# Mathematical model for water rocket

• Mathematica
• allistair
In summary, the speaker needs to write a program in Maple to calculate the movement of a water rocket. They are unsure about the accuracy of their values for pressure and water volume in the rocket. They question if the estimated time for all the water to be ejected is realistic and ask for input from anyone who has done this experiment. They also mention the importance of the size of the opening for the water to exit the bottle.
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?

allistair said:
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.

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!

## 1. What is a mathematical model for water rocket?

A mathematical model for water rocket is a representation of the physical laws and principles that govern the flight of a water rocket, using mathematical equations and calculations. It allows scientists and engineers to predict the performance and behavior of a water rocket before it is actually launched.

## 2. Why is a mathematical model important for water rocket design?

A mathematical model is important for water rocket design because it helps to optimize the rocket's performance and improve its stability. By using a mathematical model, engineers can make informed design decisions and avoid potential design flaws that could result in a failed launch.

## 3. What factors are included in a mathematical model for water rocket?

A mathematical model for water rocket typically includes factors such as the rocket's mass, the amount of water and air inside the rocket, the thrust produced by the water and air, and the drag and lift forces acting on the rocket during flight. It may also take into account external factors such as wind and gravity.

## 4. How accurate is a mathematical model for water rocket?

The accuracy of a mathematical model for water rocket depends on the complexity of the model and the accuracy of the input data. In general, a well-developed and validated model can provide reasonably accurate predictions of a water rocket's flight behavior. However, there may be some discrepancies between the model's predictions and the actual performance of the rocket due to factors such as variations in external conditions and manufacturing tolerances.

## 5. Can a mathematical model be used for different types of water rockets?

Yes, a mathematical model for water rocket can be applied to different types of water rockets as long as the basic principles of flight and the rocket's design and parameters are taken into account. However, some adjustments or modifications may be necessary to account for the specific characteristics of each type of water rocket.

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