The Laminar Boundary-Layer Equations. I. Motion of an Elliptic and Circular Cylinders

摘要: The main results obtained are as follows: (a) problem is reduced, for the front part of a cylinder, to non-linear differential equation same form that studied by Falkner & Skan (1930), namely, f$^{\prime \prime \prime}$ + ff$^{\prime = $\lambda $(1 - 2}$). This has been numerically solved Hartree (1937), so evaluation velocities and surface friction requires only very simple short computations. Near separation point leads more complicated (3$\cdot $20). (b) Elliptic cylinder. calculated observed agree up including x 1$\cdot $457 (section 5), where distance along boundary ellipse from forward stagnation point, expressed multiple minor axis. An approximate integration, neglecting certain terms in $20), gives at about 108 degrees 30$^{\prime}$ against 103 observed, angle corresponds elliptic co-ordinate (4$\cdot $1). (c) Circular In all cases shows good agreement with results, previously experimental pressure distributions, case cylinder diameter d 5$\cdot $89 in. (by $20)) show observations almost point. (d) Pressure consists two terms: one equal potential flow, other depends on thickness layer.