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Submerged Unit Weight given Critical Depth and Cohesion Formula

GoSubmerged Unit Weight given Effective Normal Stress Formula

GoSubmerged Unit Weight given Upward Force Formula

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Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course. Check FAQs

y S = \frac{(γ saturated \cdot \tan (\frac{i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}) - (\frac{C}{h c})}{- \tan (\frac{Φ i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

y_S - Submerged Unit Weight in KN per Cubic Meter?γ_saturated - Saturated Unit Weight of Soil?i - Angle of Inclination to Horizontal in Soil?C - Cohesion in Soil as Kilopascal?h_c - Critical Depth?Φ_i - Angle of Internal Friction of Soil?π - Archimedes' constant?

Submerged Unit Weight given Critical Depth and Cohesion Example

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

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

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

40.6381 = \frac{(11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}) - (\frac{1.27}{1.01})}{- \tan (\frac{82.87 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

40.6381kN/m³ = \frac{(11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}) - (\frac{1.27kPa}{1.01m})}{- \tan (\frac{82.87° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

40.6381 = \frac{(11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}) - (\frac{1.27}{1.01})}{- \tan (\frac{82.87 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Submerged Unit Weight given Critical Depth and Cohesion Solution

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

FIRST Step Consider the formula

y S = \frac{(γ saturated \cdot \tan (\frac{i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}) - (\frac{C}{h c})}{- \tan (\frac{Φ i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Next Step Substitute values of Variables

∴

y S = \frac{(11.89kN/m³ \cdot \tan (\frac{64° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}) - (\frac{1.27kPa}{1.01m})}{- \tan (\frac{82.87° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

y S = \frac{(11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}) - (\frac{1.27kPa}{1.01m})}{- \tan (\frac{82.87° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

y S = \frac{(11890N/m³ \cdot \tan (\frac{1.117rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}) - (\frac{1270Pa}{1.01m})}{- \tan (\frac{1.4464rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

y S = \frac{(11890 \cdot \tan (\frac{1.117 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}) - (\frac{1270}{1.01})}{- \tan (\frac{1.4464 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

y S = 40638.1388863606N/m³

Next Step Convert to Output's Unit

∴

y S = 40.6381388863607kN/m³

LAST Step Rounding Answer

∴

y S = 40.6381kN/m³

Submerged Unit Weight given Critical Depth and Cohesion Formula Elements

Variables

Constants

Functions

Submerged Unit Weight in KN per Cubic Meter

Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.

Symbol: y_S

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight in KN per Cubic Meter

Saturated Unit Weight of Soil

Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

Symbol: γ_saturated

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight 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

Cohesion in Soil as Kilopascal

Cohesion in Soil as Kilopascal 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

Measurement: PressureUnit: kPa

Note: Value should be between 0 to 50.

Formulas to find Cohesion in Soil as Kilopascal

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 of Soil

Angle of Internal Friction of Soil is is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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)

Other Formulas to find Submerged Unit Weight in KN per Cubic Meter

Go Submerged Unit Weight given Effective Normal Stress

y S = \frac{σ'}{z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Go Submerged Unit Weight given Upward Force

y S = \frac{σ n - F u}{z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Go Submerged Unit Weight given Factor of Safety

y S = \frac{F s}{\frac{\tan (\frac{Φ i \cdot π}{180})}{γ saturated \cdot \tan (\frac{i \cdot π}{180})}}

Go Submerged Unit Weight given Shear Strength

y S = \frac{\frac{τ f}{ζ soil}}{\frac{\tan ((Φ i))}{γ saturated \cdot \tan ((i))}}

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

W prism = (γ saturated \cdot z \cdot b \cdot \cos (\frac{i \cdot π}{180}))

Go Inclined Length of Prism given Saturated Unit Weight

b = \frac{W prism}{γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180})}

Go Vertical Stress on Prism given Saturated Unit Weight

σ zkp = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}))

Go Normal Stress Component given Saturated Unit Weight

σ n = (γ saturated \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

How to Evaluate Submerged Unit Weight given Critical Depth and Cohesion?

Submerged Unit Weight given Critical Depth and Cohesion evaluator uses Submerged Unit Weight in KN per Cubic Meter = ((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Cohesion in Soil as Kilopascal/Critical Depth))/(-tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Submerged Unit Weight in KN per Cubic Meter, The Submerged Unit Weight given Critical Depth and Cohesion is defined as the value of submerged unit weight when we have prior information of other parameters used. Submerged Unit Weight in KN per Cubic Meter is denoted by y_S symbol.

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

FAQs on Submerged Unit Weight given Critical Depth and Cohesion

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

The formula of Submerged Unit Weight given Critical Depth and Cohesion is expressed as Submerged Unit Weight in KN per Cubic Meter = ((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Cohesion in Soil as Kilopascal/Critical Depth))/(-tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.040638 = ((11890*tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2)-(1270/1.01))/(-tan((1.44635435112743*pi)/180)*(cos((1.11701072127616*pi)/180))^2).

How to calculate Submerged Unit Weight given Critical Depth and Cohesion?

With Saturated Unit Weight of Soil (γ_saturated), Angle of Inclination to Horizontal in Soil (i), Cohesion in Soil as Kilopascal (C), Critical Depth (h_c) & Angle of Internal Friction of Soil (Φ_i) we can find Submerged Unit Weight given Critical Depth and Cohesion using the formula - Submerged Unit Weight in KN per Cubic Meter = ((Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)-(Cohesion in Soil as Kilopascal/Critical Depth))/(-tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). This formula also uses Archimedes' constant and , Cosine (cos), Tangent (tan) function(s).

What are the other ways to Calculate Submerged Unit Weight in KN per Cubic Meter?

Here are the different ways to Calculate Submerged Unit Weight in KN per Cubic Meter-

Submerged Unit Weight in KN per Cubic Meter=Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Submerged Unit Weight in KN per Cubic Meter=(Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Submerged Unit Weight in KN per Cubic Meter=Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)))

Can the Submerged Unit Weight given Critical Depth and Cohesion be negative?

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

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

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

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Submerged Unit Weight given Critical Depth and Cohesion Formula

​GoSubmerged Unit Weight given Effective Normal Stress Formula

​GoSubmerged Unit Weight given Upward Force Formula

Submerged Unit Weight given Critical Depth and Cohesion Example

Submerged Unit Weight given Critical Depth and Cohesion Solution

Submerged Unit Weight given Critical Depth and Cohesion Formula Elements

Other Formulas to find Submerged Unit Weight in KN per Cubic Meter

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Submerged Unit Weight given Critical Depth and Cohesion?

FAQs on Submerged Unit Weight given Critical Depth and Cohesion

Variable Name

GoSubmerged Unit Weight given Effective Normal Stress Formula

GoSubmerged Unit Weight given Upward Force Formula