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

GoCoefficient of Discharge given Discharge through Free Weir Portion Formula

GoCoefficient of Discharge given Discharge through Drowned Portion Formula

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

C d = \frac{3 \cdot Q 1}{2 \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}})}

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

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

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Here is how the Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir equation looks like with Values.

Here is how the Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir equation looks like with Units.

Here is how the Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir equation looks like.

0.4228 = \frac{3 \cdot 50.1}{2 \cdot 3 \cdot \sqrt{2 \cdot 9.8} \cdot ({((10.1 - 5.1) + (\frac{{4.1}^{2}}{2 \cdot 9.8}))}^{\frac{3}{2}} - {(\frac{{4.1}^{2}}{2 \cdot 9.8})}^{\frac{3}{2}})}

0.4228 = \frac{3 \cdot 50.1m³/s}{2 \cdot 3m \cdot \sqrt{2 \cdot 9.8m/s²} \cdot ({((10.1m - 5.1m) + (\frac{{4.1m/s}^{2}}{2 \cdot 9.8m/s²}))}^{\frac{3}{2}} - {(\frac{{4.1m/s}^{2}}{2 \cdot 9.8m/s²})}^{\frac{3}{2}})}

0.4228 = \frac{3 \cdot 50.1}{2 \cdot 3 \cdot \sqrt{2 \cdot 9.8} \cdot ({((10.1 - 5.1) + (\frac{{4.1}^{2}}{2 \cdot 9.8}))}^{\frac{3}{2}} - {(\frac{{4.1}^{2}}{2 \cdot 9.8})}^{\frac{3}{2}})}

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Home » Engineering » Civil » Hydraulics and Waterworks » Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir

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

Follow our step by step solution on how to calculate Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir?

FIRST Step Consider the formula

C d = \frac{3 \cdot Q 1}{2 \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}})}

Next Step Substitute values of Variables

∴

C d = \frac{3 \cdot 50.1m³/s}{2 \cdot 3m \cdot \sqrt{2 \cdot 9.8m/s²} \cdot ({((10.1m - 5.1m) + (\frac{{4.1m/s}^{2}}{2 \cdot 9.8m/s²}))}^{\frac{3}{2}} - {(\frac{{4.1m/s}^{2}}{2 \cdot 9.8m/s²})}^{\frac{3}{2}})}

Next Step Prepare to Evaluate

∴

C d = \frac{3 \cdot 50.1}{2 \cdot 3 \cdot \sqrt{2 \cdot 9.8} \cdot ({((10.1 - 5.1) + (\frac{{4.1}^{2}}{2 \cdot 9.8}))}^{\frac{3}{2}} - {(\frac{{4.1}^{2}}{2 \cdot 9.8})}^{\frac{3}{2}})}

Next Step Evaluate

∴

C d = 0.422798795247991

LAST Step Rounding Answer

∴

C d = 0.4228

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

Variables

Functions

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.

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.

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.

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.

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.

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.

Velocity over Submerged Weir

Velocity over Submerged Weir is the rate of change of the position of an object with respect to time.

Symbol: v_su

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

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)

Credits

Created by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has created this Formula and 500+ more formulas!

Verified by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has verified this Formula and 400+ more formulas!

Other Formulas to find Coefficient of Discharge

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 Coefficient of Discharge given Discharge through Drowned Portion

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

Other formulas in Submerged Weirs category

Go Discharge through Free Weir Portion

Q 1 = (\frac{2}{3}) \cdot C d \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}}}

How to Evaluate Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir?

Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir evaluator uses 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))) to evaluate the Coefficient of Discharge, The Coefficient of discharge if velocity is approached given discharge through free weir is stated as the ratio between the actual flow discharge and theoretical flow discharge. Coefficient of Discharge is denoted by C_d symbol.

How to evaluate Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir using this online evaluator? To use this online evaluator for Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir, enter Discharge through Free Portion (Q₁), 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.

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

What is the formula to find Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir?

The formula of Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir is expressed as 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))). Here is an example- 0.422799 = (3*50.1)/(2*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))).

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

With Discharge through Free Portion (Q₁), 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) we can find Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir using the formula - 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))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Coefficient of Discharge?

Here are the different ways to Calculate Coefficient of Discharge-

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))
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)))
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)))

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

​GoCoefficient of Discharge given Discharge through Free Weir Portion Formula

​GoCoefficient of Discharge given Discharge through Drowned Portion Formula

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

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

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

Credits

Other Formulas to find Coefficient of Discharge

Other formulas in Submerged Weirs category

How to Evaluate Coefficient of Discharge if Velocity is Approached given Discharge through Free Weir?

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

Variable Name

GoCoefficient of Discharge given Discharge through Free Weir Portion Formula

GoCoefficient of Discharge given Discharge through Drowned Portion Formula