Discharge through Free Weir if Velocity is Approached Calculator

✖The 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 of Weir [h₂]			+10% -10%
✖Velocity over Submerged Weir is the rate of change of the position of an object with respect to time.ⓘ Velocity over Submerged Weir [v_su]			+10% -10%

✖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 Weir if Velocity is Approached [Q₁]

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Discharge through Free Weir if Velocity is Approached Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Q₁ = (2/3)*C_d*L_w*sqrt(2*g)*(((H_Upstream-h₂)+(v_su^2/(2*g)))^(3/2)-(v_su^2/(2*g))^(3/2))
This formula uses 1 Functions, 7 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

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 - The 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.
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.
Velocity over Submerged Weir - (Measured in Meter per Second) - Velocity over Submerged Weir is the rate of change of the position of an object with respect to time.

STEP 1: Convert Input(s) to Base Unit

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
Head on Downstream of Weir: 5.1 Meter --> 5.1 Meter No Conversion Required
Velocity over Submerged Weir: 4.1 Meter per Second --> 4.1 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q₁ = (2/3)*C_d*L_w*sqrt(2*g)*(((H_Upstream-h₂)+(v_su^2/(2*g)))^(3/2)-(v_su^2/(2*g))^(3/2)) --> (2/3)*0.66*3*sqrt(2*9.8)*(((10.1-5.1)+(4.1^2/(2*9.8)))^(3/2)-(4.1^2/(2*9.8))^(3/2))

Evaluating ... ...

Q₁ = 78.2074130097869

STEP 3: Convert Result to Output's Unit

78.2074130097869 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

78.2074130097869 ≈ 78.20741 Cubic Meter per Second <-- Discharge through Free Portion

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Flow Over Notches and Weirs » Submerged Weirs » Discharge through Free Weir if Velocity is Approached

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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< Submerged Weirs Calculators

Coefficient of Discharge given Discharge through Free Weir Portion

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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 if Velocity is Approached Formula

LaTeX Go

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 Discharge through Free Weir if Velocity is Approached?

Discharge through Free Weir if Velocity is Approached calculator uses 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)) to calculate the Discharge through Free Portion, The Discharge through free weir if velocity is approached is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass. Discharge through Free Portion is denoted by Q₁ symbol.

How to calculate Discharge through Free Weir if Velocity is Approached using this online calculator? To use this online calculator for Discharge through Free Weir if Velocity is Approached, enter Coefficient of Discharge (C_d), Length of Weir Crest (L_w), Acceleration due to Gravity (g), Head on Upstream of Weir (H_Upstream), Head on Downstream of Weir (h₂) & Velocity over Submerged Weir (v_su) and hit the calculate button. Here is how the Discharge through Free Weir if Velocity is Approached calculation can be explained with given input values -> 78.20741 = (2/3)*0.66*3*sqrt(2*9.8)*(((10.1-5.1)+(4.1^2/(2*9.8)))^(3/2)-(4.1^2/(2*9.8))^(3/2)).

FAQ

What is Discharge through Free Weir if Velocity is Approached?

The Discharge through free weir if velocity is approached is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass and is represented as Q₁ = (2/3)*C_d*L_w*sqrt(2*g)*(((H_Upstream-h₂)+(v_su^2/(2*g)))^(3/2)-(v_su^2/(2*g))^(3/2)) or 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)). The 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, 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 & Velocity over Submerged Weir is the rate of change of the position of an object with respect to time.

How to calculate Discharge through Free Weir if Velocity is Approached?

The Discharge through free weir if velocity is approached is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass is calculated using 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)). To calculate Discharge through Free Weir if Velocity is Approached, you need Coefficient of Discharge (C_d), Length of Weir Crest (L_w), Acceleration due to Gravity (g), Head on Upstream of Weir (H_Upstream), Head on Downstream of Weir (h₂) & Velocity over Submerged Weir (v_su). With our tool, you need to enter the respective value for Coefficient of Discharge, Length of Weir Crest, Acceleration due to Gravity, Head on Upstream of Weir, Head on Downstream of Weir & Velocity over Submerged Weir 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 Discharge through Free Portion?

In this formula, Discharge through Free Portion uses Coefficient of Discharge, Length of Weir Crest, Acceleration due to Gravity, Head on Upstream of Weir, Head on Downstream of Weir & Velocity over Submerged Weir. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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