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Section Factor for Circle Formula

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Section Factor of Circular Channel is ratio of normal to critical channel depth. Check FAQs

Z cir = ((\frac{\sqrt{2}}{32}) \cdot ({d section}^{2.5}) \cdot \frac{{((\frac{180}{π}) \cdot θ Angle - \sin (θ Angle))}^{1.5}}{{(\sin (\frac{θ Angle}{2}))}^{0.5}})

Z_cir - Section Factor of Circular Channel?d_section - Diameter of Section?θ_Angle - Subtended Angle in Radians?π - Archimedes' constant?

Section Factor for Circle Example

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Here is how the Section Factor for Circle equation looks like with Values.

Here is how the Section Factor for Circle equation looks like with Units.

Here is how the Section Factor for Circle equation looks like.

80.8833 = ((\frac{\sqrt{2}}{32}) \cdot (5^{2.5}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14 - \sin (3.14))}^{1.5}}{{(\sin (\frac{3.14}{2}))}^{0.5}})

80.8833m^2.5 = ((\frac{\sqrt{2}}{32}) \cdot ({5m}^{2.5}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14° - \sin (3.14°))}^{1.5}}{{(\sin (\frac{3.14°}{2}))}^{0.5}})

80.8833 = ((\frac{\sqrt{2}}{32}) \cdot (5^{2.5}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14 - \sin (3.14))}^{1.5}}{{(\sin (\frac{3.14}{2}))}^{0.5}})

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Section Factor for Circle Solution

Follow our step by step solution on how to calculate Section Factor for Circle?

FIRST Step Consider the formula

Z cir = ((\frac{\sqrt{2}}{32}) \cdot ({d section}^{2.5}) \cdot \frac{{((\frac{180}{π}) \cdot θ Angle - \sin (θ Angle))}^{1.5}}{{(\sin (\frac{θ Angle}{2}))}^{0.5}})

Next Step Substitute values of Variables

∴

Z cir = ((\frac{\sqrt{2}}{32}) \cdot ({5m}^{2.5}) \cdot \frac{{((\frac{180}{π}) \cdot 3.14° - \sin (3.14°))}^{1.5}}{{(\sin (\frac{3.14°}{2}))}^{0.5}})

Next Step Substitute values of Constants

∴

Z cir = ((\frac{\sqrt{2}}{32}) \cdot ({5m}^{2.5}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14° - \sin (3.14°))}^{1.5}}{{(\sin (\frac{3.14°}{2}))}^{0.5}})

Next Step Convert Units

∴

Z cir = ((\frac{\sqrt{2}}{32}) \cdot ({5m}^{2.5}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 0.0548rad - \sin (0.0548rad))}^{1.5}}{{(\sin (\frac{0.0548rad}{2}))}^{0.5}})

Next Step Prepare to Evaluate

∴

Z cir = ((\frac{\sqrt{2}}{32}) \cdot (5^{2.5}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 0.0548 - \sin (0.0548))}^{1.5}}{{(\sin (\frac{0.0548}{2}))}^{0.5}})

Next Step Evaluate

∴

Z cir = 80.883282114459m^2.5

LAST Step Rounding Answer

∴

Z cir = 80.8833m^2.5

Section Factor for Circle Formula Elements

Variables

Constants

Functions

Section Factor of Circular Channel

Section Factor of Circular Channel is ratio of normal to critical channel depth.

Symbol: Z_cir

Measurement: Section FactorUnit: m^2.5

Note: Value should be greater than 0.

Formulas to find Section Factor of Circular Channel

Diameter of Section

The Diameter of Section refers to the length of the segment that passes through the center of the circle and touches two points on the edge of the circle.

Symbol: d_section

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Section

Subtended Angle in Radians

Subtended Angle in Radians is the angle made by something from a given viewpoint.

Symbol: θ_Angle

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Subtended Angle in Radians

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(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 in Geometrical Properties of Circular Channel Section category

Go Wetted Area for Circle

A w(cir) = (\frac{1}{8}) \cdot ((\frac{180}{π}) \cdot θ Angle - \sin (θ Angle) \cdot ({d section}^{2}))

Go Diameter of Section given Wetted Area

d section = \sqrt{\frac{(\frac{180}{π}) \cdot (θ Angle) - (8 \cdot A w(cir))}{\sin (θ Angle)}}

Go Diameter of Section given Wetted Perimeter

d section = \frac{p}{0.5 \cdot θ Angle \cdot (\frac{180}{π})}

Go Angle of Sector given Wetted Perimeter

θ Angle = \frac{p}{0.5 \cdot d section} \cdot (\frac{π}{180})

How to Evaluate Section Factor for Circle?

Section Factor for Circle evaluator uses Section Factor of Circular Channel = (((sqrt(2))/32)*(Diameter of Section^2.5)*(((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians))^1.5)/((sin(Subtended Angle in Radians/2))^0.5)) to evaluate the Section Factor of Circular Channel, The Section Factor for Circle is defined as the ratio depending on the angle and geometrical property of section. Section Factor of Circular Channel is denoted by Z_cir symbol.

How to evaluate Section Factor for Circle using this online evaluator? To use this online evaluator for Section Factor for Circle, enter Diameter of Section (d_section) & Subtended Angle in Radians (θ_Angle) and hit the calculate button.

FAQs on Section Factor for Circle

What is the formula to find Section Factor for Circle?

The formula of Section Factor for Circle is expressed as Section Factor of Circular Channel = (((sqrt(2))/32)*(Diameter of Section^2.5)*(((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians))^1.5)/((sin(Subtended Angle in Radians/2))^0.5)). Here is an example- 80.88328 = (((sqrt(2))/32)*(5^2.5)*(((180/pi)*0.0548033385126116-sin(0.0548033385126116))^1.5)/((sin(0.0548033385126116/2))^0.5)).

How to calculate Section Factor for Circle?

With Diameter of Section (d_section) & Subtended Angle in Radians (θ_Angle) we can find Section Factor for Circle using the formula - Section Factor of Circular Channel = (((sqrt(2))/32)*(Diameter of Section^2.5)*(((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians))^1.5)/((sin(Subtended Angle in Radians/2))^0.5)). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

Can the Section Factor for Circle be negative?

No, the Section Factor for Circle, measured in Section Factor cannot be negative.

Which unit is used to measure Section Factor for Circle?

Section Factor for Circle is usually measured using the Meter^2.5[m^2.5] for Section Factor. Yard^2.5[m^2.5], Foot^2.5[m^2.5], Decimeter^2.5[m^2.5] are the few other units in which Section Factor for Circle can be measured.

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Section Factor for Circle Formula

Section Factor for Circle Example

Section Factor for Circle Solution

Section Factor for Circle Formula Elements

Other formulas in Geometrical Properties of Circular Channel Section category

How to Evaluate Section Factor for Circle?

FAQs on Section Factor for Circle

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