Studies of the movement of ice through low-pressure waterworks

Passage of ice through hydraulic structures is a significant and urgent issue for study. When examining this issue, various conditions should be taken into account. Thus, the successful passage of ice through hydraulic structures depends both on ice characteristics, the parameters of the spillway structures, and on the ice movement velocity in front of the spillway. The goals have been formed; the research tasks have been set. As a result, a theoretical solution to determine the bending moments necessary for calculating the fracture of ice floes has been obtained. The proposed analytical solution for determining the bending moments is found based on a system solution of differential equations of a rigid body motion in a fluid. The assumptions made for this case are set out in the article. The resulting dependence makes it possible to determine the bending moments in any section of the ice section and take into account the flow dynamics. A complex of laboratory studies was carried out, aimed at studying the ice movement velocities on the developed and manufactured model of a spillway with a wide threshold, in front of which an auxiliary threshold is installed to create a concentrated fall. The dependence for determining the velocity in the form of a trigonometric function is obtained and converted into a convenient formula. The performed calculations are compared with the field data and satisfactory results are given.

Convenient and accurate formulas for stress intensity factor distribution of semi-elliptical surface crack

In this paper, the stress intensity factor (SIF) formula [Formula: see text] along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution [Formula: see text] is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio [Formula: see text]/[Formula: see text] is focused considering the exact solution [Formula: see text] of an elliptical crack. By applying the least squares method to the ratio [Formula: see text]/[Formula: see text], accurate and convenient formula is proposed. The proposed formulas may provide the accurate SIF distributions for the aspect ratio [Formula: see text]–4 better than 0.2% accuracy.

ABOUT SOME FEATURES OF LABORATORY RESEARCHES FOR PROCESS OF PULVERIZED FUEL BURNING

The analysis of scientific publications containing information about the equipment and methods of modeling the process of pulverized fuel combustion is carried out. The basic requirements for ensuring the reliability of research results are formulated. The conclusion is made about the possibility and expediency of using installations of the type "vertical tubular furnace" to find ways to increase the completeness of pulverized coal combustion in the blast furnaces raceway. Emphasis is placed on the importance of ensuring a uniform supply of fuel to the reaction zone, a time-stable ratio of fuel and oxidant, qualitative technical analysis of the source fuel, as well as the residue after its combustion. Based on a comparative analysis of methods for determining the completeness of burnout of pulverized fuel used in such studies, a convenient formula for its calculations is proposed.

TOPOLOGICAL PROPERTIES OF BERRY'S PHASE

By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval T. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born–Oppenheimer approximation, where a large but finite ratio of two time scales is involved.

On the eigenvectors for a class of matrices arising from quasi-derivatives

SynopsisLet A be a product of symmetric matrices, A = RQ, with R non-singular, and let v be an eigenvector of A. For certain R and Q, a convenient formula for the expression (R−1v)tv is obtained. This expression occurs in the diagonalization of A and, in the particular case where A is associated with the quasi-derivative formulation of higher-order differential equations, the expression occurs in the asymptotic theory of solutions of the differential equation.

Runway Slipperiness and Slush

SummaryA review is made of recent research in the United States relating to runway slipperiness and to slush-drag or fluid-drag effects on aircraft ground performance. The formation of fluid spray and its drag effects on aircraft are traced from spray origin at the intersection of the tyre and runway to impingement on the aircraft over the complete aircraft ground-velocity range. Six manifestations of tyre hydroplaning are presented and discussed: fluid-drag peak, tyre spin-down, loss of aircraft directional stability, loss of aircraft braking traction, suppression of bow wave, and progressive detachment of the tyre footprint from the fluid-covered runway surface as ground speed is increased. A convenient formula for estimating tyre-hydroplaning speed is indicated to bewhere Vp=hydroplaning speed, knotsp=tyre-inflation pressure, lb/sq in.Comparison with available experimental data is shown. The effects of fluid viscosity and density on runway slipperiness are discussed. The effects of some runway-surface textures, tyre-tread patterns, and aircraft landing-gear wheel arrangements on slipperiness are described. The paper also includes indications of areas of interest that need further study.

NOTE ON THE THEORY OF ELECTROLYTIC DOUBLE LAYERS

The mechanism suggested by Gurney for the formation of a double layer at the interface of a metal and a solution containing its ions is applied to a diffuse double layer. The diffuse part of the double layer is treated in a way that differs from Stern's method, leading to a more convenient formula for the potential ψδ of the diffuse part. Numerical values and a comparison with Stern's results are given.