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Critical Depth given Submerged Unit Weight Formula

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The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge. Check FAQs

h c = \frac{C s \cdot {(\sec ((i)))}^{2}}{γ' \cdot (\tan ((i)) - \tan ((φ)))}

h_c - Critical Depth?C_s - Cohesion of Soil?i - Angle of Inclination to Horizontal in Soil?γ^' - Submerged Unit Weight?φ - Angle of Internal Friction?

Critical Depth given Submerged Unit Weight Example

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Here is how the Critical Depth given Submerged Unit Weight equation looks like with Values.

Here is how the Critical Depth given Submerged Unit Weight equation looks like with Units.

Here is how the Critical Depth given Submerged Unit Weight equation looks like.

5.1178 = \frac{5 \cdot {(\sec ((64)))}^{2}}{5.01 \cdot (\tan ((64)) - \tan ((46)))}

5.1178m = \frac{5kPa \cdot {(\sec ((64°)))}^{2}}{5.01N/m³ \cdot (\tan ((64°)) - \tan ((46°)))}

5.1178 = \frac{5 \cdot {(\sec ((64)))}^{2}}{5.01 \cdot (\tan ((64)) - \tan ((46)))}

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Critical Depth given Submerged Unit Weight Solution

Follow our step by step solution on how to calculate Critical Depth given Submerged Unit Weight?

FIRST Step Consider the formula

h c = \frac{C s \cdot {(\sec ((i)))}^{2}}{γ' \cdot (\tan ((i)) - \tan ((φ)))}

Next Step Substitute values of Variables

∴

h c = \frac{5kPa \cdot {(\sec ((64°)))}^{2}}{5.01N/m³ \cdot (\tan ((64°)) - \tan ((46°)))}

Next Step Convert Units

∴

h c = \frac{5kPa \cdot {(\sec ((1.117rad)))}^{2}}{5.01N/m³ \cdot (\tan ((1.117rad)) - \tan ((0.8029rad)))}

Next Step Prepare to Evaluate

∴

h c = \frac{5 \cdot {(\sec ((1.117)))}^{2}}{5.01 \cdot (\tan ((1.117)) - \tan ((0.8029)))}

Next Step Evaluate

∴

h c = 5.11775187500408m

LAST Step Rounding Answer

∴

h c = 5.1178m

Critical Depth given Submerged Unit Weight Formula Elements

Variables

Functions

Critical Depth

The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge.

Symbol: h_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Critical Depth

Cohesion of Soil

Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.

Symbol: C_s

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

Angle of Inclination to Horizontal in Soil

Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination to Horizontal in Soil

Submerged Unit Weight

Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force .

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

Other formulas in Stability Analysis of Submerged Slopes category

Go Normal Stress Component given Submerged Unit Weight

σ Normal = γ' \cdot z \cdot {(\cos ((i)))}^{2}

Go Submerged Unit Weight given Normal Stress Component

γ' = \frac{σ Normal}{z \cdot {(\cos ((i)))}^{2}}

Go Depth of Prism given Submerged Unit Weight

z = \frac{σ Normal}{γ' \cdot {(\cos ((i)))}^{2}}

Go Shear Stress Component given Submerged Unit Weight

𝜏 = (γ' \cdot z \cdot \cos ((i)) \cdot \sin ((i)))

How to Evaluate Critical Depth given Submerged Unit Weight?

Critical Depth given Submerged Unit Weight evaluator uses Critical Depth = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))) to evaluate the Critical Depth, The Critical Depth given Submerged Unit Weight is defined as the depth at which submerged unit weight equals fluid unit weight, influencing open channel flow behavior. Critical Depth is denoted by h_c symbol.

How to evaluate Critical Depth given Submerged Unit Weight using this online evaluator? To use this online evaluator for Critical Depth given Submerged Unit Weight, enter Cohesion of Soil (C_s), Angle of Inclination to Horizontal in Soil (i), Submerged Unit Weight (γ^') & Angle of Internal Friction (φ) and hit the calculate button.

FAQs on Critical Depth given Submerged Unit Weight

What is the formula to find Critical Depth given Submerged Unit Weight?

The formula of Critical Depth given Submerged Unit Weight is expressed as Critical Depth = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))). Here is an example- 5.127987 = (5000*(sec((1.11701072127616)))^2)/(5.01*(tan((1.11701072127616))-tan((0.802851455917241)))).

How to calculate Critical Depth given Submerged Unit Weight?

With Cohesion of Soil (C_s), Angle of Inclination to Horizontal in Soil (i), Submerged Unit Weight (γ^') & Angle of Internal Friction (φ) we can find Critical Depth given Submerged Unit Weight using the formula - Critical Depth = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))). This formula also uses Tangent (tan), Secant (sec) function(s).

Can the Critical Depth given Submerged Unit Weight be negative?

No, the Critical Depth given Submerged Unit Weight, measured in Length cannot be negative.

Which unit is used to measure Critical Depth given Submerged Unit Weight?

Critical Depth given Submerged Unit Weight is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Critical Depth given Submerged Unit Weight can be measured.

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Critical Depth given Submerged Unit Weight Formula

Critical Depth given Submerged Unit Weight Example

Critical Depth given Submerged Unit Weight Solution

Critical Depth given Submerged Unit Weight Formula Elements

Other formulas in Stability Analysis of Submerged Slopes category

How to Evaluate Critical Depth given Submerged Unit Weight?

FAQs on Critical Depth given Submerged Unit Weight

Variable Name