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Discharge through Free Weir Portion Formula

GoDischarge through Free Weir Portion given Total Discharge over Submerged Weir Formula

GoDischarge through Free Weir if Velocity is Approached Formula

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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. Check FAQs

Q 1 = (\frac{2}{3}) \cdot C d \cdot L w \cdot \sqrt{2 \cdot g} \cdot {(H Upstream - h 2)}^{\frac{3}{2}}

Q₁ - Discharge through Free Portion?C_d - Coefficient of Discharge?L_w - Length of Weir Crest?g - Acceleration due to Gravity?H_Upstream - Head on Upstream of Weir?h₂ - Head on Downstream of Weir?

Discharge through Free Weir Portion Example

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Here is how the Discharge through Free Weir Portion equation looks like with Values.

Here is how the Discharge through Free Weir Portion equation looks like with Units.

Here is how the Discharge through Free Weir Portion equation looks like.

65.3367 = (\frac{2}{3}) \cdot 0.66 \cdot 3 \cdot \sqrt{2 \cdot 9.8} \cdot {(10.1 - 5.1)}^{\frac{3}{2}}

65.3367m³/s = (\frac{2}{3}) \cdot 0.66 \cdot 3m \cdot \sqrt{2 \cdot 9.8m/s²} \cdot {(10.1m - 5.1m)}^{\frac{3}{2}}

65.3367 = (\frac{2}{3}) \cdot 0.66 \cdot 3 \cdot \sqrt{2 \cdot 9.8} \cdot {(10.1 - 5.1)}^{\frac{3}{2}}

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Discharge through Free Weir Portion Solution

Follow our step by step solution on how to calculate Discharge through Free Weir Portion?

FIRST Step Consider the formula

Q 1 = (\frac{2}{3}) \cdot C d \cdot L w \cdot \sqrt{2 \cdot g} \cdot {(H Upstream - h 2)}^{\frac{3}{2}}

Next Step Substitute values of Variables

∴

Q 1 = (\frac{2}{3}) \cdot 0.66 \cdot 3m \cdot \sqrt{2 \cdot 9.8m/s²} \cdot {(10.1m - 5.1m)}^{\frac{3}{2}}

Next Step Prepare to Evaluate

∴

Q 1 = (\frac{2}{3}) \cdot 0.66 \cdot 3 \cdot \sqrt{2 \cdot 9.8} \cdot {(10.1 - 5.1)}^{\frac{3}{2}}

Next Step Evaluate

∴

Q 1 = 65.336666581637m³/s

LAST Step Rounding Answer

∴

Q 1 = 65.3367m³/s

Discharge through Free Weir Portion Formula Elements

Variables

Functions

Discharge through Free Portion

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.

Symbol: Q₁

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value can be positive or negative.

Formulas to find Discharge through Free Portion

Coefficient of Discharge

The Coefficient of Discharge is ratio of actual discharge to theoretical discharge.

Symbol: C_d

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.2.

Formulas to find Coefficient of Discharge

Length of Weir Crest

Length of Weir Crest is the measurement or extent of Weir Crest from end to end.

Symbol: L_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Weir Crest

Acceleration due to Gravity

The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Head on Upstream of Weir

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.

Symbol: H_Upstream

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Head on Upstream of Weir

Head on Downstream of Weir

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.

Symbol: h₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Head on Downstream of Weir

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.

Syntax: sqrt(Number)

Other Formulas to find Discharge through Free Portion

Go Discharge through Free Weir Portion given Total Discharge over Submerged Weir

Q 1 = Q T - Q 2

Go Discharge through Free Weir if Velocity is Approached

Q 1 = (\frac{2}{3}) \cdot C d \cdot L w \cdot \sqrt{2 \cdot g} \cdot ({((H Upstream - h 2) + (\frac{{v su}^{2}}{2 \cdot g}))}^{\frac{3}{2}} - {(\frac{{v su}^{2}}{2 \cdot g})}^{\frac{3}{2}})

Other formulas in Submerged Weirs category

Go Coefficient of Discharge given Discharge through Free Weir Portion

C d = \frac{3 \cdot Q 1}{2 \cdot L w \cdot \sqrt{2 \cdot g} \cdot {(H Upstream - h 2)}^{\frac{3}{2}}}

Go Length of Crest for Discharge through Free Weir Portion

L w = \frac{3 \cdot Q 1}{2 \cdot C d \cdot \sqrt{2 \cdot g} \cdot {(H Upstream - h 2)}^{\frac{3}{2}}}

Go Head on Upstream Weir given Discharge through Free Weir Portion

H Upstream = {(\frac{3 \cdot Q 1}{2 \cdot C d \cdot L w \cdot \sqrt{2 \cdot g}})}^{\frac{2}{3}} + h 2

Go Head on Downstream Weir for Discharge through Free Weir Portion

h 2 = - {(\frac{3 \cdot Q 1}{2 \cdot C d \cdot L w \cdot \sqrt{2 \cdot g}})}^{\frac{2}{3}} + H Upstream

How to Evaluate Discharge through Free Weir Portion?

Discharge through Free Weir Portion evaluator 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)^(3/2) to evaluate the Discharge through Free Portion, The Discharge through free weir portion 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 evaluate Discharge through Free Weir Portion using this online evaluator? To use this online evaluator for Discharge through Free Weir Portion, 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) and hit the calculate button.

FAQs on Discharge through Free Weir Portion

What is the formula to find Discharge through Free Weir Portion?

The formula of Discharge through Free Weir Portion is expressed as 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). Here is an example- 65.33667 = (2/3)*0.66*3*sqrt(2*9.8)*(10.1-5.1)^(3/2).

How to calculate Discharge through Free Weir Portion?

With 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) we can find Discharge through Free Weir Portion using the formula - 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). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Discharge through Free Portion?

Here are the different ways to Calculate Discharge through Free Portion-

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

Can the Discharge through Free Weir Portion be negative?

Yes, the Discharge through Free Weir Portion, measured in Volumetric Flow Rate can be negative.

Which unit is used to measure Discharge through Free Weir Portion?

Discharge through Free Weir Portion is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Discharge through Free Weir Portion can be measured.

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Discharge through Free Weir Portion Formula

​GoDischarge through Free Weir Portion given Total Discharge over Submerged Weir Formula

​GoDischarge through Free Weir if Velocity is Approached Formula

Discharge through Free Weir Portion Example

Discharge through Free Weir Portion Solution

Discharge through Free Weir Portion Formula Elements

Other Formulas to find Discharge through Free Portion

Other formulas in Submerged Weirs category

How to Evaluate Discharge through Free Weir Portion?

FAQs on Discharge through Free Weir Portion

Variable Name

GoDischarge through Free Weir Portion given Total Discharge over Submerged Weir Formula

GoDischarge through Free Weir if Velocity is Approached Formula