As they say, a picture is worth a thousand words, so I sketched up a nozzle
free-body diagram ( https://en.wikipedia.org/wiki/Free_body_diagram), a
favourite tool of engineers. Attached.
This neglects minor forces such as those due to flow friction and
atmospheric pressure.
The reaction "R" is the force being applied to the nozzle at the snap ring.
The length of the red arrows represents the magnitude of the force due to
pressure.
If the x-direction component of the forces are added up, it can be seen by
inspection that the net force is to the left, which means a positive
reaction is developed at the snap ring, as expected.
(note "Pa" is ambient pressure, "Po" is chamber pressure)
Richard
On Thu, Jun 2, 2022 at 10:07 AM Kelly Jones <kellyjones1@xxxxxxxxx> wrote:
If you draw a free body diagram on the nozzle, you have:
1) acting rearward, the chamber pressure times the (cross sectional area
of the chamber minus the throat),
2) acting forward, the throat pressure (which will always be less than the
chamber pressure) times the (cross sectional area of the divergent cone
minus the throat), and
3) acting rearward, some drag force of the flow on the throat.
Even neglecting (3), which always pushes to the rear anyway, we can see
that (2) is always less than (1) because the chamber pressure is always
higher, and the area upon which it acts is generally smaller. (If the
divergent nozzle is actually wider than the chamber, then you're probably
over expanding, in which case now you're starting to apply negative
(rearward) pressure to the nozzle over a portion of it's area).
So, force on the nozzle should always be in the rearward direction.
On Thu, Jun 2, 2022 at 7:21 AM Bill Kuker <bkuker@xxxxxxxxxxxxx> wrote:
Having read through a fair bit online, I am thinking that since the mach
1 choked flow at the throat would prevent the chamber side from "feeling"
any change in pressure on the diverging side, the additional thrust created
by the diverging side must be acting upon the diverging side.
At the absolute limit - perfect infinite massless nozzle expelling to a
vacuum where the beer is never warm - the entirety of the chamber pressure
up to the throat would be balanced out and net zero force, wouldn't it?
My gut agrees that the sum of forces on the nozzle is dominated by
pressure "out", not thrust "in". No one ever complains about their motor
imploding!
On Wed, Jun 1, 2022 at 1:38 PM Brinker, Mike <mikebrinker@xxxxxxx> wrote:
Yep. The pressure on the convergent chamber side should always be
greater than the pressure on the divergent side of the nozzle, while the
motor is burning. I believe the primary “pushing force” is against the
forward closure of the motor and not the divergent side of the nozzle. So,
even a motor with no liner or forward retention should stay in place during
the burn (assuming pointy end stays up).
If you want to go really deep on the topic, the book “Rocket Propulsion
Elements” has 50 pages in chapter three dedicated to nozzle theory and how
the different forces interact under different conditions.
On Jun 1, 2022, at 10:22 AM, Oliver Arend ("oarend") <
dmarc-noreply@xxxxxxxxxxxxx> wrote:
The highest pressure in a rocket motor is in the combustion chamber. In
the convergent section speed is increasing, pressure decreasing, and both
of these even further in the divergent part. So pressure is higher on the
inside and pushing the nozzle out the back. The action=reaction to the
thrust you're looking for happens at the forward bulkhead of the motor, I'd
say.
Oliver
Bill Kuker <bkuker@xxxxxxxxxxxxx> schrieb am Mi., 1. Juni 2022, 13:02:
My motors tend to have a convergent-divergent nozzle slid into the
casing with an o-ring and retained with a clip or something that prevents
them from being ejected, but would allow it to slide further up into the
motor.
Obviously the pressure is trying to push it out, right? That's how
rocket motors work!
Except the interaction of the expanding gas with the convergent part of
the nozzle is actually where the magic happens, accelerating the exhaust by
trading pressure and temperature for velocity.
I'm ready to be wrong here, but wouldn't a large proportion of the
total thrust be pushing the nozzle IN TO the motor? All the forces have to
balance, and you can't accelerate the gas without something to push against
(I do NOT mean that like the question "how do rockets work in space with no
ground to push against?")
I haven't sat down to work out the net force on the nozzle of an
example motor, any of you ever done so, or suspect that the answer might be
surprising?
-Bill
Attachment:
nozzle-fbd.jpg
Description: JPEG image
