= Flat-plate boundary-layer traverse experiment
The Louisiana Tech <ME 354 - Thermofluids Laboratory/LAB 8 - Velocity Profile above a Flat Plate> describes a 14-inch plate in a <wind tunnel>. A <Pitot-static tube> of 0.10-inch outside diameter traverses normally about 12 inches downstream; its screw scale has 0.001-inch increments. A water-column <manometer> reads the difference between <stagnation pressure> and <static pressure>. The procedure establishes a wall position, zeros the tunnel indicator, sets fan speed, and records at least ten positions inside the <boundary layer>, together with room <temperature> and barometric <pressure>. The instrument list includes a flow-stream <thermometer> implemented with a temperature-sensitive resistor. The manual requests comparison of outer <velocity> with the tunnel indicator and of the recovered <velocity profile> with laminar or turbulent predictions; it provides no observed dataset. These are apparatus specifications and instructions, not a reported confirmation of <laminar flow>.
\Image[/flat-plate-velocity-traverse-apparatus.png]
{title=Pressure-based sampling model for a flat-plate velocity traverse}
{description=An original <wind tunnel> apparatus schematic and synthetic <Blasius boundary layer> readout. Hollow points are idealized averages of <dynamic pressure> over a hypothetical $0.50\,\mathrm{mm}$ normal sampling footprint, not laboratory observations or the quoted probe bore. No sample centre reaches the wall. The schematic exaggerates normal distances and tubing spacing.}
Under <incompressible flow> conditions, an ideal aligned <Pitot tube> gives $q(y)=p_0(y)-p(y)=\rho u(y)^2/2$. Convert the <manometer> head $h$ to $q=(\rho_{\mathrm{water}}-\rho)gh$, then infer $u=\sqrt{2q/\rho}$. Here $g$ is <gravitational acceleration>; <mass density> $\rho$ can be estimated from <temperature> and absolute <pressure> using the <ideal gas law>. A normalized <velocity profile> rises from the unresolved near-wall region to a plateau, whose value defines $U$; downstream profiles should broaden and collapse when plotted against $\eta$ if the <Blasius boundary layer> assumptions hold. Integrating a recovered <velocity profile> gives <displacement thickness> and <momentum thickness>.
Additional controls for interpreting this experiment follow from the measurement model: check <differential-pressure calibration> with equal port <pressures> and known liquid heads; leak-check tubing; align the <Pitot tube> with the incoming <velocity>; convert wall contact to the inlet-centre coordinate rather than treating outside contact as $y=0$; repeat traverses and outer <velocity> readings to detect drift. Keep the plate smooth and aligned, and check outer <static pressure> at multiple downstream stations before assuming zero <pressure gradient>. Repeating at another station or outer <velocity> tests the predicted <boundary-layer scaling> more directly than fitting one curve. These controls are proposed checks, not actions documented as completed in the manual.
Finite probe size, wall interference, flow fluctuations, and weak near-wall <dynamic pressure> limit inference. Even the manual's probe-based <Reynolds number> criterion, $\mathrm{Re}_d=ud/\nu>1000$ for its ideal <Bernoulli equation> conversion, must be checked with local $u$, not just $U$. In the illustrative model at $x=0.3048\,\mathrm m$, $\delta_{99}\simeq3.32\,\mathrm{mm}$; the quoted outside diameter is $2.54\,\mathrm{mm}$, a substantial fraction of that thickness. A real inlet's sensing footprint and correction cannot be deduced from outside diameter alone. For an ideal footprint that averages <dynamic pressure>, the inferred <velocity> is $\sqrt{\langle u^2\rangle}$ rather than $\langle u\rangle$. Differentiating such sparse readings to obtain <wall shear stress> magnifies <measurement error>; the <momentum thickness> route is less sensitive to this differentiation but still needs the unresolved near-wall contribution. The <no-slip boundary condition> is a model constraint here, not a direct reading from a probe centred on the wall.
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