Question 1 of 3 · External Flow, Boundary Layers and Forces · Advanced · About 25 min

Laminar shear on a flat instrument vane

A smooth flat instrument vane is aligned parallel to a steady water stream. Its streamwise length is $0.400\,\mathrm m$ and wetted span is $0.600\,\mathrm m$ ; only one face is exposed to the stream for this estimate. Water has speed $0.550\,\mathrm{m/s}$ , density $998\,\mathrm{kg/m^3}$ and kinematic viscosity . Assume a laminar zero-pressure-gradient boundary layer. Determine plate-length Reynolds number, approximate boundary-layer thickness at trailing edge, average laminar skin-friction coefficient and total tangential drag on the wetted face. Use and .

Smooth single-face water vane with a growing boundary layer from leading edge to trailing edge. — Schematic, not to scale unless dimensions are given.

Given

Length: 0.400 m
Wetted span: 0.600 m
One wetted face
Free-stream speed: 0.550 m/s
Water density: 998 kg/m³
Kinematic viscosity: 1.10×10⁻⁶ m²/s

Find

Plate-length Reynolds number
Trailing-edge boundary-layer thickness
Average skin-friction coefficient
One-face friction drag

Assumptions

Laminar plate boundary layer for entire length.
Smooth plate and zero streamwise pressure gradient.
Other surfaces excluded.

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Laminar shear on a flat instrument vane

Given

Find

Assumptions

Worked solution