Unit Weight of Water given Effective Normal Stress Calculator

✖Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.ⓘ Saturated Unit Weight of Soil [γ_saturated]			+10% -10%
✖Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.ⓘ Effective Normal Stress in Soil Mechanics [σ^']			+10% -10%
✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism [z]			+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%

✖Unit Weight of Water is mass per unit of water.ⓘ Unit Weight of Water given Effective Normal Stress [γ_water]

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Formula

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Unit Weight of Water given Effective Normal Stress

Formula

`"γ"_{"water"} = "γ"_{"saturated"}-("σ"^{"'"}/("z"*(cos(("i"*pi)/180))^2))`

Example

`"3.66354kN/m³"="11.89kN/m³"-("24.67kN/m²"/("3m"*(cos(("64°"*pi)/180))^2))`

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Unit Weight of Water given Effective Normal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
γ_water = γ_saturated-(σ^'/(z*(cos((i*pi)/180))^2))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Unit Weight of Water - (Measured in Newton per Cubic Meter) - Unit Weight of Water is mass per unit of water.
Saturated Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.
Effective Normal Stress in Soil Mechanics - (Measured in Pascal) - Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
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.

STEP 1: Convert Input(s) to Base Unit

Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)
Effective Normal Stress in Soil Mechanics: 24.67 Kilonewton per Square Meter --> 24670 Pascal (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ_water = γ_saturated-(σ^'/(z*(cos((i*pi)/180))^2)) --> 11890-(24670/(3*(cos((1.11701072127616*pi)/180))^2))

Evaluating ... ...

γ_water = 3663.54039031203

STEP 3: Convert Result to Output's Unit

3663.54039031203 Newton per Cubic Meter -->3.66354039031203 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

3.66354039031203 ≈ 3.66354 Kilonewton per Cubic Meter <-- Unit Weight of Water

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Seepage Analysis » Steady State Seepage Analysis Along The Slopes » Unit Weight of Water given Effective Normal Stress

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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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< 25 Steady State Seepage Analysis Along The Slopes Calculators

Factor of Safety for Cohesive Soil given Saturated Unit Weight

Go Factor of Safety in Soil Mechanics = (Effective Cohesion+(Submerged Unit Weight*Depth of Prism*tan((Angle of Internal Friction))*(cos((Angle of Inclination to Horizontal in Soil)))^2))/(Saturated Unit Weight in Newton per Cubic Meter*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Shear Strength given Submerged Unit Weight

Go Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Factor of Safety

Go 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)))

Factor of Safety given Submerged Unit Weight

Go Factor of Safety in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Submerged Unit Weight given Shear Strength

Go Submerged Unit Weight in KN per Cubic Meter = (Shear Strength in KN per Cubic Meter/Shear Stress in Soil Mechanics)/((tan((Angle of Internal Friction of Soil)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress given Submerged Unit Weight

Go Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Shear Stress Component given Saturated Unit Weight

Go Shear Stress 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))

Submerged Unit Weight given Upward Force

Go 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)

Normal Stress Component given Submerged Unit Weight and Depth of Prism

Go Normal Stress in Soil Mechanics = Upward Force in Seepage Analysis+(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water given Submerged Unit Weight

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

Effective Normal Stress given Saturated Unit Weight

Go Effective Normal Stress in Soil Mechanics = ((Saturated Unit Weight of Soil-Unit Weight of Water)*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Effective Normal Stress

Go Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))

Inclined Length of Prism given Saturated Unit Weight

Go Inclined Length of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Weight of Soil Prism given Saturated Unit Weight

Go Weight of Prism in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Effective Normal Stress given Submerged Unit Weight

Go Effective Normal Stress in Soil Mechanics = (Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Submerged Unit Weight given Effective Normal Stress

Go 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)

Effective Normal Stress given Factor of Safety

Go Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics)

Factor of Safety given Effective Normal Stress

Go Factor of Safety in Soil Mechanics = (Effective Normal Stress in Soil Mechanics*tan((Angle of Internal Friction*pi)/180))/Shear Stress in Soil Mechanics

Vertical Stress on Prism given Saturated Unit Weight

Go Vertical Stress at a Point in Kilopascal = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Normal Stress Component given Saturated Unit Weight

Go Normal Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Unit Weight of Water given Upward Force due to Seepage Water

Go Unit Weight of Water = Upward Force in Seepage Analysis/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Upward Force due to Seepage Water

Go Upward Force in Seepage Analysis = (Unit Weight of Water*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Effective Normal Stress given Upward Force due to Seepage Water

Go Effective Normal Stress in Soil Mechanics = Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis

Upward Force due to Seepage Water given Effective Normal Stress

Go Upward Force in Seepage Analysis = Normal Stress in Soil Mechanics-Effective Normal Stress in Soil Mechanics

Normal Stress Component given Effective Normal Stress

Go Normal Stress in Soil Mechanics = Effective Normal Stress in Soil Mechanics+Upward Force in Seepage Analysis

Unit Weight of Water given Effective Normal Stress Formula

What is Unit Weight of Water?

The specific weight, also known as the unit weight, is the weight per unit volume of a material. A commonly used value is the specific weight of water on Earth at 4°C, which is 9.807 kN/m3 or 62.43 lbf/ft3.

How to Calculate Unit Weight of Water given Effective Normal Stress?

Unit Weight of Water given Effective Normal Stress calculator uses Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)) to calculate the Unit Weight of Water, The Unit Weight of Water given Effective Normal Stress is defined as the value of unit weight of water when we have prior information of other parameters used. Unit Weight of Water is denoted by γ_water symbol.

How to calculate Unit Weight of Water given Effective Normal Stress using this online calculator? To use this online calculator for Unit Weight of Water given Effective Normal Stress, enter Saturated Unit Weight of Soil (γ_saturated), Effective Normal Stress in Soil Mechanics (σ^'), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Unit Weight of Water given Effective Normal Stress calculation can be explained with given input values -> 0.009774 = 11890-(24670/(3*(cos((1.11701072127616*pi)/180))^2)).

FAQ

What is Unit Weight of Water given Effective Normal Stress?

The Unit Weight of Water given Effective Normal Stress is defined as the value of unit weight of water when we have prior information of other parameters used and is represented as γ_water = γ_saturated-(σ^'/(z*(cos((i*pi)/180))^2)) or Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)). Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume, Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure, Depth of Prism is the length of prism along z direction & Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

How to calculate Unit Weight of Water given Effective Normal Stress?

The Unit Weight of Water given Effective Normal Stress is defined as the value of unit weight of water when we have prior information of other parameters used is calculated using Unit Weight of Water = Saturated Unit Weight of Soil-(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)). To calculate Unit Weight of Water given Effective Normal Stress, you need Saturated Unit Weight of Soil (γ_saturated), Effective Normal Stress in Soil Mechanics (σ^'), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Saturated Unit Weight of Soil, Effective Normal Stress in Soil Mechanics, Depth of Prism & Angle of Inclination to Horizontal in Soil 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 Unit Weight of Water?

In this formula, Unit Weight of Water uses Saturated Unit Weight of Soil, Effective Normal Stress in Soil Mechanics, Depth of Prism & Angle of Inclination to Horizontal in Soil. We can use 1 other way(s) to calculate the same, which is/are as follows -

Unit Weight of Water = Upward Force in Seepage Analysis/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

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