Max Velocity of a Water Rocket

AI Thread Summary
To find the maximum velocity of a PET bottle rocket, the relationship between pressure and exhaust velocity is crucial. The formula Δp = 1/2 ρ v² can be used, where Δp is the pressure difference, ρ is the density of water, and v is the exhaust velocity. The density of water does indeed vary with temperature, so adjustments may be necessary for accurate calculations. Understanding Tsiolkovsky's equation can also aid in determining the rocket's performance. Accurate calculations will yield the rocket's maximum velocity under the specified conditions.
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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 :smile:

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.
 
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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?
 

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