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Submerged Unit Weight for Steady Seepage along Slope 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{(F s \cdot γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})) - C}{z \cdot \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?F_s - Factor of Safety in Soil Mechanics?γ_saturated - Saturated Unit Weight of Soil?z - Depth of Prism?i - Angle of Inclination to Horizontal in Soil?C - Cohesion in Soil as Kilopascal?Φ_i - Angle of Internal Friction of Soil?π - Archimedes' constant?

Submerged Unit Weight for Steady Seepage along Slope Example

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Here is how the Submerged Unit Weight for Steady Seepage along Slope equation looks like with Values.

Here is how the Submerged Unit Weight for Steady Seepage along Slope equation looks like with Units.

Here is how the Submerged Unit Weight for Steady Seepage along Slope equation looks like.

8.9363 = \frac{(2.8 \cdot 11.89 \cdot 3 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180})) - 1.27}{3 \cdot \tan (\frac{82.87 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

8.9363kN/m³ = \frac{(2.8 \cdot 11.89kN/m³ \cdot 3m \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180})) - 1.27kPa}{3m \cdot \tan (\frac{82.87° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

8.9363 = \frac{(2.8 \cdot 11.89 \cdot 3 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180})) - 1.27}{3 \cdot \tan (\frac{82.87 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Submerged Unit Weight for Steady Seepage along Slope Solution

Follow our step by step solution on how to calculate Submerged Unit Weight for Steady Seepage along Slope?

FIRST Step Consider the formula

y S = \frac{(F s \cdot γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})) - C}{z \cdot \tan (\frac{Φ i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Next Step Substitute values of Variables

∴

y S = \frac{(2.8 \cdot 11.89kN/m³ \cdot 3m \cdot \cos (\frac{64° \cdot π}{180}) \cdot \sin (\frac{64° \cdot π}{180})) - 1.27kPa}{3m \cdot \tan (\frac{82.87° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

y S = \frac{(2.8 \cdot 11.89kN/m³ \cdot 3m \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180})) - 1.27kPa}{3m \cdot \tan (\frac{82.87° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

y S = \frac{(2.8 \cdot 11890N/m³ \cdot 3m \cdot \cos (\frac{1.117rad \cdot 3.1416}{180}) \cdot \sin (\frac{1.117rad \cdot 3.1416}{180})) - 1270Pa}{3m \cdot \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{(2.8 \cdot 11890 \cdot 3 \cdot \cos (\frac{1.117 \cdot 3.1416}{180}) \cdot \sin (\frac{1.117 \cdot 3.1416}{180})) - 1270}{3 \cdot \tan (\frac{1.4464 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

y S = 8936.29722379064N/m³

Next Step Convert to Output's Unit

∴

y S = 8.93629722379064kN/m³

LAST Step Rounding Answer

∴

y S = 8.9363kN/m³

Submerged Unit Weight for Steady Seepage along Slope 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

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics expresses how much stronger a system is than it needs to be for an intended load.

Symbol: F_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety in Soil Mechanics

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

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

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

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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}}

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})}

How to Evaluate Submerged Unit Weight for Steady Seepage along Slope?

Submerged Unit Weight for Steady Seepage along Slope evaluator uses Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety in Soil Mechanics*Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))-Cohesion in Soil as Kilopascal)/(Depth of Prism*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 for Steady Seepage along Slope 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 for Steady Seepage along Slope using this online evaluator? To use this online evaluator for Submerged Unit Weight for Steady Seepage along Slope, enter Factor of Safety in Soil Mechanics (F_s), Saturated Unit Weight of Soil (γ_saturated), Depth of Prism (z), Angle of Inclination to Horizontal in Soil (i), Cohesion in Soil as Kilopascal (C) & Angle of Internal Friction of Soil (Φ_i) and hit the calculate button.

FAQs on Submerged Unit Weight for Steady Seepage along Slope

What is the formula to find Submerged Unit Weight for Steady Seepage along Slope?

The formula of Submerged Unit Weight for Steady Seepage along Slope is expressed as Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety in Soil Mechanics*Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))-Cohesion in Soil as Kilopascal)/(Depth of Prism*tan((Angle of Internal Friction of Soil*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.008936 = ((2.8*11890*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180))-1270)/(3*tan((1.44635435112743*pi)/180)*(cos((1.11701072127616*pi)/180))^2).

How to calculate Submerged Unit Weight for Steady Seepage along Slope?

With Factor of Safety in Soil Mechanics (F_s), Saturated Unit Weight of Soil (γ_saturated), Depth of Prism (z), Angle of Inclination to Horizontal in Soil (i), Cohesion in Soil as Kilopascal (C) & Angle of Internal Friction of Soil (Φ_i) we can find Submerged Unit Weight for Steady Seepage along Slope using the formula - Submerged Unit Weight in KN per Cubic Meter = ((Factor of Safety in Soil Mechanics*Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))-Cohesion in Soil as Kilopascal)/(Depth of Prism*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 , Sine (sin), 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 for Steady Seepage along Slope be negative?

No, the Submerged Unit Weight for Steady Seepage along Slope, measured in Specific Weight cannot be negative.

Which unit is used to measure Submerged Unit Weight for Steady Seepage along Slope?

Submerged Unit Weight for Steady Seepage along Slope 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 for Steady Seepage along Slope can be measured.

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Submerged Unit Weight for Steady Seepage along Slope Formula

​GoSubmerged Unit Weight given Effective Normal Stress Formula

​GoSubmerged Unit Weight given Upward Force Formula

Submerged Unit Weight for Steady Seepage along Slope Example

Submerged Unit Weight for Steady Seepage along Slope Solution

Submerged Unit Weight for Steady Seepage along Slope 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 for Steady Seepage along Slope?

FAQs on Submerged Unit Weight for Steady Seepage along Slope

Variable Name

GoSubmerged Unit Weight given Effective Normal Stress Formula

GoSubmerged Unit Weight given Upward Force Formula