Boundary Layer Thickness On Vertical Surfaces Calculator

Boundary Layer Thickness Formula:

\[ \delta_x = 3.93 \times x \times Pr^{-0.5} \times (0.952 + Pr)^{0.25} \times Gr_x^{-0.25} \]

Boundary Layer Thickness (δx):

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1. What is Boundary Layer Thickness?

Boundary Layer Thickness is defined as the distance from the solid body to the point at which the viscous flow velocity is 99% of the freestream velocity. It represents the region where viscous effects are significant in fluid flow.

2. How Does the Calculator Work?

The calculator uses the Boundary Layer Thickness formula:

\[ \delta_x = 3.93 \times x \times Pr^{-0.5} \times (0.952 + Pr)^{0.25} \times Gr_x^{-0.25} \]

Where:

\( \delta_x \) — Boundary Layer Thickness (m)
\( x \) — Distance From Point to YY Axis (m)
\( Pr \) — Prandtl Number (dimensionless)
\( Gr_x \) — Local Grashof Number (dimensionless)

Explanation: This formula calculates the boundary layer thickness on vertical surfaces, accounting for the effects of Prandtl number and local Grashof number.

3. Importance of Boundary Layer Thickness Calculation

Details: Accurate boundary layer thickness calculation is crucial for analyzing heat transfer, fluid flow characteristics, and designing efficient thermal systems in various engineering applications.

4. Using the Calculator

Tips: Enter distance from point to YY axis in meters, Prandtl number, and local Grashof number. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Prandtl Number?
A: Prandtl Number (Pr) is a dimensionless number defined as the ratio of momentum diffusivity to thermal diffusivity, representing the relative thickness of velocity and thermal boundary layers.

Q2: What is the Local Grashof Number?
A: Local Grashof Number is a dimensionless number that approximates the ratio of buoyancy to viscous force acting on a fluid in natural convection scenarios.

Q3: When is this formula applicable?
A: This formula is specifically designed for calculating boundary layer thickness on vertical surfaces in natural convection flows.

Q4: What are typical values for boundary layer thickness?
A: Boundary layer thickness varies significantly depending on flow conditions, but typically ranges from millimeters to centimeters in most engineering applications.

Q5: How does boundary layer thickness affect heat transfer?
A: Thinner boundary layers generally result in higher heat transfer rates due to steeper temperature gradients at the surface.