Adding a v Term to a v² Term Got Both Ends Right and Missed the Middle by 42% — Prony's Two-Term Drag Law and Re = 60
Bossut measured drag growing with v², Du Buat with v. Prony's sum a·v²+b·v hands over control at Re = 60 and overpredicts settling speed by up to 42% right there.
Refining the Grid 8x Never Moved 2.4674 — Two Constants Fourier Left Behind in 1807
The convergence objection that got Fourier's 1807 memoir rejected comes back on today's grids as two stubborn constants: 8.9490% and pi^2/4.
Four times the speed, still 19.47 degrees — where water depth blows the Kelvin wedge open to 90
The Kelvin half-angle in deep water stays at 19.47° even if speed quadruples. A shallow bottom opens it toward 90° once the depth Froude number reaches 1.
Where Total Pressure Dropped 1,080 Pa, Dissipation Was Zero — When the Bernoulli Constant Crosses Streamlines
Inside a spinning vortex core the total pressure falls 1,080 Pa while viscous dissipation stays exactly zero. A Rankine vortex marks where a head deficit stops meaning loss.
A 1% Error in Diameter Is a 4% Error in Flow Rate — Half a Cell of Wall and Poiseuille's Constant
Pipe flow rate rides on the fourth power of the diameter. The same exponent explains a mesh with the wall half a cell off and Poiseuille's 1838 tubes.
The Coriolis Force Did Zero Work, Yet the Impeller Added 1800 J/kg — Energy in a Rotating Frame
A rotating frame conserves rothalpy, not total enthalpy. Coriolis work stays at 0 J/kg while impeller head still rises by 1800 J/kg.
The Kinked String Was Fine, the Cut String Overshot by 9% — How the 1747 Wave-Equation Fight Ended Numerically
d'Alembert's traveling waves and Bernoulli's sines agree until the series is cut. A jump keeps a 9% overshoot; a smooth bell is already exact by 32 modes.
Sending the smoke down 1 m cost 7 Pa of draft — Franklin's stove and the buoyancy budget
One metre of down-leg removes 6.16 Pa and the longer chimney gives back less, 38.32 Pa instead of 39.15. Net draft falls from 44.72 Pa to 37.72 Pa.
1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling
The von Neumann term xi^2 (du)^2 kills post-shock sawteeth on a Sod tube. Omit the code's factor 0.25 and the same xi makes Q four times larger.