Rocket propulsion explained only through pressure differential

[Aeronautic Freek]

Fluid can exert force to object(move object) only through pressure and tangential stress caused by viscosity.

if we look at balloon rocket ,here is Newton 3 law action-reaction,but this 3 law as usual don't tell nothing how fluid really exert force to the ballon..
it exert through pressure imbalance,because on open end there is no internal pressure to push against,so thrust = (Pc-Pa) x A(area of open end)
just like sail /wing pressure differentila x area = force(lift)

But if we have balloon with water at 5bars and balloon with air at 5bars,same nozzles,ballon with water will have far more bigger thrust..
How we can explain why balloon with water will has bigger thrust IN SENSE OF PRESSURE DFFERENTIAL?(i know that thrust formula inculde mass flow rate(so water due to higher density has bigger mass flow rate,so that make difference in thurst magnitude),but i want explanation through pressure differetnial because that is really and only physical way how fluid can move object...)

So if both balloon are at 5 bars where is that bigger pressure differential(imbalance) in water case??

 

[Aeronautic Freek]

so...

when valve is closed both manometer will show 5 bars(if you don't take to account water height-additional hydrostatic pressure compare to air..)
when vlave is open will manomenter at right tank(with water) show greater pressure than left(with air),so this will "justifay" in sense of pressure differential why tank with water will have greater thrust??(if you put this tanks on skateboard,tank with water will accelerate faster than with air)

so will right manometer in same manner show higher pressure,when water accelarate to the right when valve is open,compare to tank with air?

 

[cjl]

How sure are you that there is a thrust difference?

I'd expect the exhaust velocity from an air filled balloon to be significantly higher, and the balloon to empty faster (given identical internal pressure), so you'll have more factors than just the difference in density to cause a thrust difference.

In addition, your diagram will underestimate the thrust, since the fluid velocity near the nozzle will be nonzero, and thus the pressure on the balloon near the nozzle will actually be lower than the pressure on the balloon far from the nozzle. In addition to there being no internal pressure on the balloon where the hole itself exists, there will be a larger region around it with reduced pressure, causing greater thrust than you expect.

(Things are further complicated in your "5 bar" case by the fact that this will cause the air flow to choke in the nozzle, creating sonic flow, but we can solve that for now by just imagining a much smaller internal pressure such that the flow velocities remain small instead)

 

[A.T.]

(tank with water will accelerate faster than with air)

Will it accelerate more initially, or will it accelerate over a longer period of time, and thus gain more momentum in total.

 

[russ_watters]

it exert through pressure imbalance,because on open end there is no internal pressure to push against...

You got some good responses, but one other point to keep in mind is that the simplified explanation that says there is zero pressure at the open end is only approximately true for low pressures/velocities, but is very wrong for higher pressures and velocities. Heck, a real rocket has a diverging nozzle and the gases are pushing against it as well. For a water rocket (jet ski?), the nozzle is converging only because the fluid is incompressible.

 

[Aeronautic Freek]

Will it accelerate more initially, or will it accelerate over a longer period of time, and thus gain more momentum in total.

lets assume that we can keep pressure in tank constant 5bars(with pump) all the time when skate is moving,for simplicity ...nozzle area is the same in both case.. so we have only different fluids(density),but for sure velocity of water in the nozzle will be smaller compare to air..

1)
what is difference in internal pressure distribution in tank with air and with water when valve is open,what will show my manometers from pictures,so how we can explain difference in thrust force through difference in internal pressure distribution?

2)
does water accelaration from nozzle cause increase in pressure on opposite wall from nozzle(my manometer on picture) in same manner as weight scale increase reading when I push ball to the right(example in pictrue,post#2)??

(or maybe yout think that thrust force will be the same?)

 

[Aeronautic Freek]

You got some good responses, but one other point to keep in mind is that the simplified explanation that says there is zero pressure at the open end is only approximately true for low pressures/velocities, but is very wrong for higher pressures and velocities. Heck, a real rocket has a diverging nozzle and the gases are pushing against it as well. For a water rocket (jet ski?), the nozzle is converging only because the fluid is incompressible.

it doesn't matter,my nozzle is straight,so fluid goes parallel to the walls ,so it can not exert force which will contribution to the thrust,whenever nozzel is open there is no wall surface where internal pressure will push against,so difference in static pressure in nozzle in air and water can not make difference too..

so where come from this difference?

 

[A.T.]

lets assume that we can keep pressure in tank constant 5bars(with pump) all the time when skate is moving,for simplicity ...nozzle area is the same in both case.. so we have only different fluids(density),but for sure velocity of water in the nozzle will be smaller compare to air..

(or maybe yout think that thrust force will be the same?)

Why do you think thrust would be different here?

 

[Aeronautic Freek]

Why do you think thrust would be different here?

when i try do this experiment ,skate with water tank is travel longer distance and seems to me that accelarte faster...
i didnt have two skates and two tanks,to compare it simultaneously..

does theory said that thrust will be equal?

 

[A.T.]

lets assume that we can keep pressure in tank constant 5bars(with pump) all the time when skate is moving...

Why do you think thrust would be different here?

when i try do this experiment ...

You did the experiment, where you kept the pressure in the tank constant 5bar?

 

[sophiecentaur]

One important point here is that propulsion / acceleration is a matter of Energy transfer (alternatively Momentum Transfer). Pressure, alone, is not Energy or Momentum; and you need to exert pressure over a distance (work) or time (impulse) to do work on the 'rocket'. Blowing air or water through the hole involves work and movement of the propellant is responsible for that.
A nozzle will increase the total force component rearwards and the mass ejected in that direction per unit time explains the momentum transfer.
There's a good class experiment with a water rocket that establishes the water to air ratio in the pumped up rocket to give maximum height. Pressure (stored energy in the air) varies, of course and the skateboard allows a shorter time for the experiment and you can assume that the pressure doesn't change too much over the first sort distance.

 

[Aeronautic Freek]

You did the experiment, where you kept the pressure in the tank constant 5bar?

no..

 

[Aeronautic Freek]

i ask again:

does water accelaration from nozzle cause increase in pressure at opposite wall from nozzle(my manometer on picture) in same manner as weight scale increase reading when I push ball to the right(example in pictrue,post#2)??

 

[A.T.]

i ask again:

does water accelaration from nozzle cause increase in pressure at opposite wall from nozzle(my manometer on picture) in same manner as weight scale increase reading when I push ball to the right(example in pictrue,post#2)??

No.

 

[Aeronautic Freek]

No.

so with constant 5bar pressure inside tank,tank with water and air will have same thrust force?

 

[A.T.]

so with constant 5bar pressure inside tank,tank with water and air will have same thrust force?

Yes, with the same pressure everywhere in the tank in both cases, and the same straight nozzle, the thrust will be the same.

 

[cjl]

I don't necessarily agree, because as I said, the pressure adjacent to the nozzle won't necessarily be the same.

 

[A.T.]

I don't necessarily agree, because as I said, the pressure adjacent to the nozzle won't necessarily be the same.

So which one will have greater thrust?

 

[Nugatory]

does theory said that thrust will be equal?

The thrust at equal tank pressure will be the same (assuming the idealized setup in post #1, which is good enough here). However, the there is no reason to assume that the tank pressure over time will be the same. The idealized setup doesn’t let you calculate an accurate time/pressure curve (for that you need a realistic setup in which fluid dynamics effects determine the flow of propellant) but you can get something qualitatively reasonable by assuming that the propellant is only subject to net force while it is in the short stem nozzle and accelerates according to $F=ma$ while there.

You will have to solve a differential equation as part of this calculation, but there’s an easier route to the conclusion: When all is said and done, you will have a mass of propellant moving to the right and a rocket with an empty tank moving to the left. The total kinetic energy of the two will be equal to the energy released by the expansion of the air. The total momentum will be zero, so you can solve for the speed of the two as a function of the ratio of their masses. You will find that as the propellant becomes relatively heavier more of the kinetic energy end up with the ship

 

[sophiecentaur]

When all is said and done, you will have a mass of propellant moving to the right

Are you sure that all the mass will be moving to the right at the same velocity ? (Earth's reference frame) As the ship speeds up, the ejecta will be slower in the inertial frame.

more of the kinetic energy end up with the ship

If you start with Momentum you can get the velocity of the ship and that will tell you the ship's final KE.

 

[Nugatory]

Are you sure that all the mass will be moving to the right at the same velocity ? (Earth's reference frame) As the ship speeds up, the ejecta will be slower in the inertial frame.

That’s right, but it doesn’t change the conclusion.

You can get arbitrarily close to that that state by assuming an arbitrarily short period of thrust and that saves having to do an integration.

 

[Aeronautic Freek]

. However, the there is no reason to assume that the tank pressure over time will be the same.

lets set my question ,with constant pressure in the tank,it is easier to solve problem...and to stope confusing mebers with my initial setup
so
-so we have pumps which pump air in the tank and hold constant pressure (5bar) even when valve is open, in both cases
-nozzle is the same
-tank is put on wheels and connect to load-cell which meassure thrust force

two questions;
1)which tank will show higher thrust,when we open valve at nozzle,with water or with air inside?
2)will both manometers show 5 bar,when we open valves?(neglect hydrostatic pressure caused by water column)

 

[cjl]

So which one will have greater thrust?

I don't know, off the top of my head. You'd have to do the experiment or simulation yourself. I would guess that you'd get more thrust in the water case than the air case, but I haven't actually done a whole lot of thought or anything to back that up - that's purely initial intuition (and could easily be wrong).

 

[Aeronautic Freek]

I don't know, off the top of my head. You'd have to do the experiment or simulation yourself. I would guess that you'd get more thrust in the water case than the air case, but I haven't actually done a whole lot of thought or anything to back that up - that's purely initial intuition (and could easily be wrong).

when i do this test,(without constant pressure) so just fill tank at 5bar and open ventil,it seems to me that water tank accelerate faster..water skate also make much more distance approx 20m,air tank maybe 5m...pressure drop in air tank very very faste so skate pass less distance...

how do you mean you don't know i am not ask this to guess ,i am ask this to explain with phyiscs,you are physicsts you must know that?



also must be some reason why amater rocket use water not air..

 

[A.T.]

when i do this test,(without constant pressure) so just fill both tank at 5bar and open ventil,it seems to me that water tank accelerate faster ...

What do you mean by "accelerate faster"? Did you measure the max. acceleration? Or just the final speed reached. These are two different things.

The pressure in the air tank will drop much faster, so you just get a very short thrust. With the water the thrust acts much longer and you are expelling more mass.

BTW: Smart phones have accelerometers and there are apps the can log the data.

 

[Aeronautic Freek]

What do you mean by "accelerate faster"? Did you measure the max. acceleration? Or just the final speed reached. These are two different things.

The pressure in the air tank will drop much faster, so you just get a very short thrust. With the water the thrust acts much longer and you are expelling more mass.

BTW: Smart phones have accelerometers and there are apps the can log the data.

no i didnt meassure acceleration,it just seems to bear eye that water tank accelarate faster...
final speed is far more higer on water tank,because thrust last far longer...

 

[Aeronautic Freek]

A.T.
look at my post #22, so load cell will show same thrust?
does theory prove that?

 

[cjl]

when i do this test,(without constant pressure) so just fill tank at 5bar and open ventil,it seems to me that water tank accelerate faster..water skate also make much more distance approx 20m,air tank maybe 5m...pressure drop in air tank very very faste so skate pass less distance...

how do you mean you don't know i am not ask this to guess ,i am ask this to explain with phyiscs,you are physicsts you must know that?

Just because something is driven by fundamental physics principles doesn't make it simple. Fluid flow, in particular, is frequently far from simple, and in your case, this is further complicated by the fact that the water will act basically incompressibly here, so your exit velocity will basically be sqrt(2P/density), while the air will act compressibly and (at least theoretically) choke in the nozzle as long as your pressure inside the bottle is greater than about twice the ambient pressure. This makes the air-powered case substantially different than the water powered case, and it is not obvious to me exactly how this would play out. There is no question though that the water powered case would provide a substantially longer duration of thrust, and more total impulse due to the much larger reaction mass.

also must be some reason why amater rocket use water not air..

Because it provides you with a much larger reaction mass, and overall rocket performance doesn't just depend on thrust or efficiency, it also depends on the mass fraction of your rocket that is structure vs propellant. With water, you can achieve a very high proportion of your overall mass as propellant, which improves overall performance even if the peak thrust is lower or the efficiency is lower (I'm not saying it necessarily is - as I said above, I honestly don't know).

 

[A.T.]

A.T.
look at my post #22, so load cell will show same thrust?
does theory prove that?

As @cjl writes, it depends on how accurately you want to be the same, because there might be minor effects that are difficult to predict.

But on your general question: Yes, the thrust is completely accounted for, by the integral of the pressure forces acting all around the tank, regardless if the pressure comes from air or water. The uncertainty here comes from your hypothetical setup, where it's not clear if you can realize the same pressure everywhere in the tank in a dynamic flow situation.

 

[Aeronautic Freek]

The uncertainty here comes from your hypothetical setup, where it's not clear if you can realize the same pressure everywhere in the tank in a dynamic flow situation.

we can have air pump which will hold constant pressure(5bar) all the time when we meassure thrust with load cell..
but what is static pressure in moving fluid in nozzle i don't know,but i think it doesn't metter ,because nozzle is flat so it doesn't has pressure component in x direction which will gives contribution to the thrust

 

[cjl]

As @cjl writes, it depends on how accurately you want to be the same, because there might be minor effects that are difficult to predict.

But on your general question: Yes, the thrust is completely accounted for, by the integral of the pressure forces acting all around the tank, regardless if the pressure comes from air or water. The uncertainty here comes from your hypothetical setup, where it's not clear if you can realize the same pressure everywhere in the tank in a dynamic flow situation.

I think the differences will be a lot more than minor. Yes, the integral around the tank will give you the thrust, but the pressure on the back of the tank in the vicinity of the nozzle will not be anywhere close to the same as the static pressure the tank was pressurized to, and I suspect that the pressure in this region around the nozzle will be substantially different in the incompressible case (water) vs the compressible case (air).

 

[cjl]

we can have air pump which will hold constant pressure(5bar) all the time when we meassure thrust with load cell..
but what is static pressure in moving fluid in nozzle i don't know,but i think it doesn't metter ,because nozzle is flat so it doesn't has pressure component in x direction which will gives contribution to the thrust

It's not the pressure in the nozzle itself that I'm concerned about, but rather the pressure on the back wall around the nozzle inlet. Flow in this area will be moving with substantial velocity, and therefore will not be at the nominal tank pressure, and this force will be contributing in the thrust direction so it is absolutely relevant to what the overall thrust of the rocket will be. You won't just have 5 bar everywhere except the nozzle - you'll have 5 bar on the front and sides, but in the area around the nozzle, the pressure will be somewhere between ambient and 5 bar, and it will be different in the water case from what it is in the air case.

 

[A.T.]

Yes, the integral around the tank will give you the thrust,

This seems to be at the core what the OP is asking about. The hypothetical same pressure scenario just seems like means to an end.

 

[cjl]

Sure, but I'm worried that the hypothetical same pressure scenario will lead to some incorrect conclusions since it is not physically possible.

 

[sophiecentaur]

Bottom line is that you need more than pressure values to get the effective propulsion.