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 glass tubes.
The Coriolis Force Did Zero Work, Yet the Impeller Added 1800 J/kg — Energy in a Rotating Frame
What a rotating frame conserves is rothalpy, not total enthalpy. Here is why the Coriolis force never does work on the fluid, and where a pump's head actually comes from, checked numerically.
The Kinked String Was Fine, the Cut String Overshot by 9% — How the 1747 Wave-Equation Fight Ended Numerically
d'Alembert's travelling waves and Bernoulli's sine series are the same solution, until you truncate. Code shows where the 9% overshoot comes from and why smoothness decides.
Sending the smoke down 1 m cost 7 Pa of draft — Franklin's stove and the buoyancy budget
The chimney top never moves, yet one descending leg breaks the draft. We write out the buoyancy ledger, then find the fire temperature at which smoke spills into the room.
1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling
The ξ²(Δu)² trick that killed post-shock wiggles, and the new problem it left behind.