Head on Upstream Weir for Discharge through Drowned Portion Calculator

✖Discharge through Drowned Portion is a measure of the quantity of fluid flow over unit time, representing the quantity of water in between the downstream and the crest of the water.ⓘ Discharge through Drowned Portion [Q₂]			+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%
✖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 of Weir [h₂]			+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 Weir for Discharge through Drowned Portion [H_Upstream]

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Formula

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Head on Upstream Weir for Discharge through Drowned Portion

Formula

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

Example

`"10.09949m"=("99.96m³/s"/("0.66"*"3m"*"5.1m"))^2*(1/(2*"9.8m/s²"))+"5.1m"`

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Head on Upstream Weir for Discharge through Drowned Portion Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
H_Upstream = (Q₂/(C_d*L_w*h₂))^2*(1/(2*g))+h₂
This formula uses 6 Variables

Variables Used

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.
Discharge through Drowned Portion - (Measured in Cubic Meter per Second) - Discharge through Drowned Portion is a measure of the quantity of fluid flow over unit time, representing the quantity of water in between the downstream and the crest of the water.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Discharge through Drowned Portion: 99.96 Cubic Meter per Second --> 99.96 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
Head on Downstream of Weir: 5.1 Meter --> 5.1 Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_Upstream = (Q₂/(C_d*L_w*h₂))^2*(1/(2*g))+h₂ --> (99.96/(0.66*3*5.1))^2*(1/(2*9.8))+5.1

Evaluating ... ...

H_Upstream = 10.0994898479747

STEP 3: Convert Result to Output's Unit

10.0994898479747 Meter --> No Conversion Required

FINAL ANSWER

10.0994898479747 ≈ 10.09949 Meter <-- Head on Upstream 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 Upstream Weir for Discharge through Drowned Portion

Credits

Created by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has created this Calculator and 500+ more calculators!

Verified by Rithik Agrawal

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 Upstream Weir for Discharge through Drowned 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 Upstream Weir for Discharge through Drowned Portion?

Head on Upstream Weir for Discharge through Drowned Portion calculator uses 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 to calculate the Head on Upstream of Weir, The Head on upstream weir for discharge through drowned portion is a measurement of head drop on the upstream weir. Head on Upstream of Weir is denoted by H_Upstream symbol.

How to calculate Head on Upstream Weir for Discharge through Drowned Portion using this online calculator? To use this online calculator for Head on Upstream Weir for Discharge through Drowned Portion, enter Discharge through Drowned Portion (Q₂), Coefficient of Discharge (C_d), Length of Weir Crest (L_w), Head on Downstream of Weir (h₂) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Head on Upstream Weir for Discharge through Drowned Portion calculation can be explained with given input values -> 12.88047 = (99.96/(0.66*3*5.1))^2*(1/(2*9.8))+5.1.

FAQ

What is Head on Upstream Weir for Discharge through Drowned Portion?

The Head on upstream weir for discharge through drowned portion is a measurement of head drop on the upstream weir and is represented as H_Upstream = (Q₂/(C_d*L_w*h₂))^2*(1/(2*g))+h₂ or 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. Discharge through Drowned Portion is a measure of the quantity of fluid flow over unit time, representing the quantity of water in between the downstream and the crest of the water, 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, 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 & The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

How to calculate Head on Upstream Weir for Discharge through Drowned Portion?

The Head on upstream weir for discharge through drowned portion is a measurement of head drop on the upstream weir is calculated using 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. To calculate Head on Upstream Weir for Discharge through Drowned Portion, you need Discharge through Drowned Portion (Q₂), Coefficient of Discharge (C_d), Length of Weir Crest (L_w), Head on Downstream of Weir (h₂) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Discharge through Drowned Portion, Coefficient of Discharge, Length of Weir Crest, Head on Downstream of Weir & Acceleration due to Gravity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Head on Upstream of Weir?

In this formula, Head on Upstream of Weir uses Discharge through Drowned Portion, Coefficient of Discharge, Length of Weir Crest, Head on Downstream of Weir & Acceleration due to Gravity. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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