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

GoShear Stress for Local Drag Coefficient Formula

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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. Check FAQs

𝜏 = 0.0225 \cdot ρ f \cdot {V ∞}^{2} \cdot {(\frac{μ}{ρ f \cdot V ∞ \cdot 𝛿})}^{\frac{1}{4}}

𝜏 - Shear Stress for Boundary Layer Flow?ρ_f - Fluid Density for Boundary Layer Flow?V_∞ - Freestream Velocity for Boundary Layer Flow?μ - Viscosity of Fluid for Boundary Layer Flow?𝛿 - Thickness of Boundary Layer?

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

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Here is how the Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate equation looks like with Values.

Here is how the Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate equation looks like with Units.

Here is how the Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate equation looks like.

0.0685 = 0.0225 \cdot 890 \cdot {0.15}^{2} \cdot {(\frac{0.001}{890 \cdot 0.15 \cdot 0.014})}^{\frac{1}{4}}

0.0685N/m² = 0.0225 \cdot 890kg/m³ \cdot {0.15m/s}^{2} \cdot {(\frac{0.001N*s/m²}{890kg/m³ \cdot 0.15m/s \cdot 0.014m})}^{\frac{1}{4}}

0.0685 = 0.0225 \cdot 890 \cdot {0.15}^{2} \cdot {(\frac{0.001}{890 \cdot 0.15 \cdot 0.014})}^{\frac{1}{4}}

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

Follow our step by step solution on how to calculate Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate?

FIRST Step Consider the formula

𝜏 = 0.0225 \cdot ρ f \cdot {V ∞}^{2} \cdot {(\frac{μ}{ρ f \cdot V ∞ \cdot 𝛿})}^{\frac{1}{4}}

Next Step Substitute values of Variables

∴

𝜏 = 0.0225 \cdot 890kg/m³ \cdot {0.15m/s}^{2} \cdot {(\frac{0.001N*s/m²}{890kg/m³ \cdot 0.15m/s \cdot 0.014m})}^{\frac{1}{4}}

Next Step Convert Units

∴

𝜏 = 0.0225 \cdot 890kg/m³ \cdot {0.15m/s}^{2} \cdot {(\frac{0.001Pa*s}{890kg/m³ \cdot 0.15m/s \cdot 0.014m})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

𝜏 = 0.0225 \cdot 890 \cdot {0.15}^{2} \cdot {(\frac{0.001}{890 \cdot 0.15 \cdot 0.014})}^{\frac{1}{4}}

Next Step Evaluate

∴

𝜏 = 0.0685255795945798Pa

Next Step Convert to Output's Unit

∴

𝜏 = 0.0685255795945798N/m²

LAST Step Rounding Answer

∴

𝜏 = 0.0685N/m²

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

Variables

Shear Stress for Boundary Layer Flow

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.

Symbol: 𝜏

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Shear Stress for Boundary Layer Flow

Fluid Density for Boundary Layer Flow

Fluid density for boundary layer flow is defined as the mass of fluid per unit volume of the fluid.

Symbol: ρ_f

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Fluid Density for Boundary Layer Flow

Freestream Velocity for Boundary Layer Flow

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.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Freestream Velocity for Boundary Layer Flow

Viscosity of Fluid for Boundary Layer Flow

Viscosity of Fluid for boundary layer flow is a measure of fluid's resistance to deformation at a given rate.

Symbol: μ

Measurement: Dynamic ViscosityUnit: N*s/m²

Note: Value should be greater than 0.

Formulas to find Viscosity of Fluid for Boundary Layer Flow

Thickness of Boundary Layer

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.

Symbol: 𝛿

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Thickness of Boundary Layer

Other Formulas to find Shear Stress for Boundary Layer Flow

Go Shear Stress for Local Drag Coefficient

𝜏 = \frac{1}{2} \cdot CD * \cdot ρ f \cdot {V ∞}^{2}

Other formulas in Boundary Layer Flow category

Go Reynold Number at End of Plate

R e = \frac{ρ f \cdot V ∞ \cdot L}{μ}

Go Length of Plate for Reynold Number

L = \frac{R e \cdot μ}{ρ f \cdot V ∞}

Go Velocity of Fluid for Reynold Number

V ∞ = \frac{R e \cdot μ}{ρ f \cdot L}

Go Thickness of Boundary Layer

𝛿 = \frac{5.48 \cdot x}{\sqrt{R e}}

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

Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate evaluator 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 evaluate 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 evaluate Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate using this online evaluator? To use this online evaluator 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.

FAQs on Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate

What is the formula to find Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate?

The formula of Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate is expressed as 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). Here is an example- 0.068526 = 0.0225*890*0.15^2*(0.001/(890*0.15*0.014))^(1/4).

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

With 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) we can find Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate using the formula - 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).

What are the other ways to Calculate Shear Stress for Boundary Layer Flow?

Here are the different ways to Calculate Shear Stress for Boundary Layer Flow-

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

Can the Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate be negative?

No, the Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate, measured in Stress cannot be negative.

Which unit is used to measure Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate?

Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate is usually measured using the Newton per Square Meter[N/m²] for Stress. Pascal[N/m²], Newton per Square Millimeter[N/m²], Kilonewton per Square Meter[N/m²] are the few other units in which Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate can be measured.

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

​GoShear Stress for Local Drag Coefficient Formula

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

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

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

Other Formulas to find Shear Stress for Boundary Layer Flow

Other formulas in Boundary Layer Flow category

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

FAQs on Shear Stress at Boundary for Turbulent Boundary Layer over Flat Plate

Variable Name

GoShear Stress for Local Drag Coefficient Formula