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Discharge over Trapezoidal Notch or Weir Formula

GoDischarge over Rectangle Notch or Weir Formula

GoDischarge over Triangular Notch or Weir Formula

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The Theoretical Discharge is given by the theoretical area and velocity. Check FAQs

Q th = \frac{2}{3} \cdot C d1 \cdot L w \cdot \sqrt{2 \cdot [g]} \cdot H^{\frac{3}{2}} + \frac{8}{15} \cdot C d2 \cdot \tan (\frac{∠A}{2}) \cdot \sqrt{2 \cdot [g]} \cdot H^{\frac{5}{2}}

Q_th - Theoretical Discharge?C_d1 - Coefficient of Discharge Rectangular?L_w - Length of Weir?H - Head of Liquid?C_d2 - Coefficient of Discharge Triangular?∠A - Angle A?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?

Discharge over Trapezoidal Notch or Weir Example

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Here is how the Discharge over Trapezoidal Notch or Weir equation looks like with Values.

Here is how the Discharge over Trapezoidal Notch or Weir equation looks like with Units.

Here is how the Discharge over Trapezoidal Notch or Weir equation looks like.

2880.4872 = \frac{2}{3} \cdot 0.63 \cdot 25 \cdot \sqrt{2 \cdot 9.8066} \cdot 10^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{142}{2}) \cdot \sqrt{2 \cdot 9.8066} \cdot 10^{\frac{5}{2}}

2880.4872m³/s = \frac{2}{3} \cdot 0.63 \cdot 25m \cdot \sqrt{2 \cdot 9.8066m/s²} \cdot {10m}^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{142°}{2}) \cdot \sqrt{2 \cdot 9.8066m/s²} \cdot {10m}^{\frac{5}{2}}

2880.4872 = \frac{2}{3} \cdot 0.63 \cdot 25 \cdot \sqrt{2 \cdot 9.8066} \cdot 10^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{142}{2}) \cdot \sqrt{2 \cdot 9.8066} \cdot 10^{\frac{5}{2}}

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Discharge over Trapezoidal Notch or Weir Solution

Follow our step by step solution on how to calculate Discharge over Trapezoidal Notch or Weir?

FIRST Step Consider the formula

Q th = \frac{2}{3} \cdot C d1 \cdot L w \cdot \sqrt{2 \cdot [g]} \cdot H^{\frac{3}{2}} + \frac{8}{15} \cdot C d2 \cdot \tan (\frac{∠A}{2}) \cdot \sqrt{2 \cdot [g]} \cdot H^{\frac{5}{2}}

Next Step Substitute values of Variables

∴

Q th = \frac{2}{3} \cdot 0.63 \cdot 25m \cdot \sqrt{2 \cdot [g]} \cdot {10m}^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{142°}{2}) \cdot \sqrt{2 \cdot [g]} \cdot {10m}^{\frac{5}{2}}

Next Step Substitute values of Constants

∴

Q th = \frac{2}{3} \cdot 0.63 \cdot 25m \cdot \sqrt{2 \cdot 9.8066m/s²} \cdot {10m}^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{142°}{2}) \cdot \sqrt{2 \cdot 9.8066m/s²} \cdot {10m}^{\frac{5}{2}}

Next Step Convert Units

∴

Q th = \frac{2}{3} \cdot 0.63 \cdot 25m \cdot \sqrt{2 \cdot 9.8066m/s²} \cdot {10m}^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{2.4784rad}{2}) \cdot \sqrt{2 \cdot 9.8066m/s²} \cdot {10m}^{\frac{5}{2}}

Next Step Prepare to Evaluate

∴

Q th = \frac{2}{3} \cdot 0.63 \cdot 25 \cdot \sqrt{2 \cdot 9.8066} \cdot 10^{\frac{3}{2}} + \frac{8}{15} \cdot 0.65 \cdot \tan (\frac{2.4784}{2}) \cdot \sqrt{2 \cdot 9.8066} \cdot 10^{\frac{5}{2}}

Next Step Evaluate

∴

Q th = 2880.48715700787m³/s

LAST Step Rounding Answer

∴

Q th = 2880.4872m³/s

Discharge over Trapezoidal Notch or Weir Formula Elements

Variables

Constants

Functions

Theoretical Discharge

The Theoretical Discharge is given by the theoretical area and velocity.

Symbol: Q_th

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Theoretical Discharge

Coefficient of Discharge Rectangular

The Coefficient of Discharge Rectangular portion is considered in discharge through the trapezoidal notch.

Symbol: C_d1

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient of Discharge Rectangular

Length of Weir

The Length of Weir is the of the base of weir through which discharge is taking place.

Symbol: L_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Length of Weir

Head of Liquid

The Head of Liquid is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column from the base of its container.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Head of Liquid

Coefficient of Discharge Triangular

The Coefficient of Discharge Triangular portion is considered in discharge through the trapezoidal notch.

Symbol: C_d2

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Coefficient of Discharge Triangular

Angle A

The angle A the space between two intersecting lines or surfaces at or close to the point where they meet.

Symbol: ∠A

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle A

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

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 Theoretical Discharge

Go Discharge over Rectangle Notch or Weir

Q th = \frac{2}{3} \cdot C d \cdot L w \cdot \sqrt{2 \cdot [g]} \cdot H^{\frac{3}{2}}

Go Discharge over Triangular Notch or Weir

Q th = \frac{8}{15} \cdot C d \cdot \tan (\frac{∠A}{2}) \cdot \sqrt{2 \cdot [g]} \cdot H^{\frac{5}{2}}

Other formulas in Discharge category

Go Head of Liquid at Crest

H = {(\frac{Q th}{\frac{2}{3} \cdot C d \cdot L w \cdot \sqrt{2 \cdot [g]}})}^{\frac{2}{3}}

Go Head of Liquid above V-notch

H = {(\frac{Q th}{\frac{8}{15} \cdot C d \cdot \tan (\frac{∠A}{2}) \cdot \sqrt{2 \cdot [g]}})}^{0.4}

Go Time Required to Empty Reservoir

t a = (\frac{3 \cdot A}{C d \cdot L w \cdot \sqrt{2 \cdot [g]}}) \cdot (\frac{1}{\sqrt{H f}} - \frac{1}{\sqrt{H i}})

Go Time Required to Empty Tank with Triangular Weir or Notch

t a = (\frac{5 \cdot A}{4 \cdot C d \cdot \tan (\frac{∠A}{2}) \cdot \sqrt{2 \cdot [g]}}) \cdot (\frac{1}{{H f}^{\frac{3}{2}}} - \frac{1}{{H i}^{\frac{3}{2}}})

How to Evaluate Discharge over Trapezoidal Notch or Weir?

Discharge over Trapezoidal Notch or Weir evaluator uses Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2) to evaluate the Theoretical Discharge, The Discharge over trapezoidal notch or weir formula is known by considering or combination of both the discharges through the rectangular and triangular notch or weir. Theoretical Discharge is denoted by Q_th symbol.

How to evaluate Discharge over Trapezoidal Notch or Weir using this online evaluator? To use this online evaluator for Discharge over Trapezoidal Notch or Weir, enter Coefficient of Discharge Rectangular (C_d1), Length of Weir (L_w), Head of Liquid (H), Coefficient of Discharge Triangular (C_d2) & Angle A (∠A) and hit the calculate button.

FAQs on Discharge over Trapezoidal Notch or Weir

What is the formula to find Discharge over Trapezoidal Notch or Weir?

The formula of Discharge over Trapezoidal Notch or Weir is expressed as Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2). Here is an example- 2880.487 = 2/3*0.63*25*sqrt(2*[g])*10^(3/2)+8/15*0.65*tan(2.47836753783148/2)*sqrt(2*[g])*10^(5/2).

How to calculate Discharge over Trapezoidal Notch or Weir?

With Coefficient of Discharge Rectangular (C_d1), Length of Weir (L_w), Head of Liquid (H), Coefficient of Discharge Triangular (C_d2) & Angle A (∠A) we can find Discharge over Trapezoidal Notch or Weir using the formula - Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and , Tangent (tan), Square Root (sqrt) function(s).

What are the other ways to Calculate Theoretical Discharge?

Here are the different ways to Calculate Theoretical Discharge-

Theoretical Discharge=2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)
Theoretical Discharge=8/15*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)

Can the Discharge over Trapezoidal Notch or Weir be negative?

No, the Discharge over Trapezoidal Notch or Weir, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Discharge over Trapezoidal Notch or Weir?

Discharge over Trapezoidal Notch or Weir 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 over Trapezoidal Notch or Weir can be measured.

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Discharge over Trapezoidal Notch or Weir Formula

​GoDischarge over Rectangle Notch or Weir Formula

​GoDischarge over Triangular Notch or Weir Formula

Discharge over Trapezoidal Notch or Weir Example

Discharge over Trapezoidal Notch or Weir Solution

Discharge over Trapezoidal Notch or Weir Formula Elements

Other Formulas to find Theoretical Discharge

Other formulas in Discharge category

How to Evaluate Discharge over Trapezoidal Notch or Weir?

FAQs on Discharge over Trapezoidal Notch or Weir

Variable Name

GoDischarge over Rectangle Notch or Weir Formula

GoDischarge over Triangular Notch or Weir Formula