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SUMMARYHamilton's variational principle is applied to derive a system of conditions which expresses the balance of momentum and energy of an ideal gas across the selvadges" of bladed zones within the flow tracts of turbines. This system provides the background for a correct formulation of optimal design problems for turbines and compressors. The exposition follows the model of a large number of blades when the basic equations can be averaged over the azimuthal co-ordinate.An analysis is given of the obtained conditions and a computational algorithm described.

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Analysis of Damages of Runner Pits at Operating Hydroelectric Stations and Their FailureCriteria. An analysis of documents and on-site inspections of a number of hydrostations revealed many causes of hydropower equipment failures and, in particular, failures related to runner pit (RP) damages. It was found that the operating time of turbine-generator units to failure depends little on the heat and climatic conditions and depends substantially on the operating regimes of the units (including in the starting period) and on the quality of works on manufacturing and installing the RP.On the basis of an analysis of the data of inspecting the units of more than 50 hydrostations we can distinguish the following main RP damages:1. Fatigue cracking accompanied by cavitation erosion of the RP. It is characteristic for bimetallic RPs (for about 8 % of hydrostations).2. Cavitation-erosion damages leading to cracking in RPs are characteristic for 51% of the inspected hydrostations.3. Fatigue failure due to defects of metal, manufacture, and assembly of RPs or design errors (for about 14% of hydrostations).Other schemes of failure of RPs are also possible, for example, loss of dynamic stability of the finned cylindrical shell of the RP with its poor fastening in the offset concrete.We can distinguish separately such a type of damage as damage of the linings of the connecting collar observed on almost all inspected hydrostations, Erosion of concrete forming behind tom-off lining sheets of the connecting collar gradually spreads upward and weakens both the RP structure as a whole and its fastening in the block.As a result of analyzing data on failures we can distinguish a number of factors affecting the reliability of the RP: 1. Absence of reliable cohesion of the concrete with the lining, presence of voids. 2. Insufficient rigidity of the RP structure as a consequence of the poor quality of its fastening in the concrete block. 3. Use of concrete of a poor quality and violation of the technology of placing concrete under winter conditions. 4. The actual thickness of the lining metal does not correspond to the design thickness. 5. Poor-quality fitting of the metalsheets to the stiffenersduring repair, including joining the linings not on the stiffeners. 6. Presence of heat-affected zones of welds (residual thermal stresses, local stress raisers). 7. Presence of notches, cracks, and other defects of the metal lining. 8. Use of metal with physical and mechanical characteristics not corresponding to those used in designing. 9. Noncorrespondence of the design hydrodynamic load acting on elements of the RP. 10. Cavitation erosion causing thinning of parts of the lining (up to local failure of the metal). 11. Poor quality of the welds. 12. Peeling of the protective (anticorrosion) stainless steel layer from the base metal of the liming. 13. Design errors.On the basis of the aforesaid we can formulate the following failure criteria of RP elements: exceeding the allowable stress values in the element (e.g., strength, yield, or fatigue li...

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