Hydraulic Radius of Section Calculator

✖Width of Trap Channel is the width of the trapezoidal cross-section of the beam parallel to the axis in consideration.ⓘ Width of Trap Channel [B_trap]			+10% -10%
✖Side slope of Trapezoidal Channel is side slope of trapezoidal channel, defined as horizontal to vertical ratio.ⓘ Side slope of Trapezoidal Channel [z_trap]			+10% -10%
✖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.ⓘ Depth of Flow of Trapezoidal Channel [d_f(trap)]			+10% -10%

✖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.ⓘ Hydraulic Radius of Section [R_H(Trap)]

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Formula

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Hydraulic Radius of Section

Formula

`"R"_{"H(Trap)"} = (("B"_{"trap"}+"z"_{"trap"}*"d"_{"f(trap)"})*"d"_{"f(trap)"})/("B"_{"trap"}+2*"d"_{"f(trap)"}*sqrt("z"_{"trap"}^2+1))`

Example

`"1.65649m"=(("3.8105m"+"0.577"*"3.32m")*"3.32m")/("3.8105m"+2*"3.32m"*sqrt(("0.577")^2+1))`

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Download Geometrical Properties of Trapezoidal Channel Section Formulas PDF

Hydraulic Radius of Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
R_H(Trap) = ((B_trap+z_trap*d_f(trap))*d_f(trap))/(B_trap+2*d_f(trap)*sqrt(z_trap^2+1))
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Hydraulic Radius of Trapezoidal Channel - (Measured in Meter) - 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.
Width of Trap Channel - (Measured in Meter) - Width of Trap Channel is the width of the trapezoidal cross-section of the beam parallel to the axis in consideration.
Side slope of Trapezoidal Channel - Side slope of Trapezoidal Channel is side slope of trapezoidal channel, defined as horizontal to vertical ratio.
Depth of Flow of Trapezoidal Channel - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Width of Trap Channel: 3.8105 Meter --> 3.8105 Meter No Conversion Required
Side slope of Trapezoidal Channel: 0.577 --> No Conversion Required
Depth of Flow of Trapezoidal Channel: 3.32 Meter --> 3.32 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_H(Trap) = ((B_trap+z_trap*d_f(trap))*d_f(trap))/(B_trap+2*d_f(trap)*sqrt(z_trap^2+1)) --> ((3.8105+0.577*3.32)*3.32)/(3.8105+2*3.32*sqrt(0.577^2+1))

Evaluating ... ...

R_H(Trap) = 1.65648967210351

STEP 3: Convert Result to Output's Unit

1.65648967210351 Meter --> No Conversion Required

FINAL ANSWER

1.65648967210351 ≈ 1.65649 Meter <-- Hydraulic Radius of Trapezoidal 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 » Geometrical Properties of Trapezoidal Channel Section » Hydraulic Radius of Section

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< 17 Geometrical Properties of Trapezoidal Channel Section Calculators

Width of Section given Hydraulic Depth

Go Width of Trap Channel = ((Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel)-Hydraulic Depth of Trapezoidal Channel*2*Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel)/(Hydraulic Depth of Trapezoidal Channel-Depth of Flow of Trapezoidal Channel)

Width of Sections given Hydraulic Radius

Go Width of Trap Channel = (2*Hydraulic Radius of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel*sqrt(Side slope of Trapezoidal Channel^2+1)-Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel^2)/(Depth of Flow of Trapezoidal Channel-Hydraulic Radius of Trapezoidal Channel)

Hydraulic Radius of Section

Go 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))

Section Factor for Trapezoidal

Go Section Factor of Trapezoidal = ((((Width of Trap Channel+Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel)*Depth of Flow of Trapezoidal Channel))^1.5)/(sqrt(Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel))

Side Slope of Section given Hydraulic Depth

Go Side slope of Trapezoidal Channel = (Width of Trap Channel*Depth of Flow of Trapezoidal Channel-Width of Trap Channel*Hydraulic Depth of Trapezoidal Channel)/(2*Hydraulic Depth of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel-(Depth of Flow of Trapezoidal Channel)^2)

Hydraulic Depth for Trapezoidal

Go Hydraulic Depth of Trapezoidal Channel = ((Width of Trap Channel+Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel)*Depth of Flow of Trapezoidal Channel)/(Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel)

Depth of Flow given Wetted Perimeter for Trapezoidal

Go Depth of Flow of Trapezoidal Channel = (Wetted Perimeter of Trapezoidal Channel-Width of Trap Channel)/(2*(sqrt(Side slope of Trapezoidal Channel*Side slope of Trapezoidal Channel+1)))

Width of Section given Wetted Perimeters in Section

Go Width of Trap Channel = Wetted Perimeter of Trapezoidal Channel-2*Depth of Flow of Trapezoidal Channel*(sqrt(Side slope of Trapezoidal Channel*Side slope of Trapezoidal Channel+1))

Wetted Perimeter for Trapezoidal

Go Wetted Perimeter of Trapezoidal Channel = Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*(sqrt(Side slope of Trapezoidal Channel*Side slope of Trapezoidal Channel+1))

Side Slope of Section given Wetted Area of Trapezoidal

Go Side slope of Trapezoidal Channel = ((Wetted Surface Area of Trapezoidal Channel/Depth of Flow of Trapezoidal Channel)-Width of Trap Channel)/Depth of Flow of Trapezoidal Channel

Width of Section given Wetted Area for Trapezoidal

Go Width of Trap Channel = (Wetted Surface Area of Trapezoidal Channel/Depth of Flow of Trapezoidal Channel)-(Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel)

Wetted Area for Trapezoidal

Go Wetted Surface Area of Trapezoidal Channel = (Width of Trap Channel+Side slope of Trapezoidal Channel*Depth of Flow of Trapezoidal Channel)*Depth of Flow of Trapezoidal Channel

Side Slope of Section given Perimeter

Go Side slope of Trapezoidal Channel = sqrt((((Wetted Perimeter of Trapezoidal Channel-Width of Trap Channel)/(2*Depth of Flow of Trapezoidal Channel))^2)-1)

Side Slope of Section given Top Width for Trapezoidal

Go Side slope of Trapezoidal Channel = (Top Width of Trapezoidal Channel-Width of Trap Channel)/(2*Depth of Flow of Trapezoidal Channel)

Depth of Flow given Top Width for Trapezoidal

Go Depth of Flow of Trapezoidal Channel = (Top Width of Trapezoidal Channel-Width of Trap Channel)/(2*Side slope of Trapezoidal Channel)

Width of Section given Top Width

Go Width of Trap Channel = Top Width of Trapezoidal Channel-2*Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel

Top Width for Trapezoidal

Go Top Width of Trapezoidal Channel = Width of Trap Channel+2*Depth of Flow of Trapezoidal Channel*Side slope of Trapezoidal Channel

Hydraulic Radius of 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 Section?

Hydraulic Radius of Section calculator 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 calculate 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 calculate Hydraulic Radius of Section using this online calculator? To use this online calculator 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. Here is how the Hydraulic Radius of Section calculation can be explained with given input values -> 1.649831 = ((3.8105+0.577*3.32)*3.32)/(3.8105+2*3.32*sqrt(0.577^2+1)).

FAQ

What is Hydraulic Radius of Section?

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 and is represented as R_H(Trap) = ((B_trap+z_trap*d_f(trap))*d_f(trap))/(B_trap+2*d_f(trap)*sqrt(z_trap^2+1)) or 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)). Width of Trap Channel is the width of the trapezoidal cross-section of the beam parallel to the axis in consideration, Side slope of Trapezoidal Channel is side slope of trapezoidal channel, defined as horizontal to vertical ratio & 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.

How to calculate Hydraulic Radius of Section?

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 is calculated using 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 calculate Hydraulic Radius of Section, you need Width of Trap Channel (B_trap), Side slope of Trapezoidal Channel (z_trap) & Depth of Flow of Trapezoidal Channel (d_f(trap)). With our tool, you need to enter the respective value for Width of Trap Channel, Side slope of Trapezoidal Channel & Depth of Flow of Trapezoidal Channel 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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