has been effected, in the case of the Borda nozzle in two dimensions, by Helmboltz, and may be found in Lamb's “Hydrodynamics,” where the solution is also given in the case of a simple two-dimensional aperture; the calculated coefficient in the latter case is .611, which does not differ hopelessly from the experimental value, usually taken for two-dimensional flow to be about .635.
We may evidently suppose the efflux to take place into a vacuous region, or into one filled with air, or even from one vessel containing liquid into another containing the same kind of liquid;
Fig. 53. the only obvious condition would appear to be that the pressure at all points on the surface of the jet should be constant. Such a system of flow bears a considerable resemblance to that which actually occurs in the case of any real fluid, but on the assumption of continuity it is not the form of flow given by mathematical theory in such a case. If the edges of the aperture are taken to be infinitely sharp, then the discrepancy can easily be accounted for, as the velocity at the sharp edge becomes infinite, and consequently an infinite hydrostatic pressure will be necessary to prevent cavitation, which is not possible; the conditions of hypothesis are therefore departed from. This, however, is not the full explanation, for the flow in practice closely resembles the
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