Shear Stress given Slope of Channel 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%
✖Depth is the distance from the top or surface to the bottom of something.ⓘ Depth [D]			+10% -10%
✖Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.ⓘ Horizontal Distance [R]			+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.ⓘ Shear Stress given Slope of Channel [𝜏]

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Formula

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Shear Stress given Slope of Channel

Formula

`"𝜏" = "γ"_{"f"}*"S̄"*("D"-"R")`

Example

`"78087.6Pa"="9.81kN/m³"*"4"*("3m"-"1.01m")`

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Shear Stress given Slope of Channel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance)
𝜏 = γ_f*S̄*(D-R)
This formula uses 5 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.
Depth - (Measured in Meter) - Depth is the distance from the top or surface to the bottom of something.
Horizontal Distance - (Measured in Meter) - Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.

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
Depth: 3 Meter --> 3 Meter No Conversion Required
Horizontal Distance: 1.01 Meter --> 1.01 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = γ_f*S̄*(D-R) --> 9810*4*(3-1.01)

Evaluating ... ...

𝜏 = 78087.6

STEP 3: Convert Result to Output's Unit

78087.6 Pascal --> No Conversion Required

FINAL ANSWER

78087.6 Pascal <-- Shear Stress

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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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

Shear Stress given Slope of Channel Formula

Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance)
𝜏 = γ_f*S̄*(D-R)

What is Shear Stress?

Shear stress, often denoted by τ, is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section.

How to Calculate Shear Stress given Slope of Channel?

Shear Stress given Slope of Channel calculator uses Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance) to calculate the Shear Stress, The Shear Stress given Slope of Channel is defined as the amount of resistance developed by the surface on to the motion of the fluid. Shear Stress is denoted by 𝜏 symbol.

How to calculate Shear Stress given Slope of Channel using this online calculator? To use this online calculator for Shear Stress given Slope of Channel, enter Specific Weight of Liquid (γ_f), Bed Slope (S̄), Depth (D) & Horizontal Distance (R) and hit the calculate button. Here is how the Shear Stress given Slope of Channel calculation can be explained with given input values -> 78087.6 = 9810*4*(3-1.01).

FAQ

What is Shear Stress given Slope of Channel?

The Shear Stress given Slope of Channel is defined as the amount of resistance developed by the surface on to the motion of the fluid and is represented as 𝜏 = γ_f*S̄*(D-R) or Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance). 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, Depth is the distance from the top or surface to the bottom of something & Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.

How to calculate Shear Stress given Slope of Channel?

The Shear Stress given Slope of Channel is defined as the amount of resistance developed by the surface on to the motion of the fluid is calculated using Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance). To calculate Shear Stress given Slope of Channel, you need Specific Weight of Liquid (γ_f), Bed Slope (S̄), Depth (D) & Horizontal Distance (R). With our tool, you need to enter the respective value for Specific Weight of Liquid, Bed Slope, Depth & Horizontal Distance 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, Depth & Horizontal Distance. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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