ALBERT

Description: This preliminary investigation was made to study the hydrodynamic properties and general behavior of simple hydrofoils. Six 5- by 30-inch plain, rectangular hydrofoils were tested in the NACA tank at various speeds, angles of attack and depths below the water surface. Two of the hydrofoils had sections representing the sections of commonly used airfoils, one had a section similar to one developed Guidoni for use with hydrofoil-equipped seaplane floats, and three had sections designed to have constant chordwise pressure distributions at given values of the lift coefficient for the purpose of delaying the speed at which cavitation begins. The experimental results are presented as curves of the lift and drag coefficients plotted against speed for the various angles of attack and depths for which the hydrofoils were tested. A number of derived curves are included for the purpose of better comparing the characteristics of the hydrofoils and to show the effects of depth. Several representative photographs show the development of cavitation on the the upper surface of the hydrofoils. The results indicate that properly designed hydrofoil sections will have excellent characteristics and that the speed at which cavitation occurs may be delayed to an appreciable extent by the use of suitable sections.

Description: The Navier-Stokes stress principle is checked in the light of Maxwell's mechanism of friction and in connection herewith the possibility of another theorem is indicated. The Navier-Stokes stress principle is in general predicated upon the conception of the plastic body. Hence the process is a purely phenomenological one, which Newton himself followed with his special theorem for one-dimensional flows. It remained for Maxwell to discover the physical mechanism by which the shear inflow direction is developed: According to it, this shear is only 'fictitious' as it merely represents the substitute for a certain transport on macroscopic motion quantity, as conditioned by Brown's moiecular motion and the diffusion, respectively. It is clear that this mechanism is not bound to the special case of the one-dimensioilal flows, but holds for any flow as expression of the diffusion, by which a fluid differs sharply from a plastic body. If it is remembered, on the other hand, that the cause of the stresses on the plastic body lies in a certain cohesion of the molecules, it appears by no means self evident that this difference in the mechanism of friction between fluid and plastic body should not prevail in the stress principle as well, although it certainly is desirable in any case, at least subsequently, to establish the general theorem in the sense of Maxwell. Actually, a different theorem is suggested which, in contrast to that by Navier-Stokes, has the form of an unsymmetrical matrix. Without anticipating a final decision several reasons are advanced by way of a special flow which seem to affirm this new theorem. To make it clear that the problem involved here still awaits its final solution, is the real purpose behind the present article.

Description: The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Description: A brief summary of the contents of this paper is presented here. In part I the differential equations of the problem of a gas flow in two dimensions is derived and the particular integrals by which the problem on jets is solved are given. Use is made of the same independent variables as Molenbroek used, but it is found to be more suitable to consider other functions. The stream function and velocity potential corresponding to the problem are given in the form of series. The investigation on the convergence of these series in connection with certain properties of the functions entering them forms the subject of part II. In part III the problem of the outflow of a gas from an infinite vessel with plane walls is solved. In part IV the impact of a gas jet on a plate is considered and the limiting case where the jet expands to infinity changing into a gas flow is taken up in more detail. This also solved the equivalent problem of the resistance of a gaseous medium to the motion of a plate. Finally, in part V, an approximate method is presented that permits a simpler solution of the problem of jet flows in the case where the velocities of the gas (velocities of the particles in the gas) are not very large.

Description: For the tunnel corrections of compressible flows those profiles are of interest for which at least the second approximation of the Janzen-Rayleigh method can be applied in closed form. One such case is presented by certain elliptical symmetrical cylinders located in the center of a tunnel with fixed walls and whose maximum velocity, incompressible, is twice the velocity of flow. In the numerical solution the maximum velocity at the profile and the tunnel wall as well as the entry of sonic velocity is computed. The velocity distribution past the contour and in the minimum cross section at various Mach numbers is illustrated on a worked out-example.

Description: One of the problems of modern cavitation research is the experimental determination of the wing loads on airfoils during cavitation. Such experiments were made on various airfoils with the support of the naval ministry at the Kaiser Wilhelm Institute for Flow Research at Goettingen.

Description: The,theory of heat.transfer from a solid body to a liquid stream could he presented previously** only with limiting assumptions about the movement of the fluid (potential flow, laminar frictional flow). (See references 1, 2, and 3). For turbulent flow, the most important practical case, the previous theoretical considerations did not go beyond dimensionless formulas and certain conclusions as to the analogy between the friction factor and the unit thermal conductance, (See references 4, 5, 6, and 7,) In order to obtain numerical results, an experimental treatment of the problem was resorted to, which gave rise to numerous investigations because of the importance of this problem in many branches of technology. However, the results of these investigations frequently deviate from one another. The experimental results are especially dependent upon the overall dimensions and the specific proportions of the equipment. In the present work, the attempt will be made to develop systematically the theory of the heat transfer and of the dependence of the unit thermal conductance upon shape and dimensions, using as a basis the velocity distribution for turbulent flow set up by Prandtl and Von Karman.

Description: The heat transfer accompanying turbulent flow in tubes has been treated by a new theory of wall turbulence, and a formula for smooth tubes has been derived which is asymptotic at Re approaches infinity. It agrees very well with the data available to date. The formula also holds for the flow along a flat plate if lambda is based on the velocity far away. For rough tubes, the unit conductance is shown to be a function of kv*/upsilon; the two empirical constants (delta(r), n) which appear in equation (52) cannot yet be determined because of lack of experimental data.

Description: The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.

Description: Problems of hydraulic flow resistance and heat transfer for streams with velocities comparable with acoustic have present great importance for various fields of technical science. Especially, they have great importance for the field of heat transfer in designing and constructing boilers.of the "Velox" type. In this article a description of experiments and their results as regards definition of the laws of heat transfer in differential form for high velocity air streams inside smooth tubes are given.