Hydraulic Radius given Angle 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 Radius of Circular Channel is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.ⓘ Hydraulic Radius given Angle [R_h(cir)]

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Formula

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Hydraulic Radius given Angle

Formula

`"R"_{"h(cir)"} = 0.25*"d"_{"section"}*(1-sin("θ"_{"Angle"})/(180/pi)*"θ"_{"Angle"})`

Example

`"1.249935m"=0.25*"5m"*(1-sin("3.14°")/(180/pi)*"3.14°")`

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Hydraulic Radius given Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hydraulic Radius of Circular Channel = 0.25*Diameter of Section*(1-sin(Subtended Angle in Radians)/(180/pi)*Subtended Angle in Radians)
R_h(cir) = 0.25*d_section*(1-sin(θ_Angle)/(180/pi)*θ_Angle)
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 Radius of Circular Channel - (Measured in Meter) - Hydraulic Radius of Circular Channel is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.
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

R_h(cir) = 0.25*d_section*(1-sin(θ_Angle)/(180/pi)*θ_Angle) --> 0.25*5*(1-sin(0.0548033385126116)/(180/pi)*0.0548033385126116)

Evaluating ... ...

R_h(cir) = 1.24993450864192

STEP 3: Convert Result to Output's Unit

1.24993450864192 Meter --> No Conversion Required

FINAL ANSWER

1.24993450864192 ≈ 1.249935 Meter <-- Hydraulic Radius of Circular Channel

(Calculation completed in 00.005 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 » Hydraulic Radius given Angle

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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)

Hydraulic Radius given Angle Formula

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

What is Hydraulic Radius?

Hydraulic radius, R, a measure of channel flow efficiency, is defined as the ratio of the cross-sectional area of fluid flow, A, to the length of the wetted perimeter, P. The hydraulic radius is one of the main properties that control the amount of fluid discharge of a channel and its ability to move sediments.

How to Calculate Hydraulic Radius given Angle?

Hydraulic Radius given Angle calculator uses Hydraulic Radius of Circular Channel = 0.25*Diameter of Section*(1-sin(Subtended Angle in Radians)/(180/pi)*Subtended Angle in Radians) to calculate the Hydraulic Radius of Circular Channel, Hydraulic Radius given Angle formula is defined as ratio of wetted area to that of wetted perimeter of channel section. Hydraulic Radius of Circular Channel is denoted by R_h(cir) symbol.

How to calculate Hydraulic Radius given Angle using this online calculator? To use this online calculator for Hydraulic Radius given Angle, enter Diameter of Section (d_section) & Subtended Angle in Radians (θ_Angle) and hit the calculate button. Here is how the Hydraulic Radius given Angle calculation can be explained with given input values -> 1.249935 = 0.25*5*(1-sin(0.0548033385126116)/(180/pi)*0.0548033385126116).

FAQ

What is Hydraulic Radius given Angle?

Hydraulic Radius given Angle formula is defined as ratio of wetted area to that of wetted perimeter of channel section and is represented as R_h(cir) = 0.25*d_section*(1-sin(θ_Angle)/(180/pi)*θ_Angle) or 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 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 Radius given Angle?

Hydraulic Radius given Angle formula is defined as ratio of wetted area to that of wetted perimeter of channel section is calculated using Hydraulic Radius of Circular Channel = 0.25*Diameter of Section*(1-sin(Subtended Angle in Radians)/(180/pi)*Subtended Angle in Radians). To calculate Hydraulic Radius given Angle, 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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