Slope of Dynamic Equations of Gradually Varied Flow 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%
✖Normal Depth is a depth of flow in a channel or culvert when the slope of the water surface and channel bottom is the same and the water depth remains constant.ⓘ Normal Depth [y]			+10% -10%
✖Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.ⓘ Depth of Flow [d_f]			+10% -10%
✖The Critical Depth of Weir is defined as the depth of flow where energy is at a minimum for a particular discharge.ⓘ Critical Depth of Weir [h_c]			+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 Equations of Gradually Varied Flow [m]

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Slope of Dynamic Equations of Gradually Varied Flow

Formula

`"m" = "S"_{"0"}*((1-(("y"/"d"_{"f"})^(10/3)))/(1-(("h"_{"c"}/"d"_{"f"})^(3))))`

Example

`"3.818671"="4.001"*((1-(("1.5m"/"3.3m")^(10/3)))/(1-(("1.001m"/"3.3m")^(3))))`

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Download Gradually Varied Flow in Channels Formulas PDF

Slope of Dynamic Equations of Gradually Varied Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3))))
m = S₀*((1-((y/d_f)^(10/3)))/(1-((h_c/d_f)^(3))))
This formula uses 5 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.
Normal Depth - (Measured in Meter) - Normal Depth is a depth of flow in a channel or culvert when the slope of the water surface and channel bottom is the same and the water depth remains constant.
Depth of Flow - (Measured in Meter) - Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights.
Critical Depth of Weir - (Measured in Meter) - The Critical Depth of Weir is defined as the depth of flow where energy is at a minimum for a particular discharge.

STEP 1: Convert Input(s) to Base Unit

Bed Slope of Channel: 4.001 --> No Conversion Required
Normal Depth: 1.5 Meter --> 1.5 Meter No Conversion Required
Depth of Flow: 3.3 Meter --> 3.3 Meter No Conversion Required
Critical Depth of Weir: 1.001 Meter --> 1.001 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m = S₀*((1-((y/d_f)^(10/3)))/(1-((h_c/d_f)^(3)))) --> 4.001*((1-((1.5/3.3)^(10/3)))/(1-((1.001/3.3)^(3))))

Evaluating ... ...

m = 3.81867122370488

STEP 3: Convert Result to Output's Unit

3.81867122370488 --> No Conversion Required

FINAL ANSWER

3.81867122370488 ≈ 3.818671 <-- Slope of Line

(Calculation completed in 00.006 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Non-uniform Flow in Channels » Gradually Varied Flow in Channels » Wide Rectangular Channel » Slope of Dynamic Equations of Gradually Varied Flow

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< 8 Wide Rectangular Channel Calculators

Critical Depth of Channel given Slope of Dynamic Equation of Gradually Varied Flow

Go Critical Depth of Channel GVF Flow = ((1-(((1-((Normal Depth/Depth of Flow)^(10/3)))/(Slope of Line/Bed Slope of Channel)))^(1/3)))*Depth of Flow

Chezy Formula for Critical Depth of Channel given Slope of Dynamic Equation of GVF

Go Critical Depth of Channel GVF Flow = ((1-(((1-((Normal Depth/Depth of Flow)^(3)))/(Slope of Line/Bed Slope of Channel)))^(1/3)))*Depth of Flow

Normal Depth of Channel given Slope of Dynamic Equation of Gradually Varied Flow

Go Normal Depth = ((1-((Slope of Line/Bed Slope of Channel)*((1-(((Critical Depth of Weir/Depth of Flow)^(3)))))))^(3/10))*Depth of Flow

Chezy Formula for Normal Depth of Channel given Slope of Dynamic Equation of GVF

Go Normal Depth = ((1-((Slope of Line/Bed Slope of Channel)*((1-(((Critical Depth of Weir/Depth of Flow)^(3)))))))^(1/3))*Depth of Flow

Bed Slope of Channel given Slope of Dynamic Equation of Gradually Varied Flow

Go Bed Slope of Channel = Slope of Line/(((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3)))))

Bed Slope of Channel given Slope of Dynamic Equation of GVF through Chezy formula

Go Bed Slope of Channel = Slope of Line/(((1-((Normal Depth/Depth of Flow)^(3)))/(1-(((Critical Depth of Weir/Depth of Flow)^(3))))))

Slope of Dynamic Equations of Gradually Varied Flow

Go Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3))))

Chezy Formula for Slope of Dynamic Equation of Gradually Varied Flow

Go Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(3)))/(1-(((Critical Depth of Weir/Depth of Flow)^(3)))))

Slope of Dynamic Equations of Gradually Varied Flow Formula

Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3))))
m = S₀*((1-((y/d_f)^(10/3)))/(1-((h_c/d_f)^(3))))

What is Dynamic Equation?

In mathematics, dynamic equation can refer to: difference equation in discrete time. differential equation in continuous time. time scale calculus in combined discrete and continuous time.

How to Calculate Slope of Dynamic Equations of Gradually Varied Flow?

Slope of Dynamic Equations of Gradually Varied Flow calculator uses Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3)))) to calculate the Slope of Line, The Slope of Dynamic Equations of Gradually Varied Flow formula is defined as slope of energy line of the gradually varied flow. Slope of Line is denoted by m symbol.

How to calculate Slope of Dynamic Equations of Gradually Varied Flow using this online calculator? To use this online calculator for Slope of Dynamic Equations of Gradually Varied Flow, enter Bed Slope of Channel (S₀), Normal Depth (y), Depth of Flow (d_f) & Critical Depth of Weir (h_c) and hit the calculate button. Here is how the Slope of Dynamic Equations of Gradually Varied Flow calculation can be explained with given input values -> -162.172754 = 4.001*((1-((1.5/3.3)^(10/3)))/(1-((1.001/3.3)^(3)))).

FAQ

What is Slope of Dynamic Equations of Gradually Varied Flow?

The Slope of Dynamic Equations of Gradually Varied Flow formula is defined as slope of energy line of the gradually varied flow and is represented as m = S₀*((1-((y/d_f)^(10/3)))/(1-((h_c/d_f)^(3)))) or Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3)))). 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, Normal Depth is a depth of flow in a channel or culvert when the slope of the water surface and channel bottom is the same and the water depth remains constant, Depth of Flow is the distance from the top or surface of the flow to the bottom of a channel or other waterway or Depth of Flow at the Vertical while measuring Sound Weights & The Critical Depth of Weir is defined as the depth of flow where energy is at a minimum for a particular discharge.

How to calculate Slope of Dynamic Equations of Gradually Varied Flow?

The Slope of Dynamic Equations of Gradually Varied Flow formula is defined as slope of energy line of the gradually varied flow is calculated using Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(10/3)))/(1-((Critical Depth of Weir/Depth of Flow)^(3)))). To calculate Slope of Dynamic Equations of Gradually Varied Flow, you need Bed Slope of Channel (S₀), Normal Depth (y), Depth of Flow (d_f) & Critical Depth of Weir (h_c). With our tool, you need to enter the respective value for Bed Slope of Channel, Normal Depth, Depth of Flow & Critical Depth of Weir 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, Normal Depth, Depth of Flow & Critical Depth of Weir. We can use 1 other way(s) to calculate the same, which is/are as follows -

Slope of Line = Bed Slope of Channel*((1-((Normal Depth/Depth of Flow)^(3)))/(1-(((Critical Depth of Weir/Depth of Flow)^(3)))))

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