Shear Stress given Friction Factor and Density Calculator

✖Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.ⓘ Density of Fluid [ρ_Fluid]			+10% -10%
✖Darcy Friction Factor is denoted by f. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D. It can be obtained from Moody's chart.ⓘ Darcy Friction Factor [f]			+10% -10%
✖Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.ⓘ Mean Velocity [V_mean]			+10% -10%

✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress given Friction Factor and Density [𝜏]

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Formula

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Shear Stress given Friction Factor and Density

Formula

`"𝜏" = "ρ"_{"Fluid"}*"f"*"V"_{"mean"}*"V"_{"mean"}/8`

Example

`"78.10141Pa"="1.225kg/m³"*"5"*"10.1m/s"*"10.1m/s"/8`

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Shear Stress given Friction Factor and Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8
𝜏 = ρ_Fluid*f*V_mean*V_mean/8
This formula uses 4 Variables

Variables Used

Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Density of Fluid - (Measured in Kilogram per Cubic Meter) - Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.
Darcy Friction Factor - Darcy Friction Factor is denoted by f. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D. It can be obtained from Moody's chart.
Mean Velocity - (Measured in Meter per Second) - Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.

STEP 1: Convert Input(s) to Base Unit

Density of Fluid: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Darcy Friction Factor: 5 --> No Conversion Required
Mean Velocity: 10.1 Meter per Second --> 10.1 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = ρ_Fluid*f*V_mean*V_mean/8 --> 1.225*5*10.1*10.1/8

Evaluating ... ...

𝜏 = 78.10140625

STEP 3: Convert Result to Output's Unit

78.10140625 Pascal --> No Conversion Required

FINAL ANSWER

78.10140625 ≈ 78.10141 Pascal <-- Shear Stress

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law » Darcy – Weisbach Equation » Shear Stress given Friction Factor and Density

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National Institute of Technology Karnataka (NITK), Surathkal

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< 14 Darcy – Weisbach Equation Calculators

Diameter of Pipe given Head Loss due to Frictional Resistance

Go Diameter of Pipe = Darcy Friction Factor*Length of Pipe*(Mean Velocity^2)/(2*[g]*Head Loss due to Friction)

Length of Pipe given Head Loss due to Frictional Resistance

Go Length of Pipe = (Head Loss due to Friction*2*[g]*Diameter of Pipe)/(Darcy Friction Factor*Mean Velocity*2)

Head Loss due to Frictional Resistance

Go Head Loss due to Friction = Darcy Friction Factor*Length of Pipe*(Mean Velocity^2)/(2*[g]*Diameter of Pipe)

Diameter of Pipe given Friction Factor

Go Diameter of Pipe = (64*Dynamic Viscosity)/(Darcy Friction Factor*Mean Velocity*Density of Fluid)

Dynamic Viscosity given Friction Factor

Go Dynamic Viscosity = (Darcy Friction Factor*Mean Velocity*Diameter of Pipe*Density of Fluid)/64

Density of Fluid given Friction Factor

Go Density of Fluid = Dynamic Viscosity*64/(Darcy Friction Factor*Diameter of Pipe*Mean Velocity)

Density of Liquid given Shear Stress and Darcy Friction Factor

Go Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*Mean Velocity*Mean Velocity)

Pressure Gradient given Total Required Power

Go Pressure Gradient = Power/(Length of Pipe*Cross Sectional Area of Pipe*Mean Velocity)

Area of Pipe given Total Required Power

Go Cross Sectional Area of Pipe = Power/(Length of Pipe*Pressure Gradient*Mean Velocity)

Shear Stress given Friction Factor and Density

Go Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8

Total Required Power

Go Power = Pressure Gradient*Cross Sectional Area of Pipe*Mean Velocity*Length of Pipe

Density of Liquid using Mean Velocity given Shear Stress with Friction Factor

Go Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2))

Shear Velocity

Go Shear Velocity = Mean Velocity*sqrt(Darcy Friction Factor/8)

Reynolds Number given Friction Factor

Go Reynolds Number = 64/Darcy Friction Factor

Shear Stress given Friction Factor and Density Formula

Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8
𝜏 = ρ_Fluid*f*V_mean*V_mean/8

What is Friction Factor ?

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow.

How to Calculate Shear Stress given Friction Factor and Density?

Shear Stress given Friction Factor and Density calculator uses Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8 to calculate the Shear Stress, The Shear Stress given Friction Factor and Density is defined as stress or resistance offered to the fluid due to friction. Shear Stress is denoted by 𝜏 symbol.

How to calculate Shear Stress given Friction Factor and Density using this online calculator? To use this online calculator for Shear Stress given Friction Factor and Density, enter Density of Fluid (ρ_Fluid), Darcy Friction Factor (f) & Mean Velocity (V_mean) and hit the calculate button. Here is how the Shear Stress given Friction Factor and Density calculation can be explained with given input values -> 78.10141 = 1.225*5*10.1*10.1/8.

FAQ

What is Shear Stress given Friction Factor and Density?

The Shear Stress given Friction Factor and Density is defined as stress or resistance offered to the fluid due to friction and is represented as 𝜏 = ρ_Fluid*f*V_mean*V_mean/8 or Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8. Density of Fluid is defined as the mass of fluid per unit volume of the said fluid, Darcy Friction Factor is denoted by f. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D. It can be obtained from Moody's chart & Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.

How to calculate Shear Stress given Friction Factor and Density?

The Shear Stress given Friction Factor and Density is defined as stress or resistance offered to the fluid due to friction is calculated using Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8. To calculate Shear Stress given Friction Factor and Density, you need Density of Fluid (ρ_Fluid), Darcy Friction Factor (f) & Mean Velocity (V_mean). With our tool, you need to enter the respective value for Density of Fluid, Darcy Friction Factor & Mean Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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