On Kuo's Solution for Laminar Viscous Flow past a Finite Flat Plate

Abstract

The present paper reexamines Kuo's (J. Math. and Phys. 32 (1953) 83) solution for laminar viscous flow past a finite flat plate set parallel to a uniform stream. The crucial assumption made in Kuo's analysis was the constant displacement thickness of the wake. In view of Imai's (Proc. Roy. Soc. A208 (1951) 487) analysis, it can be shown that this assumption leads to a contradiction in the drag force of the plate and that the wake must play a role of sink. In the present paper, an attempt is made to take the effect of change in displacement thickness into analysis, in such a way that the correct strength of the source appearing in the leading term of Imai's asymptotic expansion is always maintained. The drag coefficient C D corrected can be given as \(C_{\text{D}}=\frac{1.328}{R^{1/2}}+\frac{8.25}{R}\), R being the Reynolds number. The coefficient of 8.25 should be compared with 6.45 given by Kuo. Numerical comparison shows an excellent agreement between the present drag formula and recent numerical solutions.