Shear Stress Distribution Profile Calculator

✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%
✖Width is the measurement or extent of something from side to side.ⓘ Width [w]			+10% -10%
✖Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.ⓘ Horizontal Distance [R]			+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 Distribution Profile [𝜏]

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Formula

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Shear Stress Distribution Profile

Formula

`"𝜏" = -"dp|dr"*("w"/2-"R")`

Example

`"91.8Pa"=-"17N/m³"*("3m"/2-"6.9m")`

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Download Laminar Flow between Parallel Plates, both plates at rest Formulas PDF

Shear Stress Distribution Profile Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance)
𝜏 = -dp|dr*(w/2-R)
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.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Width - (Measured in Meter) - Width is the measurement or extent of something from side to side.
Horizontal Distance - (Measured in Meter) - Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.

STEP 1: Convert Input(s) to Base Unit

Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required
Width: 3 Meter --> 3 Meter No Conversion Required
Horizontal Distance: 6.9 Meter --> 6.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = -dp|dr*(w/2-R) --> -17*(3/2-6.9)

Evaluating ... ...

𝜏 = 91.8

STEP 3: Convert Result to Output's Unit

91.8 Pascal --> No Conversion Required

FINAL ANSWER

91.8 Pascal <-- Shear Stress

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< 20 Laminar Flow between Parallel Plates, both plates at rest Calculators

Distance between Plates given Pressure Head Drop

Go Width = sqrt((12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid*Head Loss due to Friction))

Length of Pipe given Pressure Head Drop

Go Length of Pipe = (Specific Weight of Liquid*Width*Width*Head Loss due to Friction)/(12*Dynamic Viscosity*Mean Velocity)

Velocity Distribution Profile

Go Velocity of Liquid = -(1/(2*Dynamic Viscosity))*Pressure Gradient*(Width*Horizontal Distance-(Horizontal Distance^2))

Distance between Plates using Velocity Distribution Profile

Go Width = (((-Velocity of Liquid*2*Dynamic Viscosity)/Pressure Gradient)+(Horizontal Distance^2))/Horizontal Distance

Length of Pipe given Pressure Difference

Go Length of Pipe = (Pressure Difference*Width*Width)/(Dynamic Viscosity*12*Mean Velocity)

Distance between Plates given Pressure Difference

Go Width = sqrt(12*Mean Velocity*Dynamic Viscosity*Length of Pipe/Pressure Difference)

Pressure Head Drop

Go Head Loss due to Friction = (12*Dynamic Viscosity*Length of Pipe*Mean Velocity)/(Specific Weight of Liquid)

Pressure Difference

Go Pressure Difference = 12*Dynamic Viscosity*Mean Velocity*Length of Pipe/(Width^2)

Distance between Plates given Maximum Velocity between Plates

Go Width = sqrt((8*Dynamic Viscosity*Maximum Velocity)/(Pressure Gradient))

Distance between Plates given Mean Velocity of Flow with Pressure Gradient

Go Width = sqrt((12*Dynamic Viscosity*Mean Velocity)/Pressure Gradient)

Distance between Plates given Discharge

Go Width = ((Discharge in Laminar Flow*12*Dynamic Viscosity)/Pressure Gradient)^(1/3)

Discharge given Viscosity

Go Discharge in Laminar Flow = Pressure Gradient*(Width^3)/(12*Dynamic Viscosity)

Maximum Velocity between Plates

Go Maximum Velocity = ((Width^2)*Pressure Gradient)/(8*Dynamic Viscosity)

Distance between Plates given Shear Stress Distribution Profile

Go Width = 2*(Horizontal Distance-(Shear Stress/Pressure Gradient))

Shear Stress Distribution Profile

Go Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance)

Horizontal Distance given Shear Stress Distribution Profile

Go Horizontal Distance = Width/2+(Shear Stress/Pressure Gradient)

Maximum Shear Stress in fluid

Go Maximum Shear Stress in Shaft = 0.5*Pressure Gradient*Width

Distance between Plates given Mean Velocity of Flow

Go Width = Discharge in Laminar Flow/Mean Velocity

Discharge given Mean Velocity of Flow

Go Discharge in Laminar Flow = Width*Mean Velocity

Maximum Velocity given Mean Velocity of Flow

Go Maximum Velocity = 1.5*Mean Velocity

Shear Stress Distribution Profile Formula

Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance)
𝜏 = -dp|dr*(w/2-R)

What is Roughness?

Roughness often shortened to roughness, is a component of surface texture. It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small, the surface is smooth.

How to Calculate Shear Stress Distribution Profile?

Shear Stress Distribution Profile calculator uses Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance) to calculate the Shear Stress, The Shear Stress Distribution Profile is defined as the stress or resistance developed due to boundary condition and roughness of pipe. Shear Stress is denoted by 𝜏 symbol.

How to calculate Shear Stress Distribution Profile using this online calculator? To use this online calculator for Shear Stress Distribution Profile, enter Pressure Gradient (dp|dr), Width (w) & Horizontal Distance (R) and hit the calculate button. Here is how the Shear Stress Distribution Profile calculation can be explained with given input values -> 91.8 = -17*(3/2-6.9).

FAQ

What is Shear Stress Distribution Profile?

The Shear Stress Distribution Profile is defined as the stress or resistance developed due to boundary condition and roughness of pipe and is represented as 𝜏 = -dp|dr*(w/2-R) or Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance). Pressure Gradient is the change in pressure with respect to radial distance of element, Width is the measurement or extent of something from side to side & Horizontal Distance denotes the instantaneous horizontal distance cover by an object in a projectile motion.

How to calculate Shear Stress Distribution Profile?

The Shear Stress Distribution Profile is defined as the stress or resistance developed due to boundary condition and roughness of pipe is calculated using Shear Stress = -Pressure Gradient*(Width/2-Horizontal Distance). To calculate Shear Stress Distribution Profile, you need Pressure Gradient (dp|dr), Width (w) & Horizontal Distance (R). With our tool, you need to enter the respective value for Pressure Gradient, Width & Horizontal Distance 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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