Generator

Three contours, one force, three different accounts of it

Three contours, one force, three different accounts of it
Three contours, one force, three different accounts of it. The same vortex, and the same total force on it, computed by a momentum balance over three contours of the same area. All three give ρUΓ to eight figures. What differs is the bookkeeping: the tall box gets 16 per cent of it from pressure and the rest from momentum flux, the wide box gets 84 per cent from pressure, and the circle gets exactly half. Neither part converges on its own as the contour is enlarged — each falls off like 1/r while the contour grows like r — so the split is a property of the shape of the limit rather than of the flow.

The same vortex, and the same total force on it, computed by a momentum balance over three contours of the same area. All three give ρUΓ to eight figures. What differs is the bookkeeping: the tall box gets 16 per cent of it from pressure and the rest from momentum flux, the wide box gets 84 per cent from pressure, and the circle gets exactly half. Neither part converges on its own as the contour is enlarged — each falls off like 1/r while the contour grows like r — so the split is a property of the shape of the limit rather than of the flow.

4 essays call outer-boundary. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

It is also the blast radius. Changing outer-boundary changes every figure listed here at once, and on this site it may change what they assert as well as what they show — which is what has to be rebuilt and looked at before the change is believed.

Where it is called

What each of these essays asks for instead of the defaults is on the regime index, which reads the parameters back out of the finished figures rather than out of the placements.

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