As I have now told explicitly what are the errors / approximations that have made the equation (34) deviate from a similar equation derived from (32) and (33), I hope that you finally admit, that it's just an approximate and by that a little erroneous version
of a continuity equations.
Everything is in full agreement with a description
of a continuity equation when the horizontal contributions are assumed zero and when a little lacking care is applied for the vertical part (the second term is only approximately correct).
The only way you could counter my point is to present a step - by - step explicit justification of he equation (34), and not one that's a derivation
of a continuity equation.
The equation is not an exactly correct continuity equation, but it's what can easily be written, when the continuity equation is written based on the reasoning of the three parts
of the continuity equation.
Only now I realized that the paper tells in the later chapter, what the equation is supposed to be, and it tells it with the description
of an continuity equation without any independent physics.
If it would be based on independent physics, then some specific physical input must be introduced to
that of continuity equations.
Pekka,» Everything is in full agreement with a description
of a continuity equation when the horizontal contributions are assumed zero and when a little lacking care is applied for the vertical part (the second term is only approximately correct).»
Not exact matches
It sounds like, despite questions about how exactly Colin Firth fits into the
equation and the setting
of at least part
of the film in the United States, there's going to be quite a bit
of continuity: same director, same writer and, according to Goldman, a similar mindset as the first film.
I mean there was something that I felt in my own
equation of the
continuity between Paul Klee, Duchamp, Picabia, and, oddly enough, Clyfford Still.
The basic governing
equations are Bernoulli's
Equation for hydraulic potential and the continuity equation, a time variable form of the Laplace E
Equation for hydraulic potential and the
continuity equation, a time variable form of the Laplace E
equation, a time variable form
of the Laplace
EquationEquation.
3)
Continuity equation tells, how the source term affects masses or numbers
of moles
of each substance.
For the number
of molecules
of a two - component gas two
continuity equations are independent.
No, it's not fine the consequences
of the source term are given by the
continuity equations.
iii) The other side
of the
equation is the source term exactly as it is in a
continuity equation.
In your comment you are discussing the physical process that leads to condensation, but the
equation (34) is not about that, it's derived by you to describe the outcome
of the condensation, i.e., it's derived as a superfluous
continuity equation, as I have explained several times.
The horizontal pressure gradients are determined from the
continuity equation, with the condensation rate calculated from the Clausius - Clapeyron law using temperature derived from the first law
of thermodynamics with empirically fitted turbulence.
I can not imagine any connection with an
equation of that form to anything else than the
continuity equation.
It's form is that
of an approximate
continuity equation.
These
equations do not include the purely dynamical constraints
of continuity or hydrostatics, nor do they invoke the Second Law, but nevertheless define certain relations that must hold between the state variables.
The paper makes an explicit error in the derivation
of formulas (36) and (37) when it requires that the exact
continuity equation and the approximate
continuity equation are simultaneously valid.
Could it still be a
equation for the source term in spite
of the fact that it looks an approximate
continuity equation and in spite
of the fact that AM tells that it serves as a
continuity equation?
The
continuity equations and the thermodynamic
equations related to isentropic processes
of rising air and condensation determine the whole process.
Without an independent knowledge
of S, the
continuity (mass conservation)
equation is uninformative (e.g., referred to as a «tautologism» by Truesdell and Toupin (1960) The classical field theories, Handbuch der Physik Band III / 1, 226 - 793).
The reason I ask these questions is that I am convinced that there is a fundamental limit to the predictability
of the dynamical «core»
equations (
continuity, momentum, energy) due to the ** nonlinearity **
of the system.
Structural
equation modeling
of prospective, longitudinal data from 808 participants, their parents, and their children showed low levels
of G1 to G2 cross-generational
continuity in the general tendency to use drugs.
[jounal] Quintana, S. M. / 1987 / Adolescent attachment and ego identity: A structural
equations approach to the
continuity of adaptation / Journal
of Adolescence Research 2: 393 ~ 409