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**Serial/Series Title:**NACA Technical Reports

**Collection:**National Advisory Committee for Aeronautics Collection

### Flow and Force Equations for a Body Revolving in a Fluid

**Date:**December 1, 1979

**Creator:**Zahm, A. F.

**Description:**A general method for finding the steady flow velocity relative to a body in plane curvilinear motion, whence the pressure is found by Bernoulli's energy principle is described. Integration of the pressure supplies basic formulas for the zonal forces and moments on the revolving body. The application of the steady flow method for calculating the velocity and pressure at all points of the flow inside and outside an ellipsoid and some of its limiting forms is presented and graphs those quantities for the latter forms. In some useful cases experimental pressures are plotted for comparison with theoretical. The pressure, and thence the zonal force and moment, on hulls in plane curvilinear flight are calculated. General equations for the resultant fluid forces and moments on trisymmetrical bodies moving through a perfect fluid are derived. Formulas for potential coefficients and inertia coefficients for an ellipsoid and its limiting forms are presented.

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### The Inertia Coefficients of an Airship in a Frictionless Fluid

**Date:**December 1, 1979

**Creator:**Bateman, H.

**Description:**The apparent inertia of an airship hull is examined. The exact solution of the aerodynamical problem is studied for hulls of various shapes with special attention given to the case of an ellipsoidal hull. So that the results for the ellipsoidal hull may be readily adapted to other cases, they are expressed in terms of the area and perimeter of the largest cross section perpendicular to the direction of motion by means of a formula involving a coefficient kappa which varies only slowly when the shape of the hull is changed, being 0.637 for a circular or elliptic disk, 0.5 for a sphere, and about 0.25 for a spheroid of fineness ratio. The case of rotation of an airship hull is investigated and a coefficient is defined with the same advantages as the corresponding coefficient for rectilinear motion.

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### General Theory of Aerodynamic Instability and the Mechanism of Flutter

**Date:**December 1, 1979

**Creator:**Theodorsen, Theodore

**Description:**The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.

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### General Potential Theory of Arbitrary Wing Sections

**Date:**December 1, 1979

**Creator:**Theodorsen, T. & Garrick, I. E.

**Description:**The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

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### A theoretical study of the effect of forward speed on the free-space sound-pressure field around propellers

**Date:**January 1, 1954

**Creator:**Garrick, I. E. & Watkins, C. E.

**Description:**None

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### Determination of the profile drag of an airplane wing in flight at high Reynolds numbers

**Date:**January 1, 1939

**Creator:**Bicknell, J.

**Description:**None

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### The Theory of the Pitot and Venturi Tubes, Part 2

**Date:**January 1, 1989

**Creator:**Buckingham, E.

**Description:**None

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### Applications of Modern Hydrodynamics to Aeronautics. Part 1: Fundamental Concepts and the Most Important Theorems. Part 2: Applications

**Date:**December 1, 1979

**Creator:**Prandtl, L.

**Description:**A discussion of the principles of hydrodynamics of nonviscous fluids in the case of motion of solid bodies in a fluid is presented. Formulae are derived to demonstrate the transition from the fluid surface to a corresponding 'control surface'. The external forces are compounded of the fluid pressures on the control surface and the forces which are exercised on the fluid by any solid bodies which may be inside of the control surfaces. Illustrations of these formulae as applied to the acquisition of transformations from a known simple flow to new types of flow for other boundaries are given. Theoretical and experimental investigations of models of airship bodies are presented.

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### Flow and Drag Formulas for Simple Quadrics

**Date:**December 1, 1979

**Creator:**Zahm, A. F.

**Description:**The pressure distribution and resistance found by theory and experiment for simple quadrics fixed in an infinite uniform stream of practically incompressible fluid are calculated. The experimental values pertain to air and some liquids, especially water; the theoretical refer sometimes to perfect, again to viscid fluids. Formulas for the velocity at all points of the flow field are given. Pressure and pressure drag are discussed for a sphere, a round cylinder, the elliptic cylinder, the prolate and oblate spheroid, and the circular disk. The velocity and pressure in an oblique flow are examined.

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### Determination of Stresses in Gas-turbine Disks Subjected to Plastic Flow and Creep

**Date:**January 1, 1948

**Creator:**Manson, S. S. & Millenson, M. B.

**Description:**None

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### Design of Wind Tunnels and Wind Tunnel Propellers, II

**Date:**January 1, 1921

**Creator:**Norton, F. H. & Warner, E. P.

**Description:**No abstract available.

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### The Aerodynamic Forces on Airship Hulls

**Date:**December 1, 1979

**Creator:**Munk, M. M.

**Description:**The new method for making computations in connection with the study of rigid airships, which was used in the investigation of Navy's ZR-1 by the special subcommittee of the National Advisory Committee for Aeronautics appointed for this purpose is presented. The general theory of the air forces on airship hulls of the type mentioned is described and an attempt was made to develop the results from the very fundamentals of mechanics.

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### Elements of the Wing Section Theory and of the Wing Theory

**Date:**December 1, 1979

**Creator:**Munk, Max M.

**Description:**Results are presented of the theory of wings and of wing sections which are of immediate practical value. They are proven and demonstrated by the use of the simple conceptions of kinetic energy and momentum only.

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### The Minimum Induced Drag of Aerofoils

**Date:**December 1, 1979

**Creator:**Munk, M. M.

**Description:**Equations are derived to demonstrate which distribution of lifting elements result in a minimum amount of aerodynamic drag. The lifting elements were arranged (1) in one line, (2) parallel lying in a transverse plane, and (3) in any direction in a transverse plane. It was shown that the distribution of lift which causes the least drag is reduced to the solution of the problem for systems of airfoils which are situated in a plane perpendicular to the direction of flight.

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### Blockage Corrections for Three-Dimensional-Flow Closed-Throat Wind Tunnels, with Consideration of the Effect of Compressibility

**Date:**January 1, 1951

**Creator:**Herriot, J. G.

**Description:**Theoretical blockage corrections are presented for a body of revolution and for a three-dimensional, unswept wing in a circular or rectangular wind tunnel. The theory takes account of the effects of the wake and of the compressibility of the fluid, and is based on the assumption that the dimensions of the model are small in comparison with those of the tunnel throat. Formulas are given for correcting a number of the quantities, such as dynamic pressure and Mach number, measured in wind tunnel tests. The report presents a summary and unification of the existing literature on the subject.

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### Impingement of Cloud Droplets on a Cylinder and Procedure for Measuring Liquid-Water Content and Droplet Sizes in Supercooled Clouds by Rotating Multicylinder Method

**Date:**January 1, 1955

**Creator:**Brun, R. J.; Lewis, W.; Perkins, P. J. & Serafini, J. S.

**Description:**No abstract available.

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### Investigation of turbulent flow in a two-dimensional channel

**Date:**January 1, 1951

**Creator:**Laufer, John

**Description:**A detailed exploration of the field of mean and fluctuating quantities in a two-dimensional turbulent channel flow is presented. The measurements were repeated at three Reynolds numbers, 12,300, 30,800, and 61,600, based on the half width of the channel and the maximum mean velocity. A channel of 5-inch width and 12:1 aspect ratio was used for the investigation. Mean-speed and axial-fluctuation measurements were made well within the laminar sublayer. The semitheoretical predictions concerning the extent of the laminar sublayer were confirmed. The distribution of the velocity fluctuations in the direction of mean flow u' shows that the influence of the viscosity extends farther from the wall than indicated by the mean velocity profile, the region of influence being approximately four times as wide.

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### On the theory of oscillating airfoils of finite span in subsonic compressible flow

**Date:**January 1, 1950

**Creator:**Reissner, Eric

**Description:**The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

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### A special investigation to develop a general method for three-dimensional photoelastic stress analysis

**Date:**January 1, 1953

**Creator:**Frocht, M M & Guernsey, R , Jr

**Description:**The method of strain measurement after annealing is reviewed and found to be satisfactory for the materials available in this country. A new general method is described for the photoelastic determination of the principal stresses at any point of a general body subjected to arbitrary load. The method has been applied to a sphere subjected to diametrical compressive loads. The results show possibilities of high accuracy.

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### An experimental investigation of transonic flow past two-dimensional wedge and circular-arc sections using a Mach-Zehnder interferometer

**Date:**January 1, 1952

**Creator:**Bryson, Arthur Earl, Jr

**Description:**Report presents the results of interferometer measurements of the flow field near two-dimensional wedge and circular-arc sections of zero angle of attack at high-subsonic and low-supersonic velocities. Both subsonic flow with local supersonic zone and supersonic flow with detached shock wave have been investigated. Pressure distributions and drag coefficients as a function of Mach number have been obtained. The wedge data are compared with the theoretical work on flow past wedge sections of Guderley and Yoshihara, Vincenti and Wagner, and Cole. Pressure distributions and drag coefficients for the wedge and circular-arc sections are presented throughout the entire transonic range of velocities.

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### Analysis and calculation by integral methods of laminar compressible boundary-layer with heat transfer and with and without pressure gradient

**Date:**January 1, 1955

**Creator:**Morduchow, Morris

**Description:**A survey of integral methods in laminar-boundary-layer analysis is first given. A simple and sufficiently accurate method for practical purposes of calculating the properties (including stability) of the laminar compressible boundary layer in an axial pressure gradient with heat transfer at the wall is presented. For flow over a flat plate, the method is applicable for an arbitrarily prescribed distribution of temperature along the surface and for any given constant Prandtl number close to unity. For flow in a pressure gradient, the method is based on a Prandtl number of unity and a uniform wall temperature. A simple and accurate method of determining the separation point in a compressible flow with an adverse pressure gradient over a surface at a given uniform wall temperature is developed. The analysis is based on an extension of the Karman-Pohlhausen method to the momentum and the thermal energy equations in conjunction with fourth- and especially higher degree velocity and stagnation-enthalpy profiles.

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### Diffusion of heat from a line source in isotropic turbulence

**Date:**January 1, 1953

**Creator:**Uberoi, Mahinder S & Corrsin, Stanley

**Description:**An experimental and analytical study has been made of some features of the turbulent heat diffusion behind a line heated wire stretched perpendicular to a flowing isotropic turbulence. The mean temperature distributions have been measured with systematic variations in wind speed, size of turbulence-producing grid, and downstream location of heat source. The nature of the temperature fluctuation field has been studied. A comparison of Lagrangian and Eulerian analyses for diffusion in a nondecaying turbulence yields an expression for turbulent-heat-transfer coefficient in terms of turbulence velocity and a Lagrangian "scale." the ratio of Eulerian to Lagrangian microscale has been determined theoretically by generalization of a result of Heisenberg and with arbitrary constants taken from independent sources, shows rough agreement with experimental results. A convenient form has been deduced for the criterion of interchangeability of instantaneous space and time derivatives in a flowing turbulence.

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### Free-stream boundaries of turbulent flows

**Date:**January 1, 1955

**Creator:**Corrsin, Stanley & Kistler, Alan L

**Description:**Report presents the results of an experimental and theoretical study made of the instantaneously sharp and irregular front which is always found to separate turbulent fluid from contiguous "nonturbulent" fluid at a free-stream boundary. This distinct demarcation is known to give an intermittent character to hot-wire signals in the boundary zone. The overall behavior of the front is described statistically in terms of its wrinkle-amplitude growth and its lateral propagation relative to the fluid as functions of downstream coordinate.

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### Experiments to determine neighborhood reactions to light airplanes with and without external noise reduction

**Date:**January 1, 1953

**Creator:**Elwell, Fred S

**Description:**The work reported was part of a program of experimentation with external noise reduction on light airplanes. This particular study was in effect a byproduct survey conceived to utilize already available equipment and personnel to further the findings of the original research and to determine reactions in populated neighborhoods to light aircraft with and without noise-reduction equipment. The findings indicate that at the 10 sites within and about metropolitan Boston the degree of noise reduction previously found to be aerodynamically and structurally feasible did eliminate substantially all neighborhood objections to noise per se. The evidence clearly suggests that, when the noise nuisance is minimized to the extent found feasible, the number and severity of other objections also diminish -- evidently because the flight operations are noticed less when heard less.

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