this online calculator for Head on Downstream Weir for Discharge through Free Weir Portion, enter Discharge through Free Portion (Q₁), Coefficient of Discharge (C_d), Length of Weir Crest (L_w), Acceleration due to Gravity (g) & Head on Upstream of Weir (H_Upstream) and hit the calculate button. Here is how the Head on Downstream Weir for Discharge through Free Weir Portion calculation can be explained with given input values -> 5.911192 = -((3*50.1)/(2*0.66*3*sqrt(2*9.8)))^(2/3)+10.1.

FAQ

What is Head on Downstream Weir for Discharge through Free Weir Portion?

The Head on downstream weir for discharge through free weir portion is a measurement of head drop in the weir in a free weir portion and is represented as h₂ = -((3*Q₁)/(2*C_d*L_w*sqrt(2*g)))^(2/3)+H_Upstream or Head on Downstream of Weir = -((3*Discharge through Free Portion)/(2*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)))^(2/3)+Head on Upstream of Weir. Discharge through Free Portion is a measure of the quantity of fluid flow over unit time, representing the quantity in between the upstream and downstream portion, Coefficient of Discharge is ratio of Actual discharge to theoretical discharge, Length of Weir Crest is the measurement or extent of Weir Crest from end to end, The Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Head on Upstream of Weirr pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.

How to calculate Head on Downstream Weir for Discharge through Free Weir Portion?

The Head on downstream weir for discharge through free weir portion is a measurement of head drop in the weir in a free weir portion is calculated using Head on Downstream of Weir = -((3*Discharge through Free Portion)/(2*Coefficient of Discharge*Length of Weir Crest*sqrt(2*Acceleration due to Gravity)))^(2/3)+Head on Upstream of Weir. To calculate Head on Downstream Weir for Discharge through Free Weir Portion, you need Discharge through Free Portion (Q₁), Coefficient of Discharge (C_d), Length of Weir Crest (L_w), Acceleration due to Gravity (g) & Head on Upstream of Weir (H_Upstream). With our tool, you need to enter the respective value for Discharge through Free Portion, Coefficient of Discharge, Length of Weir Crest, Acceleration due to Gravity & Head on Upstream of Weir 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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