Greg Esres wrote:
To be precise, the upward force the disk is the difference in the
pressure below the disk less the pressure above,

You're correct; equating pressure with force is a convenience to
simply discussions; it's a bit sloppy.

Force is defined as the time rate of change of momentum. ...

That's not a definition, it's an equation.

Again, to be precise, that is the equation which defines force IF
you work in a aystem in which mass and acceleration are previously
defined. In physics, definitions usually are equations.

--

FF