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Critical Depth given Saturated 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}{(γ saturated \cdot \tan (\frac{i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}) - (y S \cdot \tan (\frac{φ \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})}

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

Critical Depth given Saturated Unit Weight Example

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

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

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

7.8539 = \frac{1.27}{(11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}) - (5 \cdot \tan (\frac{46 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})}

7.8539m = \frac{1.27kPa}{(11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}) - (5kN/m³ \cdot \tan (\frac{46° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})}

7.8539 = \frac{1.27}{(11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}) - (5 \cdot \tan (\frac{46 \cdot 3.1416}{180}) \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})}

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Critical Depth given Saturated Unit Weight Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h c = \frac{1.27kPa}{(11.89kN/m³ \cdot \tan (\frac{64° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}) - (5kN/m³ \cdot \tan (\frac{46° \cdot π}{180}) \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2})}

Next Step Substitute values of Constants

∴

h c = \frac{1.27kPa}{(11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}) - (5kN/m³ \cdot \tan (\frac{46° \cdot 3.1416}{180}) \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})}

Next Step Convert Units

∴

h c = \frac{1270Pa}{(11890N/m³ \cdot \tan (\frac{1.117rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}) - (5000N/m³ \cdot \tan (\frac{0.8029rad \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2})}

Next Step Prepare to Evaluate

∴

h c = \frac{1270}{(11890 \cdot \tan (\frac{1.117 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}) - (5000 \cdot \tan (\frac{0.8029 \cdot 3.1416}{180}) \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2})}

Next Step Evaluate

∴

h c = 7.85390614906757m

LAST Step Rounding Answer

∴

h c = 7.8539m

Critical Depth given Saturated Unit Weight Formula Elements

Variables

Constants

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 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

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

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

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

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 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 Critical Depth given Saturated Unit Weight?

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

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

FAQs on Critical Depth given Saturated Unit Weight

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

The formula of Critical Depth given Saturated Unit Weight is expressed as Critical Depth = Cohesion in Soil as Kilopascal/((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)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)). Here is an example- 7.853906 = 1270/((11890*tan((1.11701072127616*pi)/180)*(cos((1.11701072127616*pi)/180))^2)-(5000*tan((0.802851455917241*pi)/180)*(cos((1.11701072127616*pi)/180))^2)).

How to calculate Critical Depth given Saturated Unit Weight?

With Cohesion in Soil as Kilopascal (C), Saturated Unit Weight of Soil (γ_saturated), Angle of Inclination to Horizontal in Soil (i), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Internal Friction (φ) we can find Critical Depth given Saturated Unit Weight using the formula - Critical Depth = Cohesion in Soil as Kilopascal/((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)-(Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*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).

Can the Critical Depth given Saturated Unit Weight be negative?

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

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

Critical Depth given Saturated 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 Saturated Unit Weight can be measured.

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Critical Depth given Saturated Unit Weight Formula

Critical Depth given Saturated Unit Weight Example

Critical Depth given Saturated Unit Weight Solution

Critical Depth given Saturated Unit Weight Formula Elements

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Critical Depth given Saturated Unit Weight?

FAQs on Critical Depth given Saturated Unit Weight

Variable Name