Bernoulli's Law of Hydro Pressure - History Q

Factual Questions
1

I am reading the book Five Equations that Changed the World by Michael Guillen - so far, a good book (although since the topic is meant to be the equations, I don’t know why his picture is on the cover - handsome he ain’t).

Anyway I just finished the section on Bernoulli’s Law:

P + p x 1/2v^2 = constant

and a couple of questions were not resolved:

  1. Apparently, Bernoulli’s original equation did not have the 1/2 in it - the quote from the book is: “A century later, a German physicist named Gustave Gaspard Coriolis would add a factor of one-half to the original formula for vis viva [the term Bernoulli used when referring to energy]. He did this while working on a wholly different problem - one having to do with the earth’s spin - solely for the convenience of his own calculations, but his version of the formula stuck.” Okay, but doesn’t including the factor of 1/2 change the proportions of the equation? It seems a little random - is this really mathematically okay?

  2. The book makes a big deal about the fact that Bernoulli and his father, Johann, ended up as rivals over the fact that they shared a prestigious French math prize. This led to another conflict - while Daniel Bernoulli was writing the book that had this famous formula in it, his father Johann ended up publishing a book with a lot of similar info, and apparently the mathemetician Lenhard Euler aided and abetted Bernoulli the dad (since Bernoulli pere tutored Euler years ago) by delaying his review of Bernoulli fils book. So how was this resolved in a way that is was clear that the son Daniel was in fact the first to discover this formula? If dad came out with his book first, wouldn’t he be given credit unless a big hullaballoo took place, such as when Leibniz published about calculus before Newton, but Newton fought for and received partial (if not most of the) credit? What happened so that Daniel got the credit?

2

I know Bernoulli’s equation as:

P + (1/2)p(v^2) + pgy = constant

where P is the sum of the pressure, p is the Greek letter “rho” (the symbol for density), v is the velocity, g is the acceleration due to gravity and y is the vertical distance (depth).

This means that the kinetic energy per unit volume ( (1/2)p(v^2) ) plus the potential energy per unit volume ( pgy ) plus the pressure ( P ) has the same value along all points along a streamline.

[from a physics text]