The natural frequencies and modes of vibration of a structure may be obtained more or less directly from experiments. The generalised masses and stiffnesses, however, are usually obtained indirectly from experimental investigations of the dynamic behaviour of the system. One of the techniques widely used for this purpose in the aircraft industry is known as the method of displaced frequenciesm.Stated briefly, the method consists of observing the changes in the natural frequencies caused by the addition of one or more small masses to the vibrating system.

It is usual to consider equilibrium between the forces and accelerations associated with individual fluid elements when deriving thrust formulae containing momentum terms. Thermodynamic energy equations for open systems, however, only rely on the premise that, as far as energy is concerned, what goes into a system must either come out or else build up inside.

In thermodynamic textbooks a distinction is usually drawn between steady flow, involving no change of energy with time inside a system, and non-steady flow, which implies a rate of change of energy within the thermodynamic system under consideration.

It is interesting to find that the thrust formula for a simple system, as shown in Fig. 1, may be derived directly from these thermodynamic energy equations by two alternative methods.

The aim of this note is to compare the plane turbulent free jet diffusing in an infinite stagnant ambient environment with the corresponding plane turbulent wall jet on a smooth boundary regarding the three important characteristics, namely the velocity distribution and the variation of the velocity and length scales, in the region of developed flow.

It is well known that in the case of turbulent flow over smooth boundaries, the velocity distribution in the neigh- i bourhood of the wall is given by the law of the wall, c written as

where u is the turbulent mean velocity at a normal distance of y from the boundary, u* is the shear velocity equal to being the boundary shear stress and ρ the mass density of the fluid and v is the coefficient of kinematic viscosity. In the viscous sublayer, eqn. (1) becomes

and in the turbulent flow region above the sublayer and the transition region, for yu*/v> 30, eqn. (1) becomes

where A and B are coefficients.

The variations of dynamic load factors of a beam subjected to axial forces are investigated when transverse impulsive loads are applied. The relationships between constant axial forces P and dynamic load factors are obtained under various end conditions. Dynamic load factors are very different from 2.

Because it is difficult to obtain an exact solution when P is a function of ξ (co-ordinate of axial direction), analyses are carried out by the energy method, where P is assumed to be in the form of (1–ξm).

In a recent paper, the author described some experiments in which the average base pressure on a two-dimensional bluff body was estimated from a random sample of instantaneous velocity measurements taken in the irrotational flow outside the separating boundary layers at the trailing edge. Although the oncoming stream was steady, the flow near the model was subject to a periodic disturbance emanating from the wake vortex street. An experimental check showed that the pressure estimates obtained by using the steady Bernouilli equation were reasonably accurate. This note points out that the method of data reduction used in ref. 1 is not an approximation; it is exact.

Recently Alexander suggested modifications to the inviscid theory of Stanton Jones for improving the agreement between theory and experiment on the cushion pressure of hovercraft. However, these simple inviscid theories can hardly be expected to represent even approximately the behaviour of peripheral jets in hovercraft and a more plausible theory taking mixing into account can easily be developed from some work of Bourque and Newman on the re-attachment of plane jets to adjacent surfaces. This theory, which is somewhat similar to a theory of Chaplin, can be used to predict the behaviour of peripheral jet models both in and out of ground effect but it is the intention here simply to compare the predictions of the mixing theory in ground effect with the simple inviscid theories which seem so commonly used in cushion craft work. Also, the advantages and potential of the mixing theory will be discussed briefly.

In his technical note in the January 1967 JOURNAL, Quarmby (pp 47-49) concludes that because he was able to predict the axial pressure gradient in a concentric smooth annulus by using Preston tubes to measure the inner and outer wall shear stress, then the Preston tubes are giving correct values for the wall shear stresses. I cannot agree that this is a valid conclusion to draw. A Preston tube can only give wall shear stress correctly if the dimensionless velocity in the wall region is the same as that for which the tube was calibrated.

In an earlier note Case reported direct measurements of entrainment on a rotating disc. More comprehensive measurements, made subsequently to those of Case and using essentially the same technique, are reported here. Two different sizes of drum were used in the present investigation, the flow within the drum in each case being smoothed by the use of a honeycomb and screens as well as a baffle at entry (see Fig. 1).

The entrainment was also deduced from yawmeter and total pressure traverses through the boundary layer on the disc in free air, the integrated crossflow component of the velocity distribution through the layer evidently representing the entrainment up to the radius at which the traverses were performed. A typical measured crossflow profile is shown in Fig. 2.