Slope of Channel given Shear Stress Calculator

✖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 [𝜏]			+10% -10%
✖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%
✖Overall diameter of section is the section without any load.ⓘ Overall diameter of section [D_O]			+10% -10%
✖Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.ⓘ Horizontal Distance [R]			+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 given Shear Stress [S̄]

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Formula

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Slope of Channel given Shear Stress

Formula

`"S̄" = "𝜏"/("γ"_{"f"}*("D"_{"O"}-"R"))`

Example

`"-12.487258"="93.1Pa"/("9.81kN/m³"*("250mm"-"1.01m"))`

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Slope of Channel given Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance))
S̄ = 𝜏/(γ_f*(D_O-R))
This formula uses 5 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 - (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 Kilonewton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
Overall diameter of section - (Measured in Meter) - Overall diameter of section is the section without any load.
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

Shear Stress: 93.1 Pascal --> 93.1 Pascal No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9.81 Kilonewton per Cubic Meter No Conversion Required
Overall diameter of section: 250 Millimeter --> 0.25 Meter (Check conversion here)
Horizontal Distance: 1.01 Meter --> 1.01 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S̄ = 𝜏/(γ_f*(D_O-R)) --> 93.1/(9.81*(0.25-1.01))

Evaluating ... ...

S̄ = -12.4872579001019

STEP 3: Convert Result to Output's Unit

-12.4872579001019 --> No Conversion Required

FINAL ANSWER

-12.4872579001019 ≈ -12.487258 <-- Bed Slope

(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 » Slope of Channel given Shear Stress

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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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

Slope of Channel given Shear Stress Formula

Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance))
S̄ = 𝜏/(γ_f*(D_O-R))

What is Bed Slope?

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, stream restoratioview the full answer.

How to Calculate Slope of Channel given Shear Stress?

Slope of Channel given Shear Stress calculator uses Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance)) to calculate the Bed Slope, The Slope of Channel given Shear Stress is defined as the angle of elevation of channel with respect to horizontal line. Bed Slope is denoted by S̄ symbol.

How to calculate Slope of Channel given Shear Stress using this online calculator? To use this online calculator for Slope of Channel given Shear Stress, enter Shear Stress (𝜏), Specific Weight of Liquid (γ_f), Overall diameter of section (D_O) & Horizontal Distance (R) and hit the calculate button. Here is how the Slope of Channel given Shear Stress calculation can be explained with given input values -> -12.487258 = 93.1/(9810*(0.25-1.01)).

FAQ

What is Slope of Channel given Shear Stress?

The Slope of Channel given Shear Stress is defined as the angle of elevation of channel with respect to horizontal line and is represented as S̄ = 𝜏/(γ_f*(D_O-R)) or Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance)). 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 represents the force exerted by gravity on a unit volume of a fluid, Overall diameter of section is the section without any load & Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.

How to calculate Slope of Channel given Shear Stress?

The Slope of Channel given Shear Stress is defined as the angle of elevation of channel with respect to horizontal line is calculated using Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance)). To calculate Slope of Channel given Shear Stress, you need Shear Stress (𝜏), Specific Weight of Liquid (γ_f), Overall diameter of section (D_O) & Horizontal Distance (R). With our tool, you need to enter the respective value for Shear Stress, Specific Weight of Liquid, Overall diameter of section & 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 Bed Slope?

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

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

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