Submerged Unit Weight given Critical Depth Calculator

✖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.ⓘ Cohesion of Soil [C_s]			+10% -10%
✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%
✖The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge.ⓘ Critical Depth [h_c]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%

✖Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.ⓘ Submerged Unit Weight given Critical Depth [γ^']

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Submerged Unit Weight given Critical Depth Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
γ^' = (C_s*(sec((i)))^2)/(h_c*(tan((i))-tan((φ))))
This formula uses 2 Functions, 5 Variables

Functions Used

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., 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., sec(Angle)

Variables Used

Submerged Unit Weight - (Measured in Newton per Cubic Meter) - Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.
Cohesion of Soil - (Measured in Kilopascal) - 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.
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.
Critical Depth - (Measured in Meter) - The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .

STEP 1: Convert Input(s) to Base Unit

Cohesion of Soil: 5 Kilopascal --> 5 Kilopascal No Conversion Required
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)
Critical Depth: 1.01 Meter --> 1.01 Meter No Conversion Required
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ^' = (C_s*(sec((i)))^2)/(h_c*(tan((i))-tan((φ)))) --> (5*(sec((1.11701072127616)))^2)/(1.01*(tan((1.11701072127616))-tan((0.802851455917241))))

Evaluating ... ...

γ^' = 25.386076132446

STEP 3: Convert Result to Output's Unit

25.386076132446 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

25.386076132446 ≈ 25.38608 Newton per Cubic Meter <-- Submerged Unit Weight

(Calculation completed in 00.020 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< Stability Analysis of Submerged Slopes Calculators

Shear Stress Component given Submerged Unit Weight

LaTeX Go Shear Stress for Submerged Slopes = (Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Normal Stress Component

LaTeX Go Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)

Depth of Prism given Submerged Unit Weight

LaTeX Go Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)

Normal Stress Component given Submerged Unit Weight

LaTeX Go Normal Stress = Submerged Unit Weight*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2

Submerged Unit Weight given Critical Depth Formula

LaTeX Go

What is Submerged Unit Weight?

The weight of the solids in air minus the weight of water displaced by the solids per unit of volume of soil mass; the saturated unit weight minus the unit weight of water.

How to Calculate Submerged Unit Weight given Critical Depth?

Submerged Unit Weight given Critical Depth calculator 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 calculate 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 calculate Submerged Unit Weight given Critical Depth using this online calculator? To use this online calculator 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. Here is how the Submerged Unit Weight given Critical Depth calculation can be explained with given input values -> 25.38608 = (5000*(sec((1.11701072127616)))^2)/(1.01*(tan((1.11701072127616))-tan((0.802851455917241)))).

FAQ

What is Submerged Unit Weight given Critical Depth?

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 and is represented as γ^' = (C_s*(sec((i)))^2)/(h_c*(tan((i))-tan((φ)))) or 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)))). 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, Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object, The Critical Depth is defined as the depth of flow where energy is at a minimum for a particular discharge & Angle of Internal Friction is the angle measured between the normal force and resultant force .

How to calculate Submerged Unit Weight given Critical Depth?

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 is calculated using 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 calculate Submerged Unit Weight given Critical Depth, you need Cohesion of Soil (C_s), Angle of Inclination to Horizontal in Soil (i), Critical Depth (h_c) & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Cohesion of Soil, Angle of Inclination to Horizontal in Soil, Critical Depth & Angle of Internal Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Submerged Unit Weight?

In this formula, Submerged Unit Weight uses Cohesion of Soil, Angle of Inclination to Horizontal in Soil, Critical Depth & Angle of Internal Friction. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))))

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