Soap-Film and Sandbed-Mapper Techniques

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Abstract
A new photographic method for indirect measurement of a soap film is presented. Only one photograph is taken of a spiderweb grid as reflected by the film; the picture is analyzed to find contour lines and lines of maximum slope. Thus the film need last only long enough to be photographed. A fluid mapper of the isolated sandbed type is shown to be an analog for the soap film and, therefore, for the torsional stress situation in a shaft of like boundary. Thus sandbed techniques might replace soap-film techniques. The sandbed mapper also is an analog for other noncircular two-dimensional distributed source situations, such as the following: Field of a space charge; heat flow, with uniform heat production in the volume, the boundary being an isothermal; eddy currents in a plate (or section of lamination) uniformly pierced by a changing flux; magnetic flux in a volume of iron of constant permeability, the iron being (axially) a conductor of uniformly distributed current; streamline fluid flow in a long straight tube (sandbed isopressure lines corresponding to the tube’s isovelocity lines); and chemical diffusion, with the diffusing material uniformly appearing or disappearing throughout the volume. Since the sandbed is an analog for the soap film, the soap film is also an analog for these other situations.

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