A hot-wire anemometer traverse measures the streamwise velocity in a laminar boundary…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch The boundary layer: Prandtl's equations and the Blasius solution

Problem

A hot-wire anemometer traverse measures the streamwise velocity

u

in a laminar boundary layer on a flat plate in air (

\rho = 1.20\,\text{kg m}^{-3}

\mu = 1.81\times10^{-5}\,\text{Pa s}

\nu = 1.51\times10^{-5}\,\text{m}^2\,\text{s}^{-1}

), at the station

x = 0.50\,\text{m}

with free-stream speed

U = 15.0\,\text{m s}^{-1}

. The measured profile, as pairs of

y

(mm) and

u/U

, is:

(0,\,0.00)

(0.71,\,0.33)

(1.42,\,0.63)

(2.13,\,0.85)

(2.84,\,0.96)

(3.55,\,0.99)

(4.26,\,1.00)

. ((a)) Using the Blasius flat-plate results, compute

Re_x

and predict

\tau_w

\delta_{99}

\delta_1

and

\delta_2

at this station. ((b)) From the measured data, estimate the wall shear stress from the slope of the first two points, read off

\delta_{99}

as the first

y

at which

u/U

reaches

0.99

, and estimate

\delta_1

and

\delta_2

by the trapezoidal rule applied to the seven tabulated points (treating

u/U = 1

beyond the last point). ((c)) Compare the measured and predicted values (percentage differences) and state whether the profile is consistent with a Blasius laminar layer.

Browse the problem library