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Slope of Channel Bed given Average Velocity in Channel Formula

GoSlope of Channel Bottom given Boundary Shear Stress Formula

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Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow. Check FAQs

S = {(\frac{V avg}{\sqrt{8 \cdot [g] \cdot \frac{R H}{f}}})}^{2}

S - Bed Slope?V_avg - Average Velocity of Flow?R_H - Hydraulic Radius of Channel?f - Darcy Friction Factor?[g] - Gravitational acceleration on Earth?

Slope of Channel Bed given Average Velocity in Channel Example

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Here is how the Slope of Channel Bed given Average Velocity in Channel equation looks like with Values.

Here is how the Slope of Channel Bed given Average Velocity in Channel equation looks like with Units.

Here is how the Slope of Channel Bed given Average Velocity in Channel equation looks like.

0.0004 = {(\frac{0.32}{\sqrt{8 \cdot 9.8066 \cdot \frac{1.6}{0.5}}})}^{2}

0.0004 = {(\frac{0.32m/s}{\sqrt{8 \cdot 9.8066m/s² \cdot \frac{1.6m}{0.5}}})}^{2}

0.0004 = {(\frac{0.32}{\sqrt{8 \cdot 9.8066 \cdot \frac{1.6}{0.5}}})}^{2}

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Slope of Channel Bed given Average Velocity in Channel Solution

Follow our step by step solution on how to calculate Slope of Channel Bed given Average Velocity in Channel?

FIRST Step Consider the formula

S = {(\frac{V avg}{\sqrt{8 \cdot [g] \cdot \frac{R H}{f}}})}^{2}

Next Step Substitute values of Variables

∴

S = {(\frac{0.32m/s}{\sqrt{8 \cdot [g] \cdot \frac{1.6m}{0.5}}})}^{2}

Next Step Substitute values of Constants

∴

S = {(\frac{0.32m/s}{\sqrt{8 \cdot 9.8066m/s² \cdot \frac{1.6m}{0.5}}})}^{2}

Next Step Prepare to Evaluate

∴

S = {(\frac{0.32}{\sqrt{8 \cdot 9.8066 \cdot \frac{1.6}{0.5}}})}^{2}

Next Step Evaluate

∴

S = 0.000407886485191171

LAST Step Rounding Answer

∴

S = 0.0004

Slope of Channel Bed given Average Velocity in Channel Formula Elements

Variables

Constants

Functions

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.

Symbol: S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bed Slope

Average Velocity of Flow

Average Velocity of Flow is defined as the mean of all different velocities.

Symbol: V_avg

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Average Velocity of Flow

Hydraulic Radius of Channel

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.

Symbol: R_H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Hydraulic Radius of Channel

Darcy Friction Factor

The Darcy Friction Factor is a dimensionless parameter used to describe the resistance to fluid flow in pipes or channels.

Symbol: f

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Darcy Friction Factor

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: sqrt(Number)

Other Formulas to find Bed Slope

Go Slope of Channel Bottom given Boundary Shear Stress

S = \frac{ζ 0}{γ l \cdot R H}

Other formulas in Average Velocity in Uniform Flow in Channels category

Go Boundary Shear Stress

ζ 0 = γ l \cdot R H \cdot S

Go Specific Weight of Liquid given Boundary Shear Stress

γ l = \frac{ζ 0}{R H \cdot S}

Go Hydraulic Radius given Boundary Shear Stress

R H = \frac{ζ 0}{γ l \cdot S}

Go Average Velocity in Channel

V avg = \sqrt{8 \cdot [g] \cdot R H \cdot \frac{S}{f}}

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

Slope of Channel Bed given Average Velocity in Channel evaluator uses Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2 to evaluate 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 evaluate Slope of Channel Bed given Average Velocity in Channel using this online evaluator? To use this online evaluator 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.

FAQs on Slope of Channel Bed given Average Velocity in Channel

What is the formula to find Slope of Channel Bed given Average Velocity in Channel?

The formula of Slope of Channel Bed given Average Velocity in Channel is expressed as Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2. Here is an example- 0.000408 = (0.32/(sqrt(8*[g]*1.6/0.5)))^2.

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

With Average Velocity of Flow (V_avg), Hydraulic Radius of Channel (R_H) & Darcy Friction Factor (f) we can find Slope of Channel Bed given Average Velocity in Channel using the formula - Bed Slope = (Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2. This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Bed Slope?

Here are the different ways to Calculate Bed Slope-

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

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Slope of Channel Bed given Average Velocity in Channel Formula

​GoSlope of Channel Bottom given Boundary Shear Stress Formula

Slope of Channel Bed given Average Velocity in Channel Example

Slope of Channel Bed given Average Velocity in Channel Solution

Slope of Channel Bed given Average Velocity in Channel Formula Elements

Other Formulas to find Bed Slope

Other formulas in Average Velocity in Uniform Flow in Channels category

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

FAQs on Slope of Channel Bed given Average Velocity in Channel

Variable Name

GoSlope of Channel Bottom given Boundary Shear Stress Formula