# Water Rocket

Which one is more correct because the two sets are different in the velocity, time that it takes for the water to fully escape rocket, flow velocity, and the adiabatic constant.

Edit: the change in total volume affected all of the above? And mfb, how did you derive your height equation, I get the same expression but without the square root. And is the area A theoretical because the area of the cross section is pi*r^2 and the radius is 0.025 meters.

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haruspex
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Which one is more correct because the two sets are different in the velocity, time that it takes for the water to fully escape rocket, flow velocity, and the adiabatic constant.
mfb, didn't understand what you said about fixing the total volume to one litre. That's what I already had: Vf = 0.001.

You can get a handle on the accuracy of the spreadsheet by making the time steps finer until it doesn't change the result much.
mfb is right that the steps were much too coarse for the early stages. I've change the time step formula in my copy to e.g.:
A5 = A4*1.01 + 0.0001
That way you get a much finer step initially, but the steps broaden as things settle down. Another approach would be to make the step size inversely proportional to the acceleration caclulated in the preceding row.
Determining the accuracy of an analytic solution, given that it necessarily simplifies some equations to be able to solve them, is much harder. OTOH, if it is at all accurate then you could differentiate wrt settings (like initial airspace) to see the effect of changing them.
Of course, you could do the same or better programmatically. Turn the spreadsheet into a C program and wrap it in a loop which hunts for max height.

Haruspex, how did you get area A?

I noticed that mfb has different values for V0 (volume of air) and Vf. Vf has another decimal place (8E-4) and it's even smaller than haruspex's (1E-3). Why the discrepancy?

haruspex
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Haruspex, how did you get area A?

I noticed that mfb has different values for V0 (volume of air) and Vf. Vf has another decimal place (8E-4) and it's even smaller than haruspex's (1E-3). Why the discrepancy?

I just plugged in some sensible numbers to see the spreadsheet work. It's up to you to put the right ones in. As I said, I used MKS throughout, so A is in sq metres.
From mfb's earlier comment about fixing the total volume, I think there might be some misunderstanding here. The spreadsheet takes Vf as a fixed total volume with air volume V=V(t) expanding from V(0) towards Vf, and the remaining water at time t is therefore Vf-V(t).
If the initial air pressure is insufficient for the given V(0) then V will never reach Vf.

mfb
Mentor
Your initial V_air is V0, and it increases to V0+Vf (assuming the pressure is enough to eject all water). Therefore, the total volume is V0+Vf. I fixed this, which gives the formula V0=Vtotal-Vf with the total volume Vtotal.

I modified the values a bit to increase the height and to increase the similarity with the coke bottle. 0.5kg are still much for the empty rocket, I think that can be reduced a bit - and the total height depends crucially on this parameter.

haruspex
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Your initial V_air is V0, and it increases to V0+Vf (assuming the pressure is enough to eject all water). Therefore, the total volume is V0+Vf. I fixed this, which gives the formula V0=Vtotal-Vf with the total volume Vtotal.

No, it increases to Vf. Have you found something in the spreadsheet that says otherwise?

mfb
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Oh... sorry, I got confused by the decimal places.
You are right.

P(t) or P0 is the pressure of the air inside the bottle? If so, that is obtained by the amount of psi used in the experiment, correct, which in my case, will vary from 50 psi to 65 psi (but in pascals)?
And how is the volume of the air, V0 obtained?

I apologize for all the questions, I just want to be completely clear with all the steps used.

mfb
Mentor
P(t) or P0 is the pressure of the air inside the bottle? If so, that is obtained by the amount of psi used in the experiment, correct, which in my case, will vary from 50 psi to 65 psi (but in pascals)?
Right

And how is the volume of the air, V0 obtained?
The volume of the bottle minus the volume of the water inside.

Okay, so haruspex's spreadsheet is fine except that I need to fix the time and change the variables to the ones I need (mass, etc).

Edit: 2 L is 0.002 cubic meters and the volume of the water is 0.001 cubic meters and that gives me 0.001 cubic meters. When I change V0 to that, all the other variables because the same.

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Help. Anyone? This is due in a few hours and I don't know how you got the volume of air so low when I get 0.001 cubic meters and that ruins the whole spreadsheet as it must be, apparently, at least 0.0001 cubic meters to take any effect.

haruspex