Slope of Channel Bottom given Boundary Shear Stress Calculator

✖Shear Stress of Wall is defined as the shear stress in the layer of fluid next to the wall of a pipe.ⓘ Shear Stress of Wall [ζ₀]			+10% -10%
✖Liquid Specific Weight is also known as the unit weight, is the weight per unit volume of the liquid. For Example - Specific weight of water on Earth at 4°C is 9.807 kN/m3 or 62.43 lbf/ft3.ⓘ Liquid Specific Weight [γ_l]			+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 Channel [R_H]			+10% -10%

✖Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.ⓘ Slope of Channel Bottom given Boundary Shear Stress [S]

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Slope of Channel Bottom given Boundary Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel)
S = ζ₀/(γ_l*R_H)
This formula uses 4 Variables

Variables Used

Bed Slope - Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.
Shear Stress of Wall - (Measured in Pascal) - Shear Stress of Wall is defined as the shear stress in the layer of fluid next to the wall of a pipe.
Liquid Specific Weight - (Measured in Newton per Cubic Meter) - Liquid Specific Weight is also known as the unit weight, is the weight per unit volume of the liquid. For Example - Specific weight of water on Earth at 4°C is 9.807 kN/m3 or 62.43 lbf/ft3.
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.

STEP 1: Convert Input(s) to Base Unit

Shear Stress of Wall: 6.3 Pascal --> 6.3 Pascal No Conversion Required
Liquid Specific Weight: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Hydraulic Radius of Channel: 1.6 Meter --> 1.6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = ζ₀/(γ_l*R_H) --> 6.3/(9810*1.6)

Evaluating ... ...

S = 0.000401376146788991

STEP 3: Convert Result to Output's Unit

0.000401376146788991 --> No Conversion Required

FINAL ANSWER

0.000401376146788991 ≈ 0.000401 <-- Bed Slope

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< Average Velocity in Uniform Flow in Channels Calculators

Specific Weight of Liquid given Boundary Shear Stress

LaTeX Go Liquid Specific Weight = Shear Stress of Wall/(Hydraulic Radius of Channel*Bed Slope)

Slope of Channel Bottom given Boundary Shear Stress

LaTeX Go Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel)

Hydraulic Radius given Boundary Shear Stress

LaTeX Go Hydraulic Radius of Channel = Shear Stress of Wall/(Liquid Specific Weight*Bed Slope)

Boundary Shear Stress

LaTeX Go Shear Stress of Wall = Liquid Specific Weight*Hydraulic Radius of Channel*Bed Slope

Slope of Channel Bottom given Boundary Shear Stress Formula

LaTeX Go

Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel)
S = ζ₀/(γ_l*R_H)

What is Slope of Bed?

The Slope of bed is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow. It is widely used in river engineering.

How to Calculate Slope of Channel Bottom given Boundary Shear Stress?

Slope of Channel Bottom given Boundary Shear Stress calculator uses Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel) to calculate the Bed Slope, The Slope of Channel Bottom given Boundary Shear Stress is defined as the elevation of the channel from the bottom. Bed Slope is denoted by S symbol.

How to calculate Slope of Channel Bottom given Boundary Shear Stress using this online calculator? To use this online calculator for Slope of Channel Bottom given Boundary Shear Stress, enter Shear Stress of Wall (ζ₀), Liquid Specific Weight (γ_l) & Hydraulic Radius of Channel (R_H) and hit the calculate button. Here is how the Slope of Channel Bottom given Boundary Shear Stress calculation can be explained with given input values -> 0.000401 = 6.3/(9810*1.6).

FAQ

What is Slope of Channel Bottom given Boundary Shear Stress?

The Slope of Channel Bottom given Boundary Shear Stress is defined as the elevation of the channel from the bottom and is represented as S = ζ₀/(γ_l*R_H) or Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel). Shear Stress of Wall is defined as the shear stress in the layer of fluid next to the wall of a pipe, Liquid Specific Weight is also known as the unit weight, is the weight per unit volume of the liquid. For Example - Specific weight of water on Earth at 4°C is 9.807 kN/m3 or 62.43 lbf/ft3 & 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.

How to calculate Slope of Channel Bottom given Boundary Shear Stress?

The Slope of Channel Bottom given Boundary Shear Stress is defined as the elevation of the channel from the bottom is calculated using Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel). To calculate Slope of Channel Bottom given Boundary Shear Stress, you need Shear Stress of Wall (ζ₀), Liquid Specific Weight (γ_l) & Hydraulic Radius of Channel (R_H). With our tool, you need to enter the respective value for Shear Stress of Wall, Liquid Specific Weight & Hydraulic Radius of 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 Bed Slope?

In this formula, Bed Slope uses Shear Stress of Wall, Liquid Specific Weight & Hydraulic Radius of Channel. We can use 1 other way(s) to calculate the same, which is/are as follows -

Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2

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