# Max Velocity of a Water Rocket

• flash
In summary, The maximum velocity of a PET bottle rocket can be found using Tsiolkovsky's equation, but it is not clear how to use it in this scenario. One way to approach it is by finding the exhaust velocity of the water, which can be calculated using the formula \Delta p = \frac{1}{2} \rho v^2, where \rho is the density of water and p is the pressure. It is unclear if this formula is applicable and if the density of water changes with temperature. Further clarification is needed.
flash
Find the maximum velocity of a PET bottle rocket on a day with temperature 30 degrees celcius and pressure 1 atmosphere, if the pressure inside the bottle was 40 psi and the volume of water in the bottle was 300 mL.

I know of Tsiolkovsky's equation but I'm not quite sure how to use it here. Any help appreciated

EDIT: Pretty sure I need to find the exhaust velocity of the water given the above details. I have a formula that says $$\Delta p = \frac{1}{2} \rho v^2$$ where $$\rho$$ is the density of water and p is pressure that (I think) gives the exhaust velocity v but I don't know where the formula came from or if it is even correct.

Last edited:
Feel free to ignore the first part of the question. I just need someone to explain that relationship between pressure and exhaust velocity there. Also I'm guessing that the density of water changes with temperature?

Firstly, Tsiolkovsky's equation is used to calculate the velocity of a rocket based on its mass, exhaust velocity, and the change in mass during the rocket's flight. This equation is not directly applicable to your situation as it involves the mass of the rocket and the change in mass, which are not given in the problem.

To calculate the maximum velocity of a water rocket, we can use the ideal gas law, which states that pressure and volume are inversely proportional at constant temperature. This means that as the pressure inside the bottle increases, the volume of air inside decreases.

Using the ideal gas law, we can calculate the volume of air inside the bottle at 40 psi and 1 atmosphere pressure. We know that the volume of the bottle is 300 mL, so we can set up the following equation:

(P1)(V1) = (P2)(V2)

Where P1 is the initial pressure (1 atmosphere), V1 is the initial volume (300 mL), P2 is the final pressure (40 psi), and V2 is the final volume (unknown).

Solving for V2, we get V2 = (P1)(V1)/(P2) = (1 atm)(300 mL)/(40 psi) = 7.5 mL

This means that the remaining volume inside the bottle is 7.5 mL of air and 292.5 mL of water.

Now, to find the exhaust velocity, we can use the equation you mentioned, \Delta p = \frac{1}{2} \rho v^2. This equation relates the change in pressure to the density of the fluid and the exhaust velocity.

In this case, the change in pressure is 40 psi (the pressure inside the bottle), and the density of water is 1000 kg/m^3. Plugging in these values and solving for v, we get v = 6.32 m/s.

Therefore, the maximum velocity of the water rocket would be 6.32 m/s. However, this calculation assumes that all the water is expelled from the bottle in one instant, which is not realistic. In reality, the water would be expelled gradually, leading to a lower maximum velocity.

I hope this helps to clarify the process of finding the maximum velocity of a water rocket. Please let me know if you have any further questions.

## What is the max velocity of a water rocket?

The max velocity of a water rocket can vary depending on the design and launch conditions, but it is typically around 200-300 mph.

## How is the max velocity of a water rocket calculated?

The max velocity of a water rocket can be calculated using the rocket equation, which takes into account the mass of the rocket, the amount of water and air inside, and the force of the launch.

## What factors can affect the max velocity of a water rocket?

The max velocity of a water rocket can be affected by factors such as the design and weight of the rocket, the amount of water and air inside, the angle and force of the launch, and air resistance.

## How can the max velocity of a water rocket be increased?

The max velocity of a water rocket can be increased by optimizing the design and weight of the rocket, using a higher pressure launch system, and reducing air resistance by using a streamlined shape and fins.

## Is there a limit to the max velocity of a water rocket?

Technically, there is no limit to the max velocity of a water rocket as long as it has enough thrust and is launched in a vacuum. However, in real-life conditions, the max velocity is limited due to factors such as air resistance and structural limitations of the rocket.

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