Rocket propulsion explained only through pressure differential

[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.

 

[Aeronautic Freek]

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.

are you mean on pressure on outside or inside the tank near the nozzle?

 

[Aeronautic Freek]

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

how do you mean it is not physicaly possible?you can allways make air pump which will hold constant pressure in the tank during load cell test...

 

[cjl]

are you mean on pressure on outside or inside the tank near the nozzle?

On the inside of the tank near the nozzle.

 

[cjl]

how do you mean it is not physicaly possible?you can allways make air pump which will hold constant pressure in the tank during load cell test...

Sure, through most of the tank, but there will be flow out the nozzle, and this means that fluid adjacent to the nozzle will be moving. This can only happen if the fluid adjacent to the nozzle is at a lower pressure than the tank's overall pressure, so you can never have a situation where the pressure is 5 bar everywhere against the tank walls (including right next to the orifice) but fluid is flowing out of the orifice. You will always have a pressure gradient as you approach the orifice.

 

[Aeronautic Freek]

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

if you integrate pressure around tank, you will know what is thrust,same like integrate static pressure around wing...
isnt it?

(indeed this is my basics question,prove thrust with pressure difference between inside and outside wall of tank)

 

[cjl]

Yes, that will definitely provide the thrust. The difficulty lies in predicting exactly what the pressure is at all points, especially in the vicinity of the nozzle.

 

[sophiecentaur]

if you integrate pressure around tank, you will know what is thrust,same like integrate static pressure around wing...
isnt it?

(indeed this is my basics question,prove thrust with pressure difference between inside and outside wall of tank)

Right. So the nature of the ejecta will affect the pressure. Fair enough; then the pressure is all you need because it will give you the net force rearwards. I guess the other performance factors like efficiency are additional if you want to find how fast the craft will end up travelling.

 

[Aeronautic Freek]

Sure, through most of the tank, but there will be flow out the nozzle, and this means that fluid adjacent to the nozzle will be moving. This can only happen if the fluid adjacent to the nozzle is at a lower pressure than the tank's overall pressure, so you can never have a situation where the pressure is 5 bar everywhere against the tank walls (including right next to the orifice) but fluid is flowing out of the orifice. You will always have a pressure gradient as you approach the orifice.

i added two red arrows on left tank,you mean this on this region?

so from this,air velocity is higher than water,so pressure drop is higher in air case,so there is less internal pressure which will push on the wall,so air tank will have grater thrust...

that is your logic?

 

[cjl]

Yes, that is the region I'm talking about. I would guess that the air would have a higher thrust, but as I said, I don't actually know that for sure (since I can't say for sure what the pressure would be in that area, and the higher velocity alone doesn't actually tell you that the air would have a lower pressure in that region).

 

[Aeronautic Freek]

Yes, that is the region I'm talking about. I would guess that the air would have a higher thrust, but as I said, I don't actually know that for sure (since I can't say for sure what the pressure would be in that area, and the higher velocity alone doesn't actually tell you that the air would have a lower pressure in that region).

yes if we put tank in CFD softwear we will see inside pressure distribution near the nozzle..
also jet of air outsite of nozzle will suck suorading air which will reduce a little bit atmospheric pressure on outside walls of tank near the nozzle,but i think this is so small...

are you also physics proffesor?

 

[cjl]

No, I am not, but I do have a masters degree in aerospace engineering, with a focus on fluid dynamics.

 

[shjacks45]

So you are comparing an aeronautical device, a wing, which operates by interacting with a fluid, with a rocket whose only interaction with fluid is air/water drag. Often we need to compare disparate objects for a specific purpose however you have not set those conditions, say comparing apples to oranges sugar content or price. It appears you want to compare force to work, which have different units. Like military generals confused by engines rated in horsepower versus pounds thrust.