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Submerged Unit Weight given Critical Depth Formula

GoSubmerged Unit Weight given Normal Stress Component Formula

GoSubmerged Unit Weight given Shear Stress Component Formula

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

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

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

Submerged Unit Weight given Critical Depth Example

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

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

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

25.3861 = \frac{5 \cdot {(\sec ((64)))}^{2}}{1.01 \cdot (\tan ((64)) - \tan ((46)))}

25.3861N/m³ = \frac{5kPa \cdot {(\sec ((64°)))}^{2}}{1.01m \cdot (\tan ((64°)) - \tan ((46°)))}

25.3861 = \frac{5 \cdot {(\sec ((64)))}^{2}}{1.01 \cdot (\tan ((64)) - \tan ((46)))}

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Submerged Unit Weight given Critical Depth Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

γ' = \frac{5kPa \cdot {(\sec ((64°)))}^{2}}{1.01m \cdot (\tan ((64°)) - \tan ((46°)))}

Next Step Convert Units

∴

γ' = \frac{5kPa \cdot {(\sec ((1.117rad)))}^{2}}{1.01m \cdot (\tan ((1.117rad)) - \tan ((0.8029rad)))}

Next Step Prepare to Evaluate

∴

γ' = \frac{5 \cdot {(\sec ((1.117)))}^{2}}{1.01 \cdot (\tan ((1.117)) - \tan ((0.8029)))}

Next Step Evaluate

∴

γ' = 25.386076132446N/m³

LAST Step Rounding Answer

∴

γ' = 25.3861N/m³

Submerged Unit Weight given Critical Depth Formula Elements

Variables

Functions

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

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

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

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 to find Submerged Unit Weight

Go Submerged Unit Weight given Normal Stress Component

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

Go Submerged Unit Weight given Shear Stress Component

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

Go Submerged Unit Weight given Factor of Safety for Cohesive Soil

γ' = (\frac{C s}{(f s - (\frac{\tan ((φ))}{\tan ((i))})) \cdot z \cdot \cos ((i)) \cdot \sin ((i))})

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 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)))

Go Depth of Prism given Submerged Unit Weight and Shear Stress

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

How to Evaluate Submerged Unit Weight given Critical Depth?

Submerged Unit Weight given Critical Depth evaluator uses Submerged Unit Weight = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))) to evaluate the Submerged Unit Weight, The Submerged Unit Weight given Critical Depth is defined as the fluid weight per unit volume at critical depth, where flow transitions between subcritical and supercritical. Submerged Unit Weight is denoted by γ^' symbol.

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

FAQs on Submerged Unit Weight given Critical Depth

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

The formula of Submerged Unit Weight given Critical Depth is expressed as Submerged Unit Weight = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))). Here is an example- 25.38608 = (5000*(sec((1.11701072127616)))^2)/(1.01*(tan((1.11701072127616))-tan((0.802851455917241)))).

How to calculate Submerged Unit Weight given Critical Depth?

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

What are the other ways to Calculate Submerged Unit Weight?

Here are the different ways to Calculate Submerged Unit Weight-

Submerged Unit Weight=Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)
Submerged Unit Weight=Shear Stress for Submerged Slopes/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))
Submerged Unit Weight=(Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

Can the Submerged Unit Weight given Critical Depth be negative?

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

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

Submerged Unit Weight given Critical Depth is usually measured using the Newton per Cubic Meter[N/m³] for Specific Weight. Newton per Cubic Centimeter[N/m³], Newton per Cubic Millimeter[N/m³], Kilonewton per Cubic Meter[N/m³] are the few other units in which Submerged Unit Weight given Critical Depth can be measured.

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Submerged Unit Weight given Critical Depth Formula

​GoSubmerged Unit Weight given Normal Stress Component Formula

​GoSubmerged Unit Weight given Shear Stress Component Formula

Submerged Unit Weight given Critical Depth Example

Submerged Unit Weight given Critical Depth Solution

Submerged Unit Weight given Critical Depth Formula Elements

Other Formulas to find Submerged Unit Weight

Other formulas in Stability Analysis of Submerged Slopes category

How to Evaluate Submerged Unit Weight given Critical Depth?

FAQs on Submerged Unit Weight given Critical Depth

Variable Name

GoSubmerged Unit Weight given Normal Stress Component Formula

GoSubmerged Unit Weight given Shear Stress Component Formula