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National Advisory Committee for Aeronautics, Report - Application of the Analogy Between Water Flow with a Free Surface and Two Dimensional Compressible Gas Flow

The theory of the hydraulic analogy—that is, the analogy
between water flow with a free surface and two—dimensional
compressible gas fl ow—and the limitations and conditions of the
analogy are discussed. A test was run using the hydraulic
analogy as applied to the flow about circular cylinders of various
diameters at subsonic celocities extending into the supercritical
range. The apparatus and techniques used in this application
are described and criticized. Reasonably satisfactory agree-
ment of pressure distributions and flow fields existed between
water and air flow about corresponding bodies- This agreement
indicated the possibility of extending erperimental compressi—
bility research by new methods.

An analogy exists between water flow with a free surface
and two—dimensional compressible gas flow (hydraulic
analogy). The water must flow over a smooth horizontal
surface bounded by vertical walls geometrically similar to
the walls bounding the corresponding compressible gas flow.

The mathematical basis of this hydraulic analogy was
presented by Riabouchinsky in reference 1, in which he also
described his apparatus for investigating the flow in a Laval
nozzle. In reference 2, be extended the theory to include
drag considerations and outlined the probable usefulness of
the hydraulic analogy. Binnie and Hooker, in reference 3,
obtained surveys along the center line of a channel With a
constriction. By employing the characteristics method to
calculate accurately the flow in a Laval nozzle, Preiswerk,
in reference 4, demonstrated conclusively that- the methods
of gas dynamics can be applied to water flow with a free
surface.

The National Advisory Committee for Aeronautics became
interested in the hydraulic analogy because it seemed an
easy and inexpensive way of studying two-dimensional com—
pressible gas flow; in particular, phenomena occurring in air
at speeds too high for visual observations could be observed
at very low speeds (3 or 4 fps) in a water channel. Pre-
liminary investigations were made in the Langley tank no. 1,
where difficulty with the vertical accelerations—assumed
negligibly small in the analogy—was experienced.