Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient Calculator

✖Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum.ⓘ Hydraulic Gradient to Head Loss [i]			+10% -10%
✖Discharge by Energy Gradient is rate of floe per unit time.ⓘ Discharge by Energy Gradient [Q_eg]			+10% -10%
✖Top Width is defined as width at top of section.ⓘ Top Width [T]			+10% -10%
✖Wetted Surface Area is the total area of outer surface in contact with the surrounding water.ⓘ Wetted Surface Area [S]			+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 Flow given Energy Gradient [m]

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Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slope of Line = Hydraulic Gradient to Head Loss/(1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))
m = i/(1-(Q_eg^2*T/([g]*S^3)))
This formula uses 1 Constants, 5 Variables

Constants Used

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

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.
Hydraulic Gradient to Head Loss - Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum.
Discharge by Energy Gradient - (Measured in Cubic Meter per Second) - Discharge by Energy Gradient is rate of floe per unit time.
Top Width - (Measured in Meter) - Top Width is defined as width at top of section.
Wetted Surface Area - (Measured in Square Meter) - Wetted Surface Area is the total area of outer surface in contact with the surrounding water.

STEP 1: Convert Input(s) to Base Unit

Hydraulic Gradient to Head Loss: 2.02 --> No Conversion Required
Discharge by Energy Gradient: 12.5 Cubic Meter per Second --> 12.5 Cubic Meter per Second No Conversion Required
Top Width: 2 Meter --> 2 Meter No Conversion Required
Wetted Surface Area: 4.01 Square Meter --> 4.01 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m = i/(1-(Q_eg^2*T/([g]*S^3))) --> 2.02/(1-(12.5^2*2/([g]*4.01^3)))

Evaluating ... ...

m = 3.99361487306497

STEP 3: Convert Result to Output's Unit

3.99361487306497 --> No Conversion Required

FINAL ANSWER

3.99361487306497 ≈ 3.993615 <-- 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 Flow given Energy Gradient Formula

LaTeX Go

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

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 Flow given Energy Gradient?

Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient calculator uses Slope of Line = Hydraulic Gradient to Head Loss/(1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3))) to calculate the Slope of Line, The Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient formula is defined as the rate of change of energy gradient along the flow. Slope of Line is denoted by m symbol.

How to calculate Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient using this online calculator? To use this online calculator for Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient, enter Hydraulic Gradient to Head Loss (i), Discharge by Energy Gradient (Q_eg), Top Width (T) & Wetted Surface Area (S) and hit the calculate button. Here is how the Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient calculation can be explained with given input values -> 4.02317 = 2.02/(1-(12.5^2*2/([g]*4.01^3))).

FAQ

What is Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient?

The Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient formula is defined as the rate of change of energy gradient along the flow and is represented as m = i/(1-(Q_eg^2*T/([g]*S^3))) or Slope of Line = Hydraulic Gradient to Head Loss/(1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3))). Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum, Discharge by Energy Gradient is rate of floe per unit time, Top Width is defined as width at top of section & Wetted Surface Area is the total area of outer surface in contact with the surrounding water.

How to calculate Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient?

The Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient formula is defined as the rate of change of energy gradient along the flow is calculated using Slope of Line = Hydraulic Gradient to Head Loss/(1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3))). To calculate Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient, you need Hydraulic Gradient to Head Loss (i), Discharge by Energy Gradient (Q_eg), Top Width (T) & Wetted Surface Area (S). With our tool, you need to enter the respective value for Hydraulic Gradient to Head Loss, Discharge by Energy Gradient, Top Width & Wetted Surface Area 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 Hydraulic Gradient to Head Loss, Discharge by Energy Gradient, Top Width & Wetted Surface Area. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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