Slope of Channel Bed given Average Velocity in Channel Calculator

✖Average Velocity of Flow is defined as the mean of all different velocities.ⓘ Average Velocity of Flow [V_avg]			+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%
✖The Darcy Friction Factor is a dimensionless parameter used to describe the resistance to fluid flow in pipes or channels.ⓘ Darcy Friction Factor [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.ⓘ Slope of Channel Bed given Average Velocity in Channel [S]

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Slope of Channel Bed given Average Velocity in Channel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2
S = (V_avg/(sqrt(8*[g]*R_H/f)))^2
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Average Velocity of Flow - (Measured in Meter per Second) - Average Velocity of Flow is defined as the mean of all different velocities.
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.
Darcy Friction Factor - The Darcy Friction Factor is a dimensionless parameter used to describe the resistance to fluid flow in pipes or channels.

STEP 1: Convert Input(s) to Base Unit

Average Velocity of Flow: 0.32 Meter per Second --> 0.32 Meter per Second No Conversion Required
Hydraulic Radius of Channel: 1.6 Meter --> 1.6 Meter No Conversion Required
Darcy Friction Factor: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = (V_avg/(sqrt(8*[g]*R_H/f)))^2 --> (0.32/(sqrt(8*[g]*1.6/0.5)))^2

Evaluating ... ...

S = 0.000407886485191171

STEP 3: Convert Result to Output's Unit

0.000407886485191171 --> No Conversion Required

FINAL ANSWER

0.000407886485191171 ≈ 0.000408 <-- Bed Slope

(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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Meerut Institute of Engineering and Technology (MIET), Meerut

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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

Slope of Channel Bed given Average Velocity in Channel Formula

LaTeX Go

Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2
S = (V_avg/(sqrt(8*[g]*R_H/f)))^2

What is Average Velocity?

The average velocity of an object is its total displacement divided by the total time taken. In other words, it is the rate at which an object changes its position from one place to another. Average velocity is a vector quantity.

How to Calculate Slope of Channel Bed given Average Velocity in Channel?

Slope of Channel Bed given Average Velocity in Channel calculator uses Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2 to calculate the Bed Slope, The Slope of Channel Bed given Average Velocity in Channel is defined as elevation of channel with respect to horizontal or Ground level. Bed Slope is denoted by S symbol.

How to calculate Slope of Channel Bed given Average Velocity in Channel using this online calculator? To use this online calculator for Slope of Channel Bed given Average Velocity in Channel, enter Average Velocity of Flow (V_avg), Hydraulic Radius of Channel (R_H) & Darcy Friction Factor (f) and hit the calculate button. Here is how the Slope of Channel Bed given Average Velocity in Channel calculation can be explained with given input values -> 0.000408 = (0.32/(sqrt(8*[g]*1.6/0.5)))^2.

FAQ

What is Slope of Channel Bed given Average Velocity in Channel?

The Slope of Channel Bed given Average Velocity in Channel is defined as elevation of channel with respect to horizontal or Ground level and is represented as S = (V_avg/(sqrt(8*[g]*R_H/f)))^2 or Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2. Average Velocity of Flow is defined as the mean of all different velocities, 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 & The Darcy Friction Factor is a dimensionless parameter used to describe the resistance to fluid flow in pipes or channels.

How to calculate Slope of Channel Bed given Average Velocity in Channel?

The Slope of Channel Bed given Average Velocity in Channel is defined as elevation of channel with respect to horizontal or Ground level is calculated using Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2. To calculate Slope of Channel Bed given Average Velocity in Channel, you need Average Velocity of Flow (V_avg), Hydraulic Radius of Channel (R_H) & Darcy Friction Factor (f). With our tool, you need to enter the respective value for Average Velocity of Flow, Hydraulic Radius of Channel & Darcy Friction Factor 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 Average Velocity of Flow, Hydraulic Radius of Channel & Darcy Friction Factor. We can use 1 other way(s) to calculate the same, which is/are as follows -

Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel)

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