This paper describes the construction of a water channel in the University of Bristol for the investigation of the analogy between the two-dimensional flow of a gas and that of shallow water with a free surface. Both continuous and discontinuous flow were examined, with a view to determining the limitations of the analogy.

Continuous “ shooting “ water flow was found to be reasonably analogous with supersonic isentropic gas flow, a static depth of about half an inch appearing to be satisfactory with this particular channel. No independent check was made of the agreement, or otherwise, between “streaming” water flow and subsonic gas flow, since the method of checking used was the measurement of the angle of the waves formed on the water surface, and such waves exist only in “ shooting” flow.

A method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.

In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

It is shown that the rotational stiffness of a crossed flexure pivot varies considerably when subjected to an applied force. The type of variation can be radically changed simply by moving the point at which the strips cross. The relation between torque and rotation for a given applied force is not exactly linear and the extent of the non-linearity is determined by taking into account the small movements of the centre of rotation of the pivot. Finally, for design purposes, an analysis of the maximum stresses in the strips is given.

Crossed flexure pivots, of the type shown in Fig. 1, are extensively used in aeronautical research equipment to replace knife edges or ball bearings. Perhaps the most frequent use is for the fulcrum of the balance arm in a wind tunnel balance. Here, a null-point method of reading is almost invariably used, so that the prime considerations influencing the design of a flexure pivot for such a purpose are (a) that the applied loads should not cause instability of the pivot, and (b) that the rotational stiffness should be small enough to give adequate sensitivity.

As is well known, standard lifting-line theory cannot be applied to a wing with sweepback in order to determine the amount and distribution of the lift. Various methods, all fairly laborious, are available, and while they give results which agree fairly well with experiment, they do not show in detail the source of the various differences due to sweep. It is with the object of separating the several effects involved, which can be regarded as distinct for practical purposes, that the present method has been developed. Since one of the items, finite-chord loss, is shared with the straight wing, although not included in simple lifting-line theory, it is calculated first for the straight wing. The wing is represented by its median or camber surface and is assumed nearly flat.