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.