Mathematical model for water rocket

[allistair]

I have to write a program in maple that calculates the water rockets movement. For this i first need to model the pressure inside the water bottle and also i have to calculate how long it would take for all the water to be ejected from the water rocket, all off this numericaly because the equation gets quite complex. But I'm uncertain if my values for the pressure and especially the amount of water left in the rocket are realistic. For a 1.5Liter bottle that is half filled with air and half with water under a pressure of 4atm my program says that after 0.1s all the water has left the rocket, which seems very little to me.

So here's my question, has anyone here ever done that experiment? (i don't have the time to put together a rocket myself) And if you have can you tell me if this value is realistic?

 

[OlderDan]

I have to write a program in maple that calculates the water rockets movement. For this i first need to model the pressure inside the water bottle and also i have to calculate how long it would take for all the water to be ejected from the water rocket, all off this numericaly because the equation gets quite complex. But I'm uncertain if my values for the pressure and especially the amount of water left in the rocket are realistic. For a 1.5Liter bottle that is half filled with air and half with water under a pressure of 4atm my program says that after 0.1s all the water has left the rocket, which seems very little to me.

So here's my question, has anyone here ever done that experiment? (i don't have the time to put together a rocket myself) And if you have can you tell me if this value is realistic?

The time it takes for all the water to leave will depend on the area of the opening it has to go through to get out of the bottle. If the opening is large, it will take very little time. A pressure difference of a few atmospheres is a lot of pressure. Convert it to Newtons per square cm and you can have several Newtons of force acting on less than a kg of mass if there is no nozzle to constrict the flow. Toy water rockets usually have an opening of a couple of mm at most and lose their water in a few seconds.

 

[tacman]

Your approach to modeling the water rocket using Maple is a good start. It is important to consider the pressure inside the water bottle and the amount of water ejected in order to accurately predict the movement of the rocket. However, as you mentioned, the equation can become complex and it is important to ensure that your values for pressure and water volume are realistic.

To address your question, I have not personally done this experiment but there are many resources available online that provide information and data on water rocket experiments. It would be beneficial for you to research and compare your results with other experiments to validate your values for pressure and water volume.

Additionally, it may be helpful to consider the specific design and materials of the water rocket you are modeling. Different designs and materials can affect the pressure and water ejection process, so it is important to take those factors into account.

Overall, it is important to validate your values and ensure that your model accurately reflects real-world results. Good luck with your project!