Width of Sections given Hydraulic Radius Calculator

✖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 Trapezoidal Channel [R_H(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%
✖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%

✖Width of Trap Channel is the width of the trapezoidal cross-section of the beam parallel to the axis in consideration.ⓘ Width of Sections given Hydraulic Radius [B_trap]

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Formula

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Width of Sections given Hydraulic Radius

Formula

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

Example

`"3.765902m"=(2*"1.65m"*"3.32m"*sqrt(("0.577")^2+1)-"0.577"*("3.32m")^2)/("3.32m"-"1.65m")`

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Download Geometrical Properties of Trapezoidal Channel Section Formulas PDF

Width of Sections given Hydraulic Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

STEP 1: Convert Input(s) to Base Unit

Hydraulic Radius of Trapezoidal Channel: 1.65 Meter --> 1.65 Meter No Conversion Required
Depth of Flow of Trapezoidal Channel: 3.32 Meter --> 3.32 Meter No Conversion Required
Side slope of Trapezoidal Channel: 0.577 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_trap = (2*R_H(Trap)*d_f(trap)*sqrt(z_trap^2+1)-z_trap*d_f(trap)^2)/(d_f(trap)-R_H(Trap)) --> (2*1.65*3.32*sqrt(0.577^2+1)-0.577*3.32^2)/(3.32-1.65)

Evaluating ... ...

B_trap = 3.76590177273188

STEP 3: Convert Result to Output's Unit

3.76590177273188 Meter --> No Conversion Required

FINAL ANSWER

3.76590177273188 ≈ 3.765902 Meter <-- Width of Trap Channel

(Calculation completed in 00.006 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Coorg Institute of Technology (CIT), Coorg

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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

Width of Sections given Hydraulic Radius 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 Width of Sections given Hydraulic Radius?

Width of Sections given Hydraulic Radius calculator uses 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) to calculate the Width of Trap Channel, The Width of Sections given Hydraulic Radius is defined as the width of channel measured perpendicular to the flow. Width of Trap Channel is denoted by B_trap symbol.

How to calculate Width of Sections given Hydraulic Radius using this online calculator? To use this online calculator for Width of Sections given Hydraulic Radius, enter Hydraulic Radius of Trapezoidal Channel (R_H(Trap)), Depth of Flow of Trapezoidal Channel (d_f(trap)) & Side slope of Trapezoidal Channel (z_trap) and hit the calculate button. Here is how the Width of Sections given Hydraulic Radius calculation can be explained with given input values -> 3.811668 = (2*1.65*3.32*sqrt(0.577^2+1)-0.577*3.32^2)/(3.32-1.65).

FAQ

What is Width of Sections given Hydraulic Radius?

The Width of Sections given Hydraulic Radius is defined as the width of channel measured perpendicular to the flow and is represented as B_trap = (2*R_H(Trap)*d_f(trap)*sqrt(z_trap^2+1)-z_trap*d_f(trap)^2)/(d_f(trap)-R_H(Trap)) or 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 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, 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 & Side slope of Trapezoidal Channel is side slope of trapezoidal channel, defined as horizontal to vertical ratio.

How to calculate Width of Sections given Hydraulic Radius?

The Width of Sections given Hydraulic Radius is defined as the width of channel measured perpendicular to the flow is calculated using 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). To calculate Width of Sections given Hydraulic Radius, you need Hydraulic Radius of Trapezoidal Channel (R_H(Trap)), Depth of Flow of Trapezoidal Channel (d_f(trap)) & Side slope of Trapezoidal Channel (z_trap). With our tool, you need to enter the respective value for Hydraulic Radius of Trapezoidal Channel, Depth of Flow of Trapezoidal Channel & Side slope of Trapezoidal Channel 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 Width of Trap Channel?

In this formula, Width of Trap Channel uses Hydraulic Radius of Trapezoidal Channel, Depth of Flow of Trapezoidal Channel & Side slope of Trapezoidal Channel. We can use 4 other way(s) to calculate the same, which is/are as follows -

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

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