2.0000 in laminar flow, 1.0322 in turbulent — the coefficient in front of the velocity head
·7 min read
A mean-velocity head is not the kinetic energy a pipe actually carries. Alpha is 2.0000 for laminar Poiseuille flow and 1.0322 at Re = 10^6.
The Weight Sits on Top and She Still Rights Herself — Metacentric Height and the Free Surface Effect
·8 min read
Capsizing is not decided by whether the centre of gravity sits above the buoyancy centre. The second moment of the waterplane, through GM, decides it.
Chaos That Begins at the Bottom of a Pot — Rayleigh–Bénard Convection and the Lorenz Equations
·5 min read
Rolls switch on at Rayleigh number 1708 with rigid walls. In the Lorenz truncation that heating, written as rho, stops settling once rho passes 24.74.
Where the Ideal Gas Starts to Lie — Compressibility Factor Z and the van der Waals Equation
·6 min read
Nitrogen at 100 bar and 200 K has Z = 0.7905. The ideal-gas density, 168.4 kg/m3, is about 26 percent lighter than the real 213.0.