Assume the flow conditions given in Example 9.3. Plot δ, δ*, and τw versus x/L for the plate.
Example 9.3 TURBULENT BOUNDARY LAYER ON A FLAT PLATE: APPROXIMATE SOLUTION USING
Water flows at U = 1 m/s past a flat plate with L = 1 min the flow direction. The boundary layer is tripped so it becomes turbulent at the leading edge. Evaluate the disturbance thickness, δ, displacement thickness, δ*, and wall shear stress, τw, at x = L. Compare with laminar flow maintained to the same position. Assume a
Given: Flat-plate boundary-layer flow; turbulent flow from the leading edge. Assume
Find: (a) Disturbance thickness, δL.
(b) Displacement thickness,
(c) Wall shear stress, τw(L).
(d) Comparison with results for laminar flow from the leading edge.
Solution: Apply results from the momentum integral equation.
Governing equations:
At x = L, with ν = 1.00 × 10−6 m2/s for water (T = 20°C),
From Eq. 9.26,
Using Eq. 9.1, with u/U = (y/δ)1/7 = η1/7, we obtain
From Eq. 9.27,
For laminar flow, use Blasius solution values. From Eq. 9.13 (on the web),
From Example W9.1, δ*/δ = 0.344, so
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