Section Factor for Circle Calculator

✖Diameter of Section is the diameter of the circular cross-section of the beam.ⓘ Diameter of Section [d_section]			+10% -10%
✖Subtended Angle in Radians is the angle made by something from a given viewpoint.ⓘ Subtended Angle in Radians [θ_Angle]			+10% -10%

✖Section Factor of Circular Channel is ratio of normal to critical channel depth.ⓘ Section Factor for Circle [Z_cir]

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Formula

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Section Factor for Circle

Formula

`"Z"_{"cir"} = (((sqrt(2))/32)*("d"_{"section"}^2.5)*(((180/pi)*"θ"_{"Angle"}-sin("θ"_{"Angle"}))^1.5)/((sin("θ"_{"Angle"}/2))^0.5))`

Example

`"80.88328m^2.5"=(((sqrt(2))/32)*(("5m")^2.5)*(((180/pi)*"3.14°"-sin("3.14°"))^1.5)/((sin("3.14°"/2))^0.5))`

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Download Geometrical Properties of Circular Channel Section Formulas PDF PDF Image

Section Factor for Circle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Z_cir = (((sqrt(2))/32)*(d_section^2.5)*(((180/pi)*θ_Angle-sin(θ_Angle))^1.5)/((sin(θ_Angle/2))^0.5))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., 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., sqrt(Number)

Variables Used

Section Factor of Circular Channel - (Measured in Meter^2.5) - Section Factor of Circular Channel is ratio of normal to critical channel depth.
Diameter of Section - (Measured in Meter) - Diameter of Section is the diameter of the circular cross-section of the beam.
Subtended Angle in Radians - (Measured in Radian) - Subtended Angle in Radians is the angle made by something from a given viewpoint.

STEP 1: Convert Input(s) to Base Unit

Diameter of Section: 5 Meter --> 5 Meter No Conversion Required
Subtended Angle in Radians: 3.14 Degree --> 0.0548033385126116 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_cir = (((sqrt(2))/32)*(d_section^2.5)*(((180/pi)*θ_Angle-sin(θ_Angle))^1.5)/((sin(θ_Angle/2))^0.5)) --> (((sqrt(2))/32)*(5^2.5)*(((180/pi)*0.0548033385126116-sin(0.0548033385126116))^1.5)/((sin(0.0548033385126116/2))^0.5))

Evaluating ... ...

Z_cir = 80.883282114459

STEP 3: Convert Result to Output's Unit

80.883282114459 Meter^2.5 --> No Conversion Required

FINAL ANSWER

80.883282114459 ≈ 80.88328 Meter^2.5 <-- Section Factor of Circular Channel

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Flow in Open Channels » Geometrical Properties of Channel Section » Geometrical Properties of Circular Channel Section » Section Factor for Circle

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< 14 Geometrical Properties of Circular Channel Section Calculators

Diameter of Section given Section Factor

Go 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)

Section Factor for Circle

Go 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))

Diameter of Section given Hydraulic Depth

Go Diameter of Section = Hydraulic Depth of Circular Channel/(0.125*((Subtended Angle in Radians*(180/pi))-sin(Subtended Angle in Radians)/sin(Subtended Angle in Radians/2)))

Hydraulic Depth of Circle

Go Hydraulic Depth of Circular Channel = (Diameter of Section*0.125)*((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians)/sin(Subtended Angle in Radians/2))

Diameter of Section given Wetted Area

Go 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 given Hydraulic Radius for Channel

Go Diameter of Section = Hydraulic Radius of Circular Channel/(0.25*(1-(sin(Subtended Angle in Radians)/((180/pi)*Subtended Angle in Radians))))

Wetted Area for Circle

Go Wetted Surface Area of Circular Channel = (1/8)*((180/pi)*Subtended Angle in Radians-sin(Subtended Angle in Radians)*(Diameter of Section^2))

Hydraulic Radius given Angle

Go Hydraulic Radius of Circular Channel = 0.25*Diameter of Section*(1-sin(Subtended Angle in Radians)/(180/pi)*Subtended Angle in Radians)

Diameter of Section given Wetted Perimeter

Go Diameter of Section = Wetted Perimeter of Channel/(0.5*Subtended Angle in Radians*(180/pi))

Angle of Sector given Wetted Perimeter

Go Subtended Angle in Radians = Wetted Perimeter of Channel/(0.5*Diameter of Section)*(pi/180)

Wetted Perimeter for circle

Go Wetted Perimeter of Channel = 0.5*Subtended Angle in Radians*Diameter of Section*180/pi

Angle of Sector given Top Width

Go Subtended Angle in Radians = 2*asin((Top Width of Circular Channel/Diameter of Section))

Diameter of Section given Top Width

Go Diameter of Section = Top Width of Circular Channel/sin(Subtended Angle in Radians/2)

Top Width for Circle

Go Top Width of Circular Channel = Diameter of Section*sin(Subtended Angle in Radians/2)

Section Factor for Circle Formula

What is Section Factor?

The section Factor for critical flow The section factor for critical flow computation (Z) is the product of the water area and the square root of the hydraulic depth.

How to Calculate Section Factor for Circle?

Section Factor for Circle calculator 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 calculate 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 calculate Section Factor for Circle using this online calculator? To use this online calculator for Section Factor for Circle, enter Diameter of Section (d_section) & Subtended Angle in Radians (θ_Angle) and hit the calculate button. Here is how the Section Factor for Circle calculation can be explained with given input values -> 80.88328 = (((sqrt(2))/32)*(5^2.5)*(((180/pi)*0.0548033385126116-sin(0.0548033385126116))^1.5)/((sin(0.0548033385126116/2))^0.5)).

FAQ

What is Section Factor for Circle?

The Section Factor for Circle is defined as the ratio depending on the angle and geometrical property of section and is represented as Z_cir = (((sqrt(2))/32)*(d_section^2.5)*(((180/pi)*θ_Angle-sin(θ_Angle))^1.5)/((sin(θ_Angle/2))^0.5)) or 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)). Diameter of Section is the diameter of the circular cross-section of the beam & Subtended Angle in Radians is the angle made by something from a given viewpoint.

How to calculate Section Factor for Circle?

The Section Factor for Circle is defined as the ratio depending on the angle and geometrical property of section is calculated using 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 calculate Section Factor for Circle, you need Diameter of Section (d_section) & Subtended Angle in Radians (θ_Angle). With our tool, you need to enter the respective value for Diameter of Section & Subtended Angle in Radians and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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