Simple theory for calculating the pressure beneath a hovercraft is well known, see for example ref. 1. Of the two results, and , the former is usually preferred on the grounds of simplicity since over a large range of jet thickness/height ratios the difference between the two results is negligible. For large values of t\h the latter equation is preferred since it tends to a possible limiting value, i.e., whereas in the former equation. This latter is a consequence of one of the basic assumptions, i.e. that and since in the limiting case h=0 there can be no jet, then However, neither equation can be regarded as valid for x > 1 since for this condition a constant jet thickness equal to the slot width t cannot be maintained. In practice what happens in this condition (x > 1) is that the rate of mass flow in the jet is reduced.

Consider a lambda matrix F(ƛ, δ). This may, for example, result from the equation of motion of a dynamical system, δ being a measure of the magnitude of some possible modification to the system or some other variable parameter. Let λ be an eigenvalue and p’ and q the corresponding left hand and right hand eigenvectors. Then

One wishes to determine the derivatives of ƛ with respect to δ. Expressions for the first two derivatives will be obtained on the assumptions that F is simply degenerate and that ƛ is not a repeated root.

Recently additional tests have been performed to measure the external pressure necessary to collapse spherical caps. Bellinfante used plastic domes that were machined readily and accurately to final size. The Douglas test data shown in Fig. 1 are considered to be excellent. (2b is the base of the dome).

Thurston used aluminium caps that were chemically etched to final size. However, he intentionally put small dents at the apex. These initial distortions cause wide scatter in the test data as shown in Figs. 2(a) and 2(b). Examination of the recorded waviness reported -by Thurston indicates that the more perfect shells reached higher loads than the others. Note, for example, specimens 1, 6, 11, 16, 28, and 38. Also, usually the more wavy specimens exhibited the lower buckling loads. See specimens 4, 7, 9, 12, 17, 22, 27. Since Thurston's specimens were chemically etched to very thin gauges, the thickness variation could be significant. He does not report actual thickness variation in the shell, but states it could be about 15 per cent at worst.

A solution of the problem of the initial flow in the entrance region of a pipe has been given by Atkinson and Goldstein. In this note the authors compute this solution in greater detail, and compare their results with those of Atkinson and Goldstein. The range of the validity of the solution is shown to be smaller than originally thought.

Atkinson and Goldstein considered the equations for the steady flow of an incompressible viscous fluid into a straight circular pipe of radius a. The flow is supposed to have axial symmetry, u being the velocity component parallel to the axis x, and v the radial velocity. The, distance from the axis is denoted by r.

The static hole error problem has been extensively investigated in the past. It has been shown that, for deep holes (for which the length l of the hole is greater than 1.5 times the diameter d of the hole), the difference between the indicated static pressure p0’ and the true static pressure p0 is a function of the boundary shear stress τ0, hole diameter d, the coefficient of dynamic viscosity μ and the mass density ρ of the fluid.