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Energy Gradient given Slope Formula

GoEnergy Gradient given Bed Slope Formula

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Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum. Check FAQs

i = (1 - ({Q eg}^{2} \cdot \frac{T}{[g] \cdot S^{3}})) \cdot m

i - Hydraulic Gradient to Head Loss?Q_eg - Discharge by Energy Gradient?T - Top Width?S - Wetted Surface Area?m - Slope of Line?[g] - Gravitational acceleration on Earth?

Energy Gradient given Slope Example

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Here is how the Energy Gradient given Slope equation looks like with Values.

Here is how the Energy Gradient given Slope equation looks like with Units.

Here is how the Energy Gradient given Slope equation looks like.

2.0232 = (1 - ({12.5}^{2} \cdot \frac{2}{9.8066 \cdot {4.01}^{3}})) \cdot 4

2.0232 = (1 - ({12.5m³/s}^{2} \cdot \frac{2m}{9.8066m/s² \cdot {4.01m²}^{3}})) \cdot 4

2.0232 = (1 - ({12.5}^{2} \cdot \frac{2}{9.8066 \cdot {4.01}^{3}})) \cdot 4

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Energy Gradient given Slope Solution

Follow our step by step solution on how to calculate Energy Gradient given Slope?

FIRST Step Consider the formula

i = (1 - ({Q eg}^{2} \cdot \frac{T}{[g] \cdot S^{3}})) \cdot m

Next Step Substitute values of Variables

∴

i = (1 - ({12.5m³/s}^{2} \cdot \frac{2m}{[g] \cdot {4.01m²}^{3}})) \cdot 4

Next Step Substitute values of Constants

∴

i = (1 - ({12.5m³/s}^{2} \cdot \frac{2m}{9.8066m/s² \cdot {4.01m²}^{3}})) \cdot 4

Next Step Prepare to Evaluate

∴

i = (1 - ({12.5}^{2} \cdot \frac{2}{9.8066 \cdot {4.01}^{3}})) \cdot 4

Next Step Evaluate

∴

i = 2.02322964452475

LAST Step Rounding Answer

∴

i = 2.0232

Energy Gradient given Slope Formula Elements

Variables

Constants

Hydraulic Gradient to Head Loss

Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum.

Symbol: i

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Hydraulic Gradient to Head Loss

Discharge by Energy Gradient

Discharge by Energy Gradient is rate of floe per unit time.

Symbol: Q_eg

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Discharge by Energy Gradient

Top Width

Top Width is defined as width at top of section.

Symbol: T

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Width

Wetted Surface Area

Wetted Surface Area is the total area of outer surface in contact with the surrounding water.

Symbol: S

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Wetted Surface Area

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.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Slope of Line

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

Other Formulas to find Hydraulic Gradient to Head Loss

Go Energy Gradient given Bed Slope

i = S 0 - S f

Other formulas in Gradually Varied Flow in Channels category

Go Slope of Dynamic Equation of Gradually Varied Flows

m = \frac{S 0 - S f}{1 - ({F r(d)}^{2})}

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

S 0 = S f + (m \cdot (1 - ({F r(d)}^{2})))

Go Froude Number given Slope of Dynamic Equation of Gradually Varied Flow

F r(d) = \sqrt{1 - (\frac{S 0 - S f}{m})}

Go Froude Number given Top Width

Fr = \sqrt{{Q f}^{2} \cdot \frac{T}{[g] \cdot S^{3}}}

How to Evaluate Energy Gradient given Slope?

Energy Gradient given Slope evaluator uses Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line to evaluate the Hydraulic Gradient to Head Loss, The Energy Gradient given Slope formula is defined as slope of energy line in the channel taken at any point of channel. Hydraulic Gradient to Head Loss is denoted by i symbol.

How to evaluate Energy Gradient given Slope using this online evaluator? To use this online evaluator for Energy Gradient given Slope, enter Discharge by Energy Gradient (Q_eg), Top Width (T), Wetted Surface Area (S) & Slope of Line (m) and hit the calculate button.

FAQs on Energy Gradient given Slope

What is the formula to find Energy Gradient given Slope?

The formula of Energy Gradient given Slope is expressed as Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line. Here is an example- 2.008367 = (1-(12.5^2*2/([g]*4.01^3)))*4.

How to calculate Energy Gradient given Slope?

With Discharge by Energy Gradient (Q_eg), Top Width (T), Wetted Surface Area (S) & Slope of Line (m) we can find Energy Gradient given Slope using the formula - Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line. This formula also uses Gravitational acceleration on Earth constant(s).

What are the other ways to Calculate Hydraulic Gradient to Head Loss?

Here are the different ways to Calculate Hydraulic Gradient to Head Loss-

Hydraulic Gradient to Head Loss=Bed Slope of Channel-Energy Slope

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Energy Gradient given Slope Formula

​GoEnergy Gradient given Bed Slope Formula

Energy Gradient given Slope Example

Energy Gradient given Slope Solution

Energy Gradient given Slope Formula Elements

Other Formulas to find Hydraulic Gradient to Head Loss

Other formulas in Gradually Varied Flow in Channels category

How to Evaluate Energy Gradient given Slope?

FAQs on Energy Gradient given Slope

Variable Name

GoEnergy Gradient given Bed Slope Formula