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Hydraulic Radius of Trapezoidal Channel Section Formula

GoHydraulic Radius of Triangular Channel Section Formula

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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. Check FAQs

R H = \frac{d f \cdot (B + d f \cdot (θ + \cot (θ)))}{B + 2 \cdot d f \cdot (θ + \cot (θ))}

R_H - Hydraulic Radius of Channel?d_f - Depth of Flow?B - Width of Trapezoidal Channel Section?θ - Theta?

Hydraulic Radius of Trapezoidal Channel Section Example

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Here is how the Hydraulic Radius of Trapezoidal Channel Section equation looks like with Values.

Here is how the Hydraulic Radius of Trapezoidal Channel Section equation looks like with Units.

Here is how the Hydraulic Radius of Trapezoidal Channel Section equation looks like.

1.661 = \frac{3.3 \cdot (100 + 3.3 \cdot (30 + \cot (30)))}{100 + 2 \cdot 3.3 \cdot (30 + \cot (30))}

1.661m = \frac{3.3m \cdot (100mm + 3.3m \cdot (30° + \cot (30°)))}{100mm + 2 \cdot 3.3m \cdot (30° + \cot (30°))}

1.661 = \frac{3.3 \cdot (100 + 3.3 \cdot (30 + \cot (30)))}{100 + 2 \cdot 3.3 \cdot (30 + \cot (30))}

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Hydraulic Radius of Trapezoidal Channel Section Solution

Follow our step by step solution on how to calculate Hydraulic Radius of Trapezoidal Channel Section?

FIRST Step Consider the formula

R H = \frac{d f \cdot (B + d f \cdot (θ + \cot (θ)))}{B + 2 \cdot d f \cdot (θ + \cot (θ))}

Next Step Substitute values of Variables

∴

R H = \frac{3.3m \cdot (100mm + 3.3m \cdot (30° + \cot (30°)))}{100mm + 2 \cdot 3.3m \cdot (30° + \cot (30°))}

Next Step Convert Units

∴

R H = \frac{3.3m \cdot (0.1m + 3.3m \cdot (0.5236rad + \cot (0.5236rad)))}{0.1m + 2 \cdot 3.3m \cdot (0.5236rad + \cot (0.5236rad))}

Next Step Prepare to Evaluate

∴

R H = \frac{3.3 \cdot (0.1 + 3.3 \cdot (0.5236 + \cot (0.5236)))}{0.1 + 2 \cdot 3.3 \cdot (0.5236 + \cot (0.5236))}

Next Step Evaluate

∴

R H = 1.66100933059197m

LAST Step Rounding Answer

∴

R H = 1.661m

Hydraulic Radius of Trapezoidal Channel Section Formula Elements

Variables

Functions

Hydraulic Radius of Channel

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.

Symbol: R_H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Hydraulic Radius of Channel

Depth of Flow

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.

Symbol: d_f

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Flow

Width of Trapezoidal Channel Section

Width of Trapezoidal Channel Section is the horizontal distance between its parallel sides or banks.

Symbol: B

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Trapezoidal Channel Section

Theta

Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Theta

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

Other Formulas to find Hydraulic Radius of Channel

Go Hydraulic Radius of Triangular Channel Section

R H = \frac{d f}{2}

Other formulas in Practical Channel Sections category

Go Wetted Area of Triangular Channel Section

A = ({d f}^{2}) \cdot (θ + \cot (θ))

Go Depth of Flow given Wetted Area of Triangular Channel Section

d f = \sqrt{\frac{A}{θ + \cot (θ)}}

Go Depth of Flow given Wetted Perimeter of Triangular Channel Section

d f = \frac{p}{2 \cdot (θ + \cot (θ))}

Go Wetted Perimeter of Triangular Channel Section

p = 2 \cdot d f \cdot (θ + \cot (θ))

How to Evaluate Hydraulic Radius of Trapezoidal Channel Section?

Hydraulic Radius of Trapezoidal Channel Section evaluator 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 evaluate 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 evaluate Hydraulic Radius of Trapezoidal Channel Section using this online evaluator? To use this online evaluator 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.

FAQs on Hydraulic Radius of Trapezoidal Channel Section

What is the formula to find Hydraulic Radius of Trapezoidal Channel Section?

The formula of Hydraulic Radius of Trapezoidal Channel Section is expressed as 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))). Here is an example- 1.661009 = (3.3*(0.1+3.3*(0.5235987755982+cot(0.5235987755982))))/(0.1+2*3.3*(0.5235987755982+cot(0.5235987755982))).

How to calculate Hydraulic Radius of Trapezoidal Channel Section?

With Depth of Flow (d_f), Width of Trapezoidal Channel Section (B) & Theta (θ) we can find Hydraulic Radius of Trapezoidal Channel Section using the formula - 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))). This formula also uses Cotangent (cot) function(s).

What are the other ways to Calculate Hydraulic Radius of Channel?

Here are the different ways to Calculate Hydraulic Radius of Channel-

Hydraulic Radius of Channel=Depth of Flow/2

Can the Hydraulic Radius of Trapezoidal Channel Section be negative?

No, the Hydraulic Radius of Trapezoidal Channel Section, measured in Length cannot be negative.

Which unit is used to measure Hydraulic Radius of Trapezoidal Channel Section?

Hydraulic Radius of Trapezoidal Channel Section is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Hydraulic Radius of Trapezoidal Channel Section can be measured.

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Hydraulic Radius of Trapezoidal Channel Section Formula

​GoHydraulic Radius of Triangular Channel Section Formula

Hydraulic Radius of Trapezoidal Channel Section Example

Hydraulic Radius of Trapezoidal Channel Section Solution

Hydraulic Radius of Trapezoidal Channel Section Formula Elements

Other Formulas to find Hydraulic Radius of Channel

Other formulas in Practical Channel Sections category

How to Evaluate Hydraulic Radius of Trapezoidal Channel Section?

FAQs on Hydraulic Radius of Trapezoidal Channel Section

Variable Name

GoHydraulic Radius of Triangular Channel Section Formula