The steady incompressible flow of a non-viscous conducting fluid about thin airfoils and slender bodies is studied for the case of a uniform applied magnetic field aligned with the undisturbed fluid stream. Solutions are found, subject to the restriction of small perturbations to the applied field. This condition determines an upper limit on the range of conductivity to which the solution are applicable. Certain results for larger values of conductivity are presented and discussed.The lift on airfoils is calculated, including the possibility of magnets and externally driven currents inside the airfoil, and a magnetohydrodynamic analogue to the Kutta condition is discussed. Drag formulae are presented for airfoils and slender bodies, and the distribution of internal currents and magnets for zero drag is shown. Optimum drag airfoils and bodies are discussed briefly.
A means for measuring the electrical conductivity of a fluid without the use of electrodes has been developed. A probe, consisting of a cylindrical single-layer solenoid enclosed within an insulating tube, is used in conjunction with an rf oscillator-detector to measure the ohmic dissipation of a small amount of rf power in the fluid. The probe samples the conductivity of the fluid in its immediate vicinity, and may therefore be used to resolve conductivity profiles in an operating MHD device, for example. Since the surface of the probe is an insulator, it is possible that the influence of Hall effects and electrostatic sheaths may be effectively eliminated under certain conditions. Electrolytic solutions have been used in calibration of the instrument. Instrumentation has been developed for the application of the measuring technique to plasmas. Probes have been operated successfully in the positive column of a hydrogen glow discharge and in a 4500°F rocket nozzle flow.
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