Bed Slope given Bed Shear Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid)
= 𝜏/(dsection*γf)
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 - (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.
Diameter of Section - (Measured in Meter) - Diameter of Section is the diameter of the circular cross-section of the beam.
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.
STEP 1: Convert Input(s) to Base Unit
Shear Stress: 93.1 Pascal --> 93.1 Pascal No Conversion Required
Diameter of Section: 5 Meter --> 5 Meter No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
S̄ = 𝜏/(dsectionf) --> 93.1/(5*9810)
Evaluating ... ...
= 0.00189806320081549
STEP 3: Convert Result to Output's Unit
0.00189806320081549 --> No Conversion Required
FINAL ANSWER
0.00189806320081549 0.001898 <-- Bed Slope
(Calculation completed in 00.020 seconds)

Credits

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

Bed Slope given Bed Shear Stress Formula

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

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 Bed Slope given Bed Shear Stress?

Bed Slope given Bed Shear Stress calculator uses Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid) to calculate the Bed Slope, The Bed Slope given Bed Shear Stress is defined as the channel elevation with respect to horizontal line in the direction of fluid flow. Bed Slope is denoted by symbol.

How to calculate Bed Slope given Bed Shear Stress using this online calculator? To use this online calculator for Bed Slope given Bed Shear Stress, enter Shear Stress (𝜏), Diameter of Section (dsection) & Specific Weight of Liquid f) and hit the calculate button. Here is how the Bed Slope given Bed Shear Stress calculation can be explained with given input values -> 0.001898 = 93.1/(5*9810).

FAQ

What is Bed Slope given Bed Shear Stress?
The Bed Slope given Bed Shear Stress is defined as the channel elevation with respect to horizontal line in the direction of fluid flow and is represented as S̄ = 𝜏/(dsectionf) or Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid). Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, Diameter of Section is the diameter of the circular cross-section of the beam & Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
How to calculate Bed Slope given Bed Shear Stress?
The Bed Slope given Bed Shear Stress is defined as the channel elevation with respect to horizontal line in the direction of fluid flow is calculated using Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid). To calculate Bed Slope given Bed Shear Stress, you need Shear Stress (𝜏), Diameter of Section (dsection) & Specific Weight of Liquid f). With our tool, you need to enter the respective value for Shear Stress, Diameter of Section & Specific Weight of Liquid 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, Diameter of Section & Specific Weight of Liquid. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance))
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