Practice Problems: Set 1
1. A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance 1.3 m
from the leading edge is 12 mm. Determine the boundary layer thickness at distances of 0.20, 2.0,
and 20 m from the leading edge. Assume laminar flow.
2. Water flows past a flat plate with an upstream velocity of U = 0.02 m/s. Determine the water
velocity a distance of 10 mm from the plate at distances of x = 1.5 m and x = 15 m from the leading
edge. Hint: Use the Blasius’ dimensionless velocity profile.
3. An airplane flies at a speed of 400 mph at an altitude of 10,000 ft. If the boundary layers on the
wing surfaces behave as those on a flat plate, estimate the extent of laminar boundary layer flow
along the wing. Assume a transitional Reynolds number of Rexcr = 5 × 105. If the airplane
maintains its 400-mph speed but descends to sea-level elevation, will the portion of the wing
covered by a laminar boundary layer increase or decrease compared with its value at 10,000 ft?
Explain.
4. Air at 20 psia and 90 °F flows over a flat plate at 100 ft/s. Find the value of x at which the Reynolds
number is 104.
5. A laminar boundary layer velocity profile is approximated by u/U = 2(y/δ) − 2(y/δ)3 + (y/δ)4 for
y ≤ δ, and u = U for y > δ. (a) Show that this profile satisfies the appropriate boundary conditions.
(b) Use the momentum integral equation to determine the boundary layer thickness, δ = δ(x).
Compare the result with the exact Blasius solution.