## Boundary Layer Thickness

We define the **thickness** of the boundary layer as the distance from the wall to the point where the velocity is 99% of the “free stream” velocity. For **laminar boundary layers** over a flat plate, the **Blasius solution** of the flow governing equations gives:

where **Re _{x}** is the Reynolds number based on the length of the plate.

For a **turbulent flow** the boundary layer thickness is given by:

This equation was derived with several assumptions. The turbulent boundary layer thickness formula assumes that the flow is turbulent right from the start of the boundary layer.

## Example: Boundary Layer Thickness

Consider a water flow (20°C) at v = **0.1 m/s** past a flat plate 1 m long. Compute the boundary layer thickness in the middle of the plate. Assume that kinematic viscosity of water at 20°C is equal to **1×10 ^{-6} m^{2}/s**.

**The Reynolds number** for the middle of the plate is equal to:

Re_{L/2} = 0.1 [m/s] x 0.5 [m] / 1×10^{-6} [m^{2}/s] = **50 000**

This satisfies the laminar conditions. The boundary layer thickness is therefore equal to:

δ ≈ 5.0 x 0.5 / (50 000)^{½} = **0.011 m**

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