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Hydraulic Radius of Section Formula

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Hydraulic Radius of Trapezoidal 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(Trap) = \frac{(B trap + z trap \cdot d f(trap)) \cdot d f(trap)}{B trap + 2 \cdot d f(trap) \cdot \sqrt{{z trap}^{2} + 1}}

R_H(Trap) - Hydraulic Radius of Trapezoidal Channel?B_trap - Width of Trap Channel?z_trap - Side slope of Trapezoidal Channel?d_f(trap) - Depth of Flow of Trapezoidal Channel?

Hydraulic Radius of Section Example

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

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

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

1.6565 = \frac{(3.8105 + 0.577 \cdot 3.32) \cdot 3.32}{3.8105 + 2 \cdot 3.32 \cdot \sqrt{{0.577}^{2} + 1}}

1.6565m = \frac{(3.8105m + 0.577 \cdot 3.32m) \cdot 3.32m}{3.8105m + 2 \cdot 3.32m \cdot \sqrt{{0.577}^{2} + 1}}

1.6565 = \frac{(3.8105 + 0.577 \cdot 3.32) \cdot 3.32}{3.8105 + 2 \cdot 3.32 \cdot \sqrt{{0.577}^{2} + 1}}

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Hydraulic Radius of Section Solution

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

FIRST Step Consider the formula

R H(Trap) = \frac{(B trap + z trap \cdot d f(trap)) \cdot d f(trap)}{B trap + 2 \cdot d f(trap) \cdot \sqrt{{z trap}^{2} + 1}}

Next Step Substitute values of Variables

∴

R H(Trap) = \frac{(3.8105m + 0.577 \cdot 3.32m) \cdot 3.32m}{3.8105m + 2 \cdot 3.32m \cdot \sqrt{{0.577}^{2} + 1}}

Next Step Prepare to Evaluate

∴

R H(Trap) = \frac{(3.8105 + 0.577 \cdot 3.32) \cdot 3.32}{3.8105 + 2 \cdot 3.32 \cdot \sqrt{{0.577}^{2} + 1}}

Next Step Evaluate

∴

R H(Trap) = 1.65648967210351m

LAST Step Rounding Answer

∴

R H(Trap) = 1.6565m

Hydraulic Radius of Section Formula Elements

Variables

Functions

Hydraulic Radius of Trapezoidal Channel

Hydraulic Radius of Trapezoidal 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(Trap)

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Hydraulic Radius of Trapezoidal Channel

Width of Trap Channel

Width of Trap Channel is the width of the trapezoidal cross-section of the beam parallel to the axis in consideration.

Symbol: B_trap

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of Trap Channel

Side slope of Trapezoidal Channel

Side slope of Trapezoidal Channel is side slope of trapezoidal channel, defined as horizontal to vertical ratio.

Symbol: z_trap

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Side slope of Trapezoidal Channel

Depth of Flow of Trapezoidal Channel

Depth of Flow of Trapezoidal Channel 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(trap)

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Flow of Trapezoidal Channel

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.

Syntax: sqrt(Number)

Other formulas in Geometrical Properties of Trapezoidal Channel Section category

Go Wetted Area for Trapezoidal

S Trap = (B trap + z trap \cdot d f(trap)) \cdot d f(trap)

Go Width of Section given Wetted Area for Trapezoidal

B trap = (\frac{S Trap}{d f(trap)}) - (z trap \cdot d f(trap))

Go Side Slope of Section given Wetted Area of Trapezoidal

z trap = \frac{(\frac{S Trap}{d f(trap)}) - B trap}{d f(trap)}

Go Wetted Perimeter for Trapezoidal

P Trap = B trap + 2 \cdot d f(trap) \cdot (\sqrt{z trap \cdot z trap + 1})

How to Evaluate Hydraulic Radius of Section?

Hydraulic Radius of Section evaluator uses Hydraulic Radius of Trapezoidal Channel = ((Width of Trap Channel+Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel)*Depth of Flow of Trapezoidal Channel)/(Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*sqrt(Side slope of Trapezoidal Channel^2+1)) to evaluate the Hydraulic Radius of Trapezoidal Channel, The Hydraulic Radius of Section is defined as the ratio of area to perimeter of section which is in contact with water called as wetted. Hydraulic Radius of Trapezoidal Channel is denoted by R_H(Trap) symbol.

How to evaluate Hydraulic Radius of Section using this online evaluator? To use this online evaluator for Hydraulic Radius of Section, enter Width of Trap Channel (B_trap), Side slope of Trapezoidal Channel (z_trap) & Depth of Flow of Trapezoidal Channel (d_f(trap)) and hit the calculate button.

FAQs on Hydraulic Radius of Section

What is the formula to find Hydraulic Radius of Section?

The formula of Hydraulic Radius of Section is expressed as Hydraulic Radius of Trapezoidal Channel = ((Width of Trap Channel+Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel)*Depth of Flow of Trapezoidal Channel)/(Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*sqrt(Side slope of Trapezoidal Channel^2+1)). Here is an example- 1.649831 = ((3.8105+0.577*3.32)*3.32)/(3.8105+2*3.32*sqrt(0.577^2+1)).

How to calculate Hydraulic Radius of Section?

With Width of Trap Channel (B_trap), Side slope of Trapezoidal Channel (z_trap) & Depth of Flow of Trapezoidal Channel (d_f(trap)) we can find Hydraulic Radius of Section using the formula - Hydraulic Radius of Trapezoidal Channel = ((Width of Trap Channel+Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel)*Depth of Flow of Trapezoidal Channel)/(Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*sqrt(Side slope of Trapezoidal Channel^2+1)). This formula also uses Square Root (sqrt) function(s).

Can the Hydraulic Radius of Section be negative?

Yes, the Hydraulic Radius of Section, measured in Length can be negative.

Which unit is used to measure Hydraulic Radius of Section?

Hydraulic Radius of 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 Section can be measured.

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Hydraulic Radius of Section Formula

Hydraulic Radius of Section Example

Hydraulic Radius of Section Solution

Hydraulic Radius of Section Formula Elements

Other formulas in Geometrical Properties of Trapezoidal Channel Section category

How to Evaluate Hydraulic Radius of Section?

FAQs on Hydraulic Radius of Section

Variable Name