Boundary Shear Stress Calculator

✖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.ⓘ Bed Slope [S]			+10% -10%

✖Shear Stress of Wall is defined as the shear stress in the layer of fluid next to the wall of a pipe.ⓘ Boundary Shear Stress [ζ₀]

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Boundary Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

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
Bed Slope: 0.0004 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ζ₀ = γ_l*R_H*S --> 9810*1.6*0.0004

Evaluating ... ...

ζ₀ = 6.2784

STEP 3: Convert Result to Output's Unit

6.2784 Pascal --> No Conversion Required

FINAL ANSWER

6.2784 Pascal <-- Shear Stress of Wall

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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

Verified by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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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

Boundary Shear Stress Formula

LaTeX Go

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

What is Boundary Shear Stress?

Boundary shear stress is the tangential component of the hydrodynamic forces acting along the channel bed. The shear force, for steady uniform flow is related to bed slope, hydraulic radius and unit weight of fluid.

How to Calculate Boundary Shear Stress?

Boundary Shear Stress calculator uses Shear Stress of Wall = Liquid Specific Weight*Hydraulic Radius of Channel*Bed Slope to calculate the Shear Stress of Wall, The Boundary Shear Stress is defined as resistance developed on the boundary or wall of the channel section. Shear Stress of Wall is denoted by ζ₀ symbol.

How to calculate Boundary Shear Stress using this online calculator? To use this online calculator for Boundary Shear Stress, enter Liquid Specific Weight (γ_l), Hydraulic Radius of Channel (R_H) & Bed Slope (S) and hit the calculate button. Here is how the Boundary Shear Stress calculation can be explained with given input values -> 6.2784 = 9810*1.6*0.0004.

FAQ

What is Boundary Shear Stress?

The Boundary Shear Stress is defined as resistance developed on the boundary or wall of the channel section and is represented as ζ₀ = γ_l*R_H*S or Shear Stress of Wall = Liquid Specific Weight*Hydraulic Radius of Channel*Bed Slope. 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 & Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.

How to calculate Boundary Shear Stress?

The Boundary Shear Stress is defined as resistance developed on the boundary or wall of the channel section is calculated using Shear Stress of Wall = Liquid Specific Weight*Hydraulic Radius of Channel*Bed Slope. To calculate Boundary Shear Stress, you need Liquid Specific Weight (γ_l), Hydraulic Radius of Channel (R_H) & Bed Slope (S). With our tool, you need to enter the respective value for Liquid Specific Weight, Hydraulic Radius of Channel & Bed Slope 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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