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Diameter of Section given Section Factor Formula

GoDiameter of Section given Wetted Area Formula

GoDiameter of Section given Wetted Perimeter Formula

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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. Check FAQs

d section = {(\frac{Z cir}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{π}) \cdot θ Angle - \sin (θ Angle))}^{1.5}}{{(\sin (\frac{θ Angle}{2}))}^{0.5}}})}^{\frac{2}{5}}

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

Diameter of Section given Section Factor Example

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Here is how the Diameter of Section given Section Factor equation looks like with Values.

Here is how the Diameter of Section given Section Factor equation looks like with Units.

Here is how the Diameter of Section given Section Factor equation looks like.

4.9999 = {(\frac{80.88}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14 - \sin (3.14))}^{1.5}}{{(\sin (\frac{3.14}{2}))}^{0.5}}})}^{\frac{2}{5}}

4.9999m = {(\frac{80.88m^2.5}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14° - \sin (3.14°))}^{1.5}}{{(\sin (\frac{3.14°}{2}))}^{0.5}}})}^{\frac{2}{5}}

4.9999 = {(\frac{80.88}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14 - \sin (3.14))}^{1.5}}{{(\sin (\frac{3.14}{2}))}^{0.5}}})}^{\frac{2}{5}}

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Diameter of Section given Section Factor Solution

Follow our step by step solution on how to calculate Diameter of Section given Section Factor?

FIRST Step Consider the formula

d section = {(\frac{Z cir}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{π}) \cdot θ Angle - \sin (θ Angle))}^{1.5}}{{(\sin (\frac{θ Angle}{2}))}^{0.5}}})}^{\frac{2}{5}}

Next Step Substitute values of Variables

∴

d section = {(\frac{80.88m^2.5}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{π}) \cdot 3.14° - \sin (3.14°))}^{1.5}}{{(\sin (\frac{3.14°}{2}))}^{0.5}}})}^{\frac{2}{5}}

Next Step Substitute values of Constants

∴

d section = {(\frac{80.88m^2.5}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 3.14° - \sin (3.14°))}^{1.5}}{{(\sin (\frac{3.14°}{2}))}^{0.5}}})}^{\frac{2}{5}}

Next Step Convert Units

∴

d section = {(\frac{80.88m^2.5}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 0.0548rad - \sin (0.0548rad))}^{1.5}}{{(\sin (\frac{0.0548rad}{2}))}^{0.5}}})}^{\frac{2}{5}}

Next Step Prepare to Evaluate

∴

d section = {(\frac{80.88}{(\frac{\sqrt{2}}{32}) \cdot \frac{{((\frac{180}{3.1416}) \cdot 0.0548 - \sin (0.0548))}^{1.5}}{{(\sin (\frac{0.0548}{2}))}^{0.5}}})}^{\frac{2}{5}}

Next Step Evaluate

∴

d section = 4.99991884220499m

LAST Step Rounding Answer

∴

d section = 4.9999m

Diameter of Section given Section Factor Formula Elements

Variables

Constants

Functions

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

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

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 to find Diameter of Section

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 Diameter of Section given Hydraulic Radius for Channel

d section = \frac{R h(cir)}{0.25 \cdot (1 - (\frac{\sin (θ Angle)}{(\frac{180}{π}) \cdot θ Angle}))}

Go Diameter of Section given Top Width

d section = \frac{T cir}{\sin (\frac{θ Angle}{2})}

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 Angle of Sector given Wetted Perimeter

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

Go Wetted Perimeter for circle

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

Go Hydraulic Radius given Angle

R h(cir) = 0.25 \cdot d section \cdot (1 - \frac{\sin (θ Angle)}{\frac{180}{π}} \cdot θ Angle)

How to Evaluate Diameter of Section given Section Factor?

Diameter of Section given Section Factor evaluator uses Diameter of Section = (Section Factor of Circular Channel/(((sqrt(2))/32)*(((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians))^1.5)/((sin(Subtended Angle in Radians/2))^0.5)))^(2/5) to evaluate the Diameter of Section, Diameter of Section given Section Factor is defined as the diameter of a structural element using its Section Factor, which is the ratio of its cross-sectional area to its perimeter. Diameter of Section is denoted by d_section symbol.

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

FAQs on Diameter of Section given Section Factor

What is the formula to find Diameter of Section given Section Factor?

The formula of Diameter of Section given Section Factor is expressed as Diameter of Section = (Section Factor of Circular Channel/(((sqrt(2))/32)*(((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians))^1.5)/((sin(Subtended Angle in Radians/2))^0.5)))^(2/5). Here is an example- 4.999919 = (80.88/(((sqrt(2))/32)*(((180/pi)*0.0548033385126116-sin(0.0548033385126116))^1.5)/((sin(0.0548033385126116/2))^0.5)))^(2/5).

How to calculate Diameter of Section given Section Factor?

With Section Factor of Circular Channel (Z_cir) & Subtended Angle in Radians (θ_Angle) we can find Diameter of Section given Section Factor using the formula - Diameter of Section = (Section Factor of Circular Channel/(((sqrt(2))/32)*(((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians))^1.5)/((sin(Subtended Angle in Radians/2))^0.5)))^(2/5). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Diameter of Section?

Here are the different ways to Calculate Diameter of Section-

Diameter of Section=sqrt(((180/pi)*(Subtended Angle in Radians)-(8*Wetted Surface Area of Circular Channel))/sin(Subtended Angle in Radians))
Diameter of Section=Wetted Perimeter of Channel/(0.5*Subtended Angle in Radians*(180/pi))
Diameter of Section=Hydraulic Radius of Circular Channel/(0.25*(1-(sin(Subtended Angle in Radians)/((180/pi)*Subtended Angle in Radians))))

Can the Diameter of Section given Section Factor be negative?

No, the Diameter of Section given Section Factor, measured in Length cannot be negative.

Which unit is used to measure Diameter of Section given Section Factor?

Diameter of Section given Section Factor is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diameter of Section given Section Factor can be measured.

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: Unit

Diameter of Section given Section Factor Formula

​GoDiameter of Section given Wetted Area Formula

​GoDiameter of Section given Wetted Perimeter Formula

Diameter of Section given Section Factor Example

Diameter of Section given Section Factor Solution

Diameter of Section given Section Factor Formula Elements

Other Formulas to find Diameter of Section

Other formulas in Geometrical Properties of Circular Channel Section category

How to Evaluate Diameter of Section given Section Factor?

FAQs on Diameter of Section given Section Factor

Variable Name

GoDiameter of Section given Wetted Area Formula

GoDiameter of Section given Wetted Perimeter Formula