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Calculating Boundary Layer Thickness to Choose Pitot Tube Height on F1 Car

August 17, 2013

First, here are some Prereq articles:

Bernoullis Equation for a Pitot Tube Example on a Formula 1 Race Car

Pitot Tube and Pressure Explanation With F1 and Pikes Peak Example

Introduction to Boundary Layers, Viscous Flow, and Velocity Profiles

The answer to the question in the Pikes Peak article will be below the examples here.

Lets begin.

We want to see what happens if we place the Pitot Tube too low, and we want to find the Boundary Layer Thickness to know how high the Pitot Tube must be in order to be outside the Boundary Layer, and therefore be measuring the free stream velocity.

If the Pitot Tube is too low, then it will be inside the Boundary Layer and therefore will not be measuring the free stream velocity.

Example 1 – Finding a Pitot Tube height that will ensure it’s measuring the vehicle speed and not a lower speed due to the boundary layer

Lets say we want to know the airspeed of an F1 car, and we want to put the Pitot Tube some distance up the nose. How high up does the Pitot Tube need to be mounted in order to be measuring the free stream velocity outside the boundary layer?

  • Pitot Tube is 1m back from the nose
  • Air Density is 1.225 kg/m^3
  • Air Viscosity is 1.8*10^-5 kg/ms
  • Speed range from 10 m/s to 100 m/s (360km/h or 224 mph)

Assumptions

  1. Infinately wide Flat Plate
  2. Incompressible
  3. Instant transition from laminar to turbulent flow
  4. Time Averaged Mean Flow
  5. Steady State
  6. Turbulent Transition at Re=500,000

Lets first introduce the equations we’ll be needing.

Re_x = \frac{\rho * V * x}{\mu}

\delta_{lam} = \frac{5*x}{\sqrt{Re_x}}

\delta_{tur} = \frac{.3747*x}{(Re_x)^{0.2}}

x_{tr} = \frac{Re_{tr}}{\frac{\rho * V}{\mu}}

To read the rest of the article please go to Calculating Boundary Layer Thickness to Choose Pitot Tube Height on F1 Car using Theory and Pitot Tube Arrays. I am in the process of migrating my website there, which is why I’m putting partial articles where my viewers can still find them.

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