Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate Calculator

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✖Fluid density for boundary layer flow is defined as the mass of fluid per unit volume of the fluid.ⓘ Fluid Density for Boundary Layer Flow [ρ_f]			+10% -10%
✖Freestream velocity for boundary layer flow is the velocity of fluid far upstream of a body, that is before the body has a chance to deflect, slow down the fluid.ⓘ Freestream Velocity for Boundary Layer Flow [V_∞]			+10% -10%
✖Viscosity of Fluid for boundary layer flow is a measure of fluid's resistance to deformation at a given rate.ⓘ Viscosity of Fluid for Boundary Layer Flow [μ]			+10% -10%
✖The Thickness of Boundary Layer is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity.ⓘ Thickness of Boundary Layer [𝛿]			+10% -10%

✖Shear stress for boundary layer flow is force tending to cause deformation of the fluid by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate [𝜏]

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Formula

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Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate

Formula

`"𝜏" = 0.0225*"ρ"_{"f"}*"V"_{"∞"}^2*("μ"/("ρ"_{"f"}*"V"_{"∞"}*"𝛿"))^(1/4)`

Example

`"0.068526N/m²"=0.0225*"890kg/m³"*("0.15m/s")^2*("0.001N*s/m²"/("890kg/m³"*"0.15m/s"*"0.014m"))^(1/4)`

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Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Stress for Boundary Layer Flow = 0.0225*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2*(Viscosity of Fluid for Boundary Layer Flow/(Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*Thickness of Boundary Layer))^(1/4)
𝜏 = 0.0225*ρ_f*V_∞^2*(μ/(ρ_f*V_∞*𝛿))^(1/4)
This formula uses 5 Variables

Variables Used

Shear Stress for Boundary Layer Flow - (Measured in Pascal) - Shear stress for boundary layer flow is force tending to cause deformation of the fluid by slippage along a plane or planes parallel to the imposed stress.
Fluid Density for Boundary Layer Flow - (Measured in Kilogram per Cubic Meter) - Fluid density for boundary layer flow is defined as the mass of fluid per unit volume of the fluid.
Freestream Velocity for Boundary Layer Flow - (Measured in Meter per Second) - Freestream velocity for boundary layer flow is the velocity of fluid far upstream of a body, that is before the body has a chance to deflect, slow down the fluid.
Viscosity of Fluid for Boundary Layer Flow - (Measured in Pascal Second) - Viscosity of Fluid for boundary layer flow is a measure of fluid's resistance to deformation at a given rate.
Thickness of Boundary Layer - (Measured in Meter) - The Thickness of Boundary Layer is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity.

STEP 1: Convert Input(s) to Base Unit

Fluid Density for Boundary Layer Flow: 890 Kilogram per Cubic Meter --> 890 Kilogram per Cubic Meter No Conversion Required
Freestream Velocity for Boundary Layer Flow: 0.15 Meter per Second --> 0.15 Meter per Second No Conversion Required
Viscosity of Fluid for Boundary Layer Flow: 0.001 Newton Second per Square Meter --> 0.001 Pascal Second (Check conversion here)
Thickness of Boundary Layer: 0.014 Meter --> 0.014 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = 0.0225*ρ_f*V_∞^2*(μ/(ρ_f*V_∞*𝛿))^(1/4) --> 0.0225*890*0.15^2*(0.001/(890*0.15*0.014))^(1/4)

Evaluating ... ...

𝜏 = 0.0685255795945798

STEP 3: Convert Result to Output's Unit

0.0685255795945798 Pascal -->0.0685255795945798 Newton per Square Meter (Check conversion here)

FINAL ANSWER

0.0685255795945798 ≈ 0.068526 Newton per Square Meter <-- Shear Stress for Boundary Layer Flow

(Calculation completed in 00.020 seconds)

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PSG College of Technology (PSGCT), Coimbatore

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< 21 Boundary Layer Flow Calculators

Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate

Go Shear Stress for Boundary Layer Flow = 0.0225*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2*(Viscosity of Fluid for Boundary Layer Flow/(Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*Thickness of Boundary Layer))^(1/4)

Viscosity of Liquid for Drag Force on Plate

Go Viscosity of Fluid for Boundary Layer Flow = Drag Force on Boundary Layer Flow Plate/(0.73*Breadth of Plate for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*sqrt(Reynolds Number for Boundary Layer Flow))

Width of Plate for Drag Force on Plate

Go Breadth of Plate for Boundary Layer Flow = Drag Force on Boundary Layer Flow Plate/(0.73*Viscosity of Fluid for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*sqrt(Reynolds Number for Boundary Layer Flow))

Drag Force on Plate

Go Drag Force on Boundary Layer Flow Plate = 0.73*Breadth of Plate for Boundary Layer Flow*Viscosity of Fluid for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*sqrt(Reynolds Number for Boundary Layer Flow)

Reynold Number for Drag Force on Plate

Go Reynolds Number for Boundary Layer Flow = (Drag Force on Boundary Layer Flow Plate/(0.73*Breadth of Plate for Boundary Layer Flow*Viscosity of Fluid for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow))^2

Area of Surface for Average Drag Coefficient

Go Area of Surface for Boundary Layer Flow = Drag Force on Boundary Layer Flow Plate/(1/2*Coefficient of Drag for Boundary Layer Flow*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2)

Average Coefficient of Drag for Drag Force

Go Coefficient of Drag for Boundary Layer Flow = Drag Force on Boundary Layer Flow Plate/(1/2*Fluid Density for Boundary Layer Flow*Area of Surface for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2)

Drag Force for Average Drag Coefficient

Go Drag Force on Boundary Layer Flow Plate = 1/2*Coefficient of Drag for Boundary Layer Flow*Fluid Density for Boundary Layer Flow*Area of Surface for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2

Velocity of Fluid for Reynold Number

Go Freestream Velocity for Boundary Layer Flow = (Reynolds Number for Boundary Layer Flow*Viscosity of Fluid for Boundary Layer Flow)/(Fluid Density for Boundary Layer Flow*Length of Plate for Boundary Layer Flow)

Length of Plate for Reynold Number

Go Length of Plate for Boundary Layer Flow = (Reynolds Number for Boundary Layer Flow*Viscosity of Fluid for Boundary Layer Flow)/(Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow)

Reynold Number at End of Plate

Go Reynolds Number for Boundary Layer Flow = (Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*Length of Plate for Boundary Layer Flow)/Viscosity of Fluid for Boundary Layer Flow

Freestream Velocity for Local Drag Coefficient

Go Freestream Velocity for Boundary Layer Flow = sqrt(Shear Stress for Boundary Layer Flow/(1/2*Fluid Density for Boundary Layer Flow*Local Drag Coefficient for Boundary Layer))

Local Drag Coefficient for Shear Stress

Go Local Drag Coefficient for Boundary Layer = Shear Stress for Boundary Layer Flow/(1/2*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2)

Shear Stress for Local Drag Coefficient

Go Shear Stress for Boundary Layer Flow = 1/2*Local Drag Coefficient for Boundary Layer*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2

Thickness of Boundary Layer for Blasius's Solution

Go Thickness of Boundary Layer = (4.91*Distance Leading Edge for Boundary Layer Flow)/(sqrt(Reynolds Number for Boundary Layer Flow))

Thickness of Boundary Layer

Go Thickness of Boundary Layer = (5.48*Distance Leading Edge for Boundary Layer Flow)/(sqrt(Reynolds Number for Boundary Layer Flow))

Distance from Leading Edge

Go Distance Leading Edge for Boundary Layer Flow = Thickness of Boundary Layer*(sqrt(Reynolds Number for Boundary Layer Flow))/5.48

Distance from Leading Edge for Blasius's Solution

Go Distance Leading Edge for Boundary Layer Flow = Thickness of Boundary Layer*sqrt(Reynolds Number for Boundary Layer Flow)/4.91

Coefficient of Drag for Blasius's Solution

Go Coefficient of Drag for Boundary Layer Flow = 1.328/(sqrt(Reynolds Number for Boundary Layer Flow))

Coefficient of Drag for Reynold Number

Go Coefficient of Drag for Boundary Layer Flow = 1.46/sqrt(Reynolds Number for Boundary Layer Flow)

Reynold Number for Drag Coefficient in Blasius's Solution

Go Reynolds Number for Boundary Layer Flow = (1.328/Coefficient of Drag for Boundary Layer Flow)^2

Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate Formula

What are the two types of flow associated with the boundary layer?

There are two different types of boundary layer flow: laminar and turbulent. The laminar boundary is a very smooth flow, while the turbulent boundary layer contains swirls or "eddies." The laminar flow creates less skin friction drag than the turbulent flow but is less stable.

Why does the thickness of boundary layer increase?

When the incoming uniform flow flows over a flat plate, the fluid particles near the plate will stick to the plate (no-slip condition). That means that the momentum of the flat plate is diffused to the fluid. And hence the boundary layer thickness increases as the fluid moves downstream.

How to Calculate Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate?

Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate calculator uses Shear Stress for Boundary Layer Flow = 0.0225*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2*(Viscosity of Fluid for Boundary Layer Flow/(Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*Thickness of Boundary Layer))^(1/4) to calculate the Shear Stress for Boundary Layer Flow, The Shear stress at boundary for turbulent boundary layer over flat plate formula is known while considering the density of the fluid, freestream velocity, viscosity of the fluid, and the thickness of the boundary layer. Shear Stress for Boundary Layer Flow is denoted by 𝜏 symbol.

How to calculate Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate using this online calculator? To use this online calculator for Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate, enter Fluid Density for Boundary Layer Flow (ρ_f), Freestream Velocity for Boundary Layer Flow (V_∞), Viscosity of Fluid for Boundary Layer Flow (μ) & Thickness of Boundary Layer (𝛿) and hit the calculate button. Here is how the Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate calculation can be explained with given input values -> 0.068526 = 0.0225*890*0.15^2*(0.001/(890*0.15*0.014))^(1/4).

FAQ

What is Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate?

The Shear stress at boundary for turbulent boundary layer over flat plate formula is known while considering the density of the fluid, freestream velocity, viscosity of the fluid, and the thickness of the boundary layer and is represented as 𝜏 = 0.0225*ρ_f*V_∞^2*(μ/(ρ_f*V_∞*𝛿))^(1/4) or Shear Stress for Boundary Layer Flow = 0.0225*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2*(Viscosity of Fluid for Boundary Layer Flow/(Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*Thickness of Boundary Layer))^(1/4). Fluid density for boundary layer flow is defined as the mass of fluid per unit volume of the fluid, Freestream velocity for boundary layer flow is the velocity of fluid far upstream of a body, that is before the body has a chance to deflect, slow down the fluid, Viscosity of Fluid for boundary layer flow is a measure of fluid's resistance to deformation at a given rate & The Thickness of Boundary Layer is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity.

How to calculate Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate?

The Shear stress at boundary for turbulent boundary layer over flat plate formula is known while considering the density of the fluid, freestream velocity, viscosity of the fluid, and the thickness of the boundary layer is calculated using Shear Stress for Boundary Layer Flow = 0.0225*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2*(Viscosity of Fluid for Boundary Layer Flow/(Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow*Thickness of Boundary Layer))^(1/4). To calculate Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate, you need Fluid Density for Boundary Layer Flow (ρ_f), Freestream Velocity for Boundary Layer Flow (V_∞), Viscosity of Fluid for Boundary Layer Flow (μ) & Thickness of Boundary Layer (𝛿). With our tool, you need to enter the respective value for Fluid Density for Boundary Layer Flow, Freestream Velocity for Boundary Layer Flow, Viscosity of Fluid for Boundary Layer Flow & Thickness of Boundary Layer 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 Shear Stress for Boundary Layer Flow?

In this formula, Shear Stress for Boundary Layer Flow uses Fluid Density for Boundary Layer Flow, Freestream Velocity for Boundary Layer Flow, Viscosity of Fluid for Boundary Layer Flow & Thickness of Boundary Layer. We can use 1 other way(s) to calculate the same, which is/are as follows -

Shear Stress for Boundary Layer Flow = 1/2*Local Drag Coefficient for Boundary Layer*Fluid Density for Boundary Layer Flow*Freestream Velocity for Boundary Layer Flow^2

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