It is fairly generally known that if, at any fixed speed of a compressor, either axial or centrifugal, the flow is reduced by throttling the outlet, then a point is eventually reached at which a complete breakdown of the air flow occurs and in most cases an actual flow reversal through the compressor takes place. Sometimes this phenomenon is gradual, taking the form of a sort of burbling, but more generally it takes the form of a sudden “ bang ” associated with a violent shake of the whole foundation of the bed on which the compressor is mounted. In most centrifugal compressors the flow reversal which takes place stops rapidly, the performance recovers, and a second “ surge ” occurs if the throttling is not reduced. The frequency of these individual surges varies greatly according to the degree of throttling and many other conditions; it may be only one isolated occurrence, in which case it would be concluded that the working point was just, but only just on the surge point, or it may take the form of a rapid series of thuds indicating that the working point is beyond the surge. In all cases of centrifugal compressors known to the authors reduction of the throttling will restore the compressor to its normal performance.

Many papers have been written on the measurement of strain by X-ray diffraction methods and on the interpretation of these strains in terms of stresses. Whereas, during the past few years, the experimental methods of determining the strains have. remained largely unchanged, research has shown that the older techniques for calculating stresses from strains are not always valid.

In this paper an attempt is made to describe some of the principles of strain measurement by X-ray diffraction methods to those who are unfamiliar with the methods. The types of stress and strain systems which may exist in polycrystalline metals are then considered, particular attention being paid to the effect of the elastic and plastic anisotropy of the individual crystals. Some indication is given as to how the earlier methods of interpreting X-ray strain measurements should be modified, but no rigid routine method is proposed for use in a general case.

• (a)Purpose of Investigation. To determine the least size of stringers necessary to prevent overall buckling of a flat stiffened panel before buckling of the plates between stringers.

• (b)Range of Investigation. The conditions for buckling of a longitudinally stiffened flat panel are established on the assumption that the rotational stiffness of the stringers is negligible. The results are applied to determine the limiting characteristics of the stringers to ensure that these members remain straight up to the stress at which the plates buckle between stringers. The analysis has been carried through in detail for panels with one, two, or three stringers and is capable of extension to four, five or more stringers. This extension appears unnecessary, because the three stringer case is moderately close to the limiting case of a wide panel with an indefinitely large number of stringers.

• (c)Conclusions. The stiffening effect of the stringers, having each the area of section A, and modulus of section AsK2, when attached to a sheet of thickness t and length a, at spacing b depends upon the three ratios (k/t), (a/b) and (As/bt) In general, the size of stringer necessary to ensure that the stringers remain straight until the plates buckle between stringers may be represented by the conditions

  .

  For a panel stiffened by one stringer only suitable values are λ = 4.5 and μ = 12.5, independent of the value of (a/b), while v=0.366 (a/b)2or 23 if 8>(a/b)>6.

  For two or more stringers the same general conditions hold, but it is impossible to assign values to λ and μ which would be fully satisfactory for all values of the ratio a/b. In these cases, therefore, it is more satisfactory to select the values of λ and μ appropriate to each value of the ratio a/b. These values may be obtained from Figs. 2 and 3 where curves of bt/As against (k/t)2for varying values of (a/b) are shown for two and three stringers respectively. For an indefinitely large number of stringers the corresponding condition is

  

  and the second condition (k/t)2 0.366 (a/b)2 is virtually included in the first.

• (d)Further Developments. In the present analysis the resistance of the stringers. to rotation is neglected. Inclusion of this characteristic in the basic analysis is straightforward, but practical interpretation of the results becomes much more difficult. Moreover, the effect of this stiffness in modifying the condition for buckling between stringers is likely to affect the conclusions more than the direct effect of their torsional stiffness in modifying the condition for buckling of the stiffened panel. This consideration is particularly important in cases of light stringers and heavy sheet, when the effective rotational stiffness of the stringers at buckling of the plates between stringers may be greatly reduced as a result of the end loading and may even be negative. Representation of the effect of both longitudinal stiffeners (stringers) and lateral stiffeners (ribs), including their stiffnesses to rotation is also straightforward; but interpretation of the results in forms suitable for practical application would be extremely difficult.

The steady two-dimensional flow of viscous incompressible fluid in the boundary layer along a solid boundary, which is governed by Prandtl's approximation to the full equations of motion, presents a problem which in general is as intractable as any in applied mathematics. The problem, however, has such an immediate and necessary application that approximate methods of varying accuracy which go beyond the formal processes of expansions in series and so on, have been devised for the rapid calculation of the principal characteristics of the laminar boundary-layer, the variation of pressure along the surface being known. Such methods usually represent approximately the boundary-layer velocity distribution at any point by one of a known family of distributions whose spacing along the surface is determined by some means, often by the use of Kármán's momentum equation.