Overview

Teaching: 0 min
Exercises: 25 min

Questions

• Can you calculate the distance at which a laminar boundary layer may transition to a turbulent one?

Objectives

• Calculate the distance at which a laminar boundary layer transitions to turbulent.

The Problem

A smooth flat plate with a sharp leading edge is placed in a free stream of water flowing at 3m/s. Calculate the distance from the leading edge and the boundary layer thickness where the transition from laminar to turbulent flow may commence. Assume the density of water as \(1000 kg/m^3\) and viscosity as 1 centipoise.

Challenge

What is a centipoise?

Solution

• A unit of measurement for viscosity defined as \(1\times10^{-3} Ns/m^2\)

Challenge

At approximately what Reynolds number does this transition occur?

Solution

• \(Re=3.2\times10^5\)

Substitute the data

Challenge

At approximately what distance does this transition occur?

Soultion

If you recall \[Re\equiv\frac{Ux}{\nu}\] Let’s substitute the data from our problem: \[\begin{align} & U=3m/s, \rho = 1000 kg/m^3, \mu=0.001 Ns/m2 \therefore \newline & x=3.2\times10^5\times0.001/(3\times1000) \newline & x=11cm \end{align} \]

Challenge

What is the height of the boundary layer at this distance?

Answer

\[\begin{align} \frac{\delta}{x} &=\frac{5}{\sqrt{Re}} \newline \delta &= 0.1cm\end{align}\]

Key Points

• The Reynolds number at which transition occurs is at \(3.2\times10^5\)

• For the above problem the transition distance is 11cm.

• The boundary layer height at this distance is 0.1cm.