Hydraulic Radius of Trapezoidal Channel Section Calculator

✖Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.ⓘ Depth of Flow [d_f]			+10% -10%
✖Width of Trapezoidal Channel Section is the horizontal distance between its parallel sides or banks.ⓘ Width of Trapezoidal Channel Section [B]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%

✖Hydraulic Radius of 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 of Trapezoidal Channel Section [R_H]

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Formula

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Hydraulic Radius of Trapezoidal Channel Section

Formula

`"R"_{"H"} = ("d"_{"f"}*("B"+"d"_{"f"}*("θ"+cot("θ"))))/("B"+2*"d"_{"f"}*("θ"+cot("θ")))`

Example

`"1.661009m"=("3.3m"*("100mm"+"3.3m"*("30°"+cot("30°"))))/("100mm"+2*"3.3m"*("30°"+cot("30°")))`

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Hydraulic Radius of Trapezoidal Channel Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hydraulic Radius of Channel = (Depth of Flow*(Width of Trapezoidal Channel Section+Depth of Flow*(Theta+cot(Theta))))/(Width of Trapezoidal Channel Section+2*Depth of Flow*(Theta+cot(Theta)))
R_H = (d_f*(B+d_f*(θ+cot(θ))))/(B+2*d_f*(θ+cot(θ)))
This formula uses 1 Functions, 4 Variables

Functions Used

cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)

Variables Used

Hydraulic Radius of Channel - (Measured in Meter) - Hydraulic Radius of 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.
Depth of Flow - (Measured in Meter) - Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.
Width of Trapezoidal Channel Section - (Measured in Meter) - Width of Trapezoidal Channel Section is the horizontal distance between its parallel sides or banks.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

STEP 1: Convert Input(s) to Base Unit

Depth of Flow: 3.3 Meter --> 3.3 Meter No Conversion Required
Width of Trapezoidal Channel Section: 100 Millimeter --> 0.1 Meter (Check conversion here)
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_H = (d_f*(B+d_f*(θ+cot(θ))))/(B+2*d_f*(θ+cot(θ))) --> (3.3*(0.1+3.3*(0.5235987755982+cot(0.5235987755982))))/(0.1+2*3.3*(0.5235987755982+cot(0.5235987755982)))

Evaluating ... ...

R_H = 1.66100933059197

STEP 3: Convert Result to Output's Unit

1.66100933059197 Meter --> No Conversion Required

FINAL ANSWER

1.66100933059197 ≈ 1.661009 Meter <-- Hydraulic Radius of 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 » Section modulus, Hydraulic Depth and Practical Channel Sections » Practical Channel Sections » Hydraulic Radius of Trapezoidal Channel Section

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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NSS College of Engineering (NSSCE), Palakkad

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< 8 Practical Channel Sections Calculators

Hydraulic Radius of Trapezoidal Channel Section

Go Hydraulic Radius of Channel = (Depth of Flow*(Width of Trapezoidal Channel Section+Depth of Flow*(Theta+cot(Theta))))/(Width of Trapezoidal Channel Section+2*Depth of Flow*(Theta+cot(Theta)))

Wetted Area of Trapezoidal Channel Section

Go Wetted Surface Area of Channel = Depth of Flow*(Width of Trapezoidal Channel Section+Depth of Flow*(Theta+cot(Theta)))

Wetted Perimeter of Trapezoidal Channel Section

Go Wetted Perimeter of Channel = (Width of Trapezoidal Channel Section+2*Depth of Flow*(Theta+cot(Theta)))

Depth of Flow given Wetted Area of Triangular Channel Section

Go Depth of Flow = sqrt(Wetted Surface Area of Channel/(Theta+cot(Theta)))

Wetted Area of Triangular Channel Section

Go Wetted Surface Area of Channel = (Depth of Flow^2)*(Theta+cot(Theta))

Depth of Flow given Wetted Perimeter of Triangular Channel Section

Go Depth of Flow = Wetted Perimeter of Channel/(2*(Theta+cot(Theta)))

Wetted Perimeter of Triangular Channel Section

Go Wetted Perimeter of Channel = 2*Depth of Flow*(Theta+cot(Theta))

Hydraulic Radius of Triangular Channel Section

Go Hydraulic Radius of Channel = Depth of Flow/2

Hydraulic Radius of Trapezoidal Channel Section Formula

What is Hydraulic Radius ?

hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wetted perimeter of the conduit.

How to Calculate Hydraulic Radius of Trapezoidal Channel Section?

Hydraulic Radius of Trapezoidal Channel Section calculator uses Hydraulic Radius of Channel = (Depth of Flow*(Width of Trapezoidal Channel Section+Depth of Flow*(Theta+cot(Theta))))/(Width of Trapezoidal Channel Section+2*Depth of Flow*(Theta+cot(Theta))) to calculate the Hydraulic Radius of Channel, The Hydraulic Radius of Trapezoidal Channel Section is defined as area to perimeter ratio in the channel section. Hydraulic Radius of Channel is denoted by R_H symbol.

How to calculate Hydraulic Radius of Trapezoidal Channel Section using this online calculator? To use this online calculator for Hydraulic Radius of Trapezoidal Channel Section, enter Depth of Flow (d_f), Width of Trapezoidal Channel Section (B) & Theta (θ) and hit the calculate button. Here is how the Hydraulic Radius of Trapezoidal Channel Section calculation can be explained with given input values -> 1.661009 = (3.3*(0.1+3.3*(0.5235987755982+cot(0.5235987755982))))/(0.1+2*3.3*(0.5235987755982+cot(0.5235987755982))).

FAQ

What is Hydraulic Radius of Trapezoidal Channel Section?

The Hydraulic Radius of Trapezoidal Channel Section is defined as area to perimeter ratio in the channel section and is represented as R_H = (d_f*(B+d_f*(θ+cot(θ))))/(B+2*d_f*(θ+cot(θ))) or Hydraulic Radius of Channel = (Depth of Flow*(Width of Trapezoidal Channel Section+Depth of Flow*(Theta+cot(Theta))))/(Width of Trapezoidal Channel Section+2*Depth of Flow*(Theta+cot(Theta))). Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights, Width of Trapezoidal Channel Section is the horizontal distance between its parallel sides or banks & Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

How to calculate Hydraulic Radius of Trapezoidal Channel Section?

The Hydraulic Radius of Trapezoidal Channel Section is defined as area to perimeter ratio in the channel section is calculated using Hydraulic Radius of Channel = (Depth of Flow*(Width of Trapezoidal Channel Section+Depth of Flow*(Theta+cot(Theta))))/(Width of Trapezoidal Channel Section+2*Depth of Flow*(Theta+cot(Theta))). To calculate Hydraulic Radius of Trapezoidal Channel Section, you need Depth of Flow (d_f), Width of Trapezoidal Channel Section (B) & Theta (θ). With our tool, you need to enter the respective value for Depth of Flow, Width of Trapezoidal Channel Section & Theta and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Hydraulic Radius of Channel?

In this formula, Hydraulic Radius of Channel uses Depth of Flow, Width of Trapezoidal Channel Section & Theta. We can use 1 other way(s) to calculate the same, which is/are as follows -

Hydraulic Radius of Channel = Depth of Flow/2

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