Hydraulic Depth of 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%

✖Hydraulic Depth of Circular Channel is defined as depth which in contact with water.ⓘ Hydraulic Depth of Circle [D_cir]

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Formula

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Hydraulic Depth of Circle

Formula

`"D"_{"cir"} = ("d"_{"section"}*0.125)*((180/pi)*"θ"_{"Angle"}-sin("θ"_{"Angle"})/sin("θ"_{"Angle"}/2))`

Example

`"0.712969m"=("5m"*0.125)*((180/pi)*"3.14°"-sin("3.14°")/sin("3.14°"/2))`

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Hydraulic Depth of Circle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
D_cir = (d_section*0.125)*((180/pi)*θ_Angle-sin(θ_Angle)/sin(θ_Angle/2))
This formula uses 1 Constants, 1 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)

Variables Used

Hydraulic Depth of Circular Channel - (Measured in Meter) - Hydraulic Depth of Circular Channel is defined as depth which in contact with water.
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

D_cir = (d_section*0.125)*((180/pi)*θ_Angle-sin(θ_Angle)/sin(θ_Angle/2)) --> (5*0.125)*((180/pi)*0.0548033385126116-sin(0.0548033385126116)/sin(0.0548033385126116/2))

Evaluating ... ...

D_cir = 0.7129692528107

STEP 3: Convert Result to Output's Unit

0.7129692528107 Meter --> No Conversion Required

FINAL ANSWER

0.7129692528107 ≈ 0.712969 Meter <-- Hydraulic Depth of Circular Channel

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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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)

Hydraulic Depth of Circle Formula

What is Hydraulic Depth?

The cross section of water flowing through a channel or pipe divided by the wetted perimeter of the conduit.

How to Calculate Hydraulic Depth of Circle?

Hydraulic Depth of Circle calculator uses 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)) to calculate the Hydraulic Depth of Circular Channel, The Hydraulic Depth of Circle formula is defined as ratio of wetted area to that of top width of section at any point in channel. Hydraulic Depth of Circular Channel is denoted by D_cir symbol.

How to calculate Hydraulic Depth of Circle using this online calculator? To use this online calculator for Hydraulic Depth of Circle, enter Diameter of Section (d_section) & Subtended Angle in Radians (θ_Angle) and hit the calculate button. Here is how the Hydraulic Depth of Circle calculation can be explained with given input values -> 0.712969 = (5*0.125)*((180/pi)*0.0548033385126116-sin(0.0548033385126116)/sin(0.0548033385126116/2)).

FAQ

What is Hydraulic Depth of Circle?

The Hydraulic Depth of Circle formula is defined as ratio of wetted area to that of top width of section at any point in channel and is represented as D_cir = (d_section*0.125)*((180/pi)*θ_Angle-sin(θ_Angle)/sin(θ_Angle/2)) or 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 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 Hydraulic Depth of Circle?

The Hydraulic Depth of Circle formula is defined as ratio of wetted area to that of top width of section at any point in channel is calculated using 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)). To calculate Hydraulic Depth of 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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