Slope of Dynamic Equation of Gradually Varied Flows Calculator

✖Bed Slope of Channel is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.ⓘ Bed Slope of Channel [S₀]			+10% -10%
✖Energy Slope is at a distance equal to the velocity head above the hydraulic gradient.ⓘ Energy Slope [S_f]			+10% -10%
✖Froude No by Dynamic Equation is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.ⓘ Froude No by Dynamic Equation [F_r(d)]			+10% -10%

✖The Slope of Line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.ⓘ Slope of Dynamic Equation of Gradually Varied Flows [m]

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Slope of Dynamic Equation of Gradually Varied Flows Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2))
m = (S₀-S_f)/(1-(F_r(d)^2))
This formula uses 4 Variables

Variables Used

Slope of Line - The Slope of Line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.
Bed Slope of Channel - Bed Slope of Channel is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.
Energy Slope - Energy Slope is at a distance equal to the velocity head above the hydraulic gradient.
Froude No by Dynamic Equation - Froude No by Dynamic Equation is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.

STEP 1: Convert Input(s) to Base Unit

Bed Slope of Channel: 4.001 --> No Conversion Required
Energy Slope: 2.001 --> No Conversion Required
Froude No by Dynamic Equation: 0.7 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m = (S₀-S_f)/(1-(F_r(d)^2)) --> (4.001-2.001)/(1-(0.7^2))

Evaluating ... ...

m = 3.92156862745098

STEP 3: Convert Result to Output's Unit

3.92156862745098 --> No Conversion Required

FINAL ANSWER

3.92156862745098 ≈ 3.921569 <-- Slope of Line

(Calculation completed in 00.004 seconds)

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< Gradually Varied Flow in Channels Calculators

Froude Number given Top Width

LaTeX Go Froude Number = sqrt(Discharge for GVF Flow^2*Top Width/([g]*Wetted Surface Area^3))

Froude Number given Slope of Dynamic Equation of Gradually Varied Flow

LaTeX Go Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line))

Bed Slope given Slope of Dynamic Equation of Gradually Varied Flow

LaTeX Go Bed Slope of Channel = Energy Slope+(Slope of Line*(1-(Froude No by Dynamic Equation^2)))

Slope of Dynamic Equation of Gradually Varied Flows

LaTeX Go Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2))

Slope of Dynamic Equation of Gradually Varied Flows Formula

LaTeX Go

Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2))
m = (S₀-S_f)/(1-(F_r(d)^2))

What is Gradually Varied Flow?

Gradually varied. flow (GVF), which is a form of steady. nonuniform flow characterized by gradual variations in flow depth and velocity (small slopes and no abrupt changes) and a free surface that always remains smooth (no discontinuities or zigzags).

How to Calculate Slope of Dynamic Equation of Gradually Varied Flows?

Slope of Dynamic Equation of Gradually Varied Flows calculator uses Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2)) to calculate the Slope of Line, The Slope of Dynamic Equation of Gradually Varied Flows formula is defined as slope of line which is formed based on the gradually varied flow condition. Slope of Line is denoted by m symbol.

How to calculate Slope of Dynamic Equation of Gradually Varied Flows using this online calculator? To use this online calculator for Slope of Dynamic Equation of Gradually Varied Flows, enter Bed Slope of Channel (S₀), Energy Slope (S_f) & Froude No by Dynamic Equation (F_r(d)) and hit the calculate button. Here is how the Slope of Dynamic Equation of Gradually Varied Flows calculation can be explained with given input values -> 3.921569 = (4.001-2.001)/(1-(0.7^2)).

FAQ

What is Slope of Dynamic Equation of Gradually Varied Flows?

The Slope of Dynamic Equation of Gradually Varied Flows formula is defined as slope of line which is formed based on the gradually varied flow condition and is represented as m = (S₀-S_f)/(1-(F_r(d)^2)) or Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2)). Bed Slope of Channel is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow, Energy Slope is at a distance equal to the velocity head above the hydraulic gradient & Froude No by Dynamic Equation is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.

How to calculate Slope of Dynamic Equation of Gradually Varied Flows?

The Slope of Dynamic Equation of Gradually Varied Flows formula is defined as slope of line which is formed based on the gradually varied flow condition is calculated using Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2)). To calculate Slope of Dynamic Equation of Gradually Varied Flows, you need Bed Slope of Channel (S₀), Energy Slope (S_f) & Froude No by Dynamic Equation (F_r(d)). With our tool, you need to enter the respective value for Bed Slope of Channel, Energy Slope & Froude No by Dynamic Equation 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 Slope of Line?

In this formula, Slope of Line uses Bed Slope of Channel, Energy Slope & Froude No by Dynamic Equation. We can use 1 other way(s) to calculate the same, which is/are as follows -

Slope of Line = Hydraulic Gradient to Head Loss/(1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))

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