being related to the kinetic energy formula
- and an excellent way to remember it too! In simple terms Msr Bernoulli's equations are based on the conservation of total energy - Pressure + KE - hence the 1/2 x m x V squared which reduces to 1/2 p in non-dimensional terms (that's Rho but I cannot be arsed to dig it out), and KE is found as an integral of v wrt dv (that's Delta V - see above) which produces the 1/2.
Time for a glass of wine, I feel.
Should, of course, say at low Mach numbers before I am jumped on.