The question at hand got resolved while you were away: the difference
between the conservation-of-momentum result and the textbook equation
is that in vacuum, the exhaust continues accelerating after it leaves
the nozzle, since there is still a downstream pressure gradient. So
when you calculate Ve (aka v2) at the exit plane of the nozzle, that's
not the final velocity.
Anyway, that's of the same general nature as the explanation you
offered (it's an issue regarding the definition of velocity), but the
specifics are different. The "effective exhaust velocity" is just
defined to be whatever velocity lets you delete the pressure terms
from the equation. So appealing to it is not particlarly enlightening
as regards the question of where the pressure thrust comes from.
On Wed, Nov 16, 2016 at 04:34:49AM +0000, Ian Woollard wrote:
Sutton? Rocket Propulsion Elements uses 'V2' instead of Ve and specifically
defines it as the exhaust velocity when the exhaust pressure and ambient
pressure are the same:
https://www.ewp.rpi.edu/hartford/~ernesto/S2013/EP/MaterialsforStudents/Lee/Sutton-Biblarz-Rocket_Propulsion_Elements.pdf
See page 32.
The equation given is:
F = m_dot v2 + (p2 -- p3)*A2
where v2 is the effective exhaust velocity when p2=p3, and p2, p3 are the
exhaust plane pressures and the ambient pressures respectively.
On 5 November 2016 at 05:35, Norman Yarvin <yarvin@xxxxxxxxxxxx> wrote:
On Fri, Nov 04, 2016 at 05:37:49AM +0000, Ian Woollard wrote:
On 2 November 2016 at 19:52, Norman Yarvin <yarvin@xxxxxxxxxxxx> wrote:
if one
takes the textbook equation and compares it under vacuum conditions to
the conservation of momentum, there's an extra term ("pressure
thrust") on one side of the textbook equation,
Yes!
so the two equations disagree.
No!
Fans of Douglas Adams will appreciate the concept of having tea and no tea
simultaneously, but the resolution for this apparent paradox is far
simpler: the Ve/Isps are different! In one case it is the vacuum Isp, and
in the other, it is the effective Isp when Pe=Pa.
Not in the textbooks I looked at. In them, Ve was the actual exhaust
velocity. Sometimes there was another variable, the "effective
exhaust velocity", but that was denoted differently and wasn't what
was in the equation in question.
Of course there may be textbooks that get this right; feel free to
point one out.
--
-Ian Woollard
Sent from my Turing machine
