Abstract
Unsteady non-homentropic flow of a gas in one dimension is studied by taking a form of the Lagrangian equations of motion. An ‘exact’ solution representing progressive waves is found, and this is applied to the problem of a shock advancing into a region in which the pressure is constant, but the density (and temperature) varies according to a simple power law. The problem is shown to depend upon a single first-order differential equation of standard type, and it is indicated how numerical solutions could be constructed if desired. For convenience in presentation, however, the discussion is limited to the case of a very strong shock, and only qualitative conclusions are offered at this stage.
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