Question

Water flows past a flat plate that is oriented parallel to the flow with an upstream velocity of 0.4 m/s. (a) Determine the approximate location downstream from the leading edge where the boundary layer becomes turbulent. (b) What is the boundary layer thickness at this location? Assume that the water tempetature is 15.6 oC. Use Approximate Physical Properties of Some Common Liquids (SI Units).

Answer 1

Answer:

1.12 m

0.08291 m

Explanation:

u = Upstream velocity = 0.4 m/s

Re = Reynold's number = $5\times 10^5$ (turbulent)

$\nu$ = Viscosity of water = $1.12\times 10^{-6}\ Pas$

Here the flow is turbulent so we have the relation

$Re_{xcr}=\frac{ux_{cr}}{\nu}\\\Rightarrow x_{cr}=\frac{Re_{xcr}\nu}{u}\\\Rightarrow x_{cr}=\frac{5\times 10^5\times 1.12\times 10^{-6}}{0.4}\\\Rightarrow x_{cr}=1.4\ m$

The approximate location downstream from the leading edge where the boundary layer becomes turbulent is 1.4 m

Boundary layer thickness relation is given by

$\delta={\frac{\nu x}{u}}^{\frac{1}{5}}\\\Rightarrow \delta={\frac{1.12\times 10^{-6}\times 1.4}{0.4}}^{\frac{1}{5}}\\\Rightarrow \delta=0.08291\ m$

The boundary layer thickness is 0.08291 m