Bed Shear Stress Calculator

✖Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.ⓘ Specific Weight of Liquid [γ_f]			+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 [S̄]			+10% -10%
✖Diameter of Section is the diameter of the circular cross-section of the beam.ⓘ Diameter of Section [d_section]			+10% -10%

✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Bed Shear Stress [𝜏]

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Formula

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Bed Shear Stress

Formula

`"𝜏" = "γ"_{"f"}*"S̄"*"d"_{"section"}`

Example

`"196200Pa"="9.81kN/m³"*"4"*"5m"`

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Bed Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section
𝜏 = γ_f*S̄*d_section
This formula uses 4 Variables

Variables Used

Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Specific Weight of Liquid - (Measured in Newton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
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.
Diameter of Section - (Measured in Meter) - Diameter of Section is the diameter of the circular cross-section of the beam.

STEP 1: Convert Input(s) to Base Unit

Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Bed Slope: 4 --> No Conversion Required
Diameter of Section: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = γ_f*S̄*d_section --> 9810*4*5

Evaluating ... ...

𝜏 = 196200

STEP 3: Convert Result to Output's Unit

196200 Pascal --> No Conversion Required

FINAL ANSWER

196200 Pascal <-- Shear Stress

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Laminar Flow of Fluid in an Open Channel » Bed Shear Stress

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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 M Naveen

National Institute of Technology (NIT), Warangal

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< 18 Laminar Flow of Fluid in an Open Channel Calculators

Slope of Channel given Mean Velocity of Flow

Go Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid)

Diameter of Section given Mean Velocity of Flow

Go Diameter of Section = ((Horizontal Distance^2+(-Dynamic Viscosity*Mean Velocity*Slope of Surface of Constant Pressure/Specific Weight of Liquid)))/Horizontal Distance

Mean Velocity in flow

Go Mean Velocity = -(Specific Weight of Liquid*Piezometric Gradient*(Diameter of Section*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity

Dynamic Viscosity given Mean Velocity of Flow in Section

Go Dynamic Viscosity = (Specific Weight of Liquid*Piezometric Gradient*(Diameter of Section*Horizontal Distance-Horizontal Distance^2))/Mean Velocity

Diameter of Section given Potential Head Drop

Go Diameter of Section = sqrt((3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Head Loss due to Friction))

Length of Pipe given Potential Head Drop

Go Length of Pipe = (Head Loss due to Friction*Specific Weight of Liquid*(Diameter of Section^2))/(3*Dynamic Viscosity*Mean Velocity)

Potential Head Drop

Go Head Loss due to Friction = (3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Diameter of Section^2)

Diameter of Section given Discharge per Unit Channel Width

Go Diameter of Section = ((3*Dynamic Viscosity*Discharge per Unit Width)/(Slope of bed*Specific Weight of Liquid))^(1/3)

Dynamic Viscosity given Discharge per Unit Channel Width

Go Dynamic Viscosity = (Specific Weight of Liquid*Slope of bed*Diameter of Section^3)/(3*Discharge per Unit Width)

Slope of Channel given Discharge per Unit Channel Width

Go Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3)

Discharge per unit channel width

Go Discharge per Unit Width = (Specific Weight of Liquid*Slope of bed*Diameter of Section^3)/(3*Dynamic Viscosity)

Slope of Channel given Shear Stress

Go Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance))

Diameter of Section given Slope of Channel

Go Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance

Horizontal Distance given Slope of Channel

Go Horizontal Distance = Diameter of Section-(Shear Stress/(Bed Slope*Specific Weight of Liquid))

Shear Stress given Slope of Channel

Go Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance)

Diameter of Section given Bed Shear Stress

Go Diameter of Section = Shear Stress/(Bed Slope*Specific Weight of Liquid)

Bed Slope given Bed Shear Stress

Go Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid)

Bed Shear Stress

Go Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section

Bed Shear Stress Formula

Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section
𝜏 = γ_f*S̄*d_section

What is Shear Stress?

Shear Stress (t) is a measure of the force of friction from a fluid acting on a body in the path of that fluid. In the case of open channel flow, it is the force of moving water against the bed of the channel.

How to Calculate Bed Shear Stress?

Bed Shear Stress calculator uses Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section to calculate the Shear Stress, The Bed Shear Stress is defined as the maximum value of shear stress at the bed point or bottom most point of the flowing stream in the channel. Shear Stress is denoted by 𝜏 symbol.

How to calculate Bed Shear Stress using this online calculator? To use this online calculator for Bed Shear Stress, enter Specific Weight of Liquid (γ_f), Bed Slope (S̄) & Diameter of Section (d_section) and hit the calculate button. Here is how the Bed Shear Stress calculation can be explained with given input values -> 196200 = 9810*4*5.

FAQ

What is Bed Shear Stress?

The Bed Shear Stress is defined as the maximum value of shear stress at the bed point or bottom most point of the flowing stream in the channel and is represented as 𝜏 = γ_f*S̄*d_section or Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section. Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid, Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow & Diameter of Section is the diameter of the circular cross-section of the beam.

How to calculate Bed Shear Stress?

The Bed Shear Stress is defined as the maximum value of shear stress at the bed point or bottom most point of the flowing stream in the channel is calculated using Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section. To calculate Bed Shear Stress, you need Specific Weight of Liquid (γ_f), Bed Slope (S̄) & Diameter of Section (d_section). With our tool, you need to enter the respective value for Specific Weight of Liquid, Bed Slope & Diameter of Section 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 Shear Stress?

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

Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance)

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