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Modeling a Bottle Rocket: Analyzing the Maximum Altitude
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[QUOTE="erobz, post: 6629909, member: 700856"] Yeah, My first round draft was using "The Energy Equation" , its basically Bernoulli's Equation repackaged to include viscous effects: Using the diagrams of the latest model it is as follows: $$ \frac{P_{b}}{ \gamma} + \frac{v_{b}^2}{2g} = \frac{v_e^2}{2g} + k\frac{v_e^2}{2g} + \frac{2 f l}{r_e} \frac{v_e^2}{2g} $$ Where: ## k ## is a contraction loss coefficient ## \frac{2 f l}{r_e}## characterizes the loss through the "pipe" of radius ## r_e## This leads to a more simple: $$ v_e^2 = \frac{2}{\rho} \left( \frac{1}{ 1 + k + \frac{2 f l}{r_e} - \left( \frac{r_e}{r_b} \right)^4 } \right) P $$ However, I abandoned it because it is derived in an inertial frame (like Bernoulli's Equation), and the process is happening in a non-inertial frame. So I decided to take a step backward ( really 2) to the "next closest " first principle in which a "non-inertial frame" can be accounted for without too much difficulty ( i.e. The Momentum Equation ), thus far seemingly without success... As for the adiabatic expansion, good point! Thank You. I'll re formulate that part, but it shouldn't correct the issue of the jet velocity passing through the sonic barrier ( and perhaps blow right by ) as the nozzle is decreased. I was counting on friction to stop that from happening. Maybe it does though, I'll work on it. As for the "Pop" as the second stage initiates . I looked at that, but that becomes massively complex very quickly with compressed gas near sonic regime. It could be that I've just bungled the application of the equation because of the reference frame issue. Thats why I was hoping some physicist could set me on the right track! P.S. I feel you. I graduated High School in 2002! 20 Years! I was planning on making a launcher for my kids this summer, and In the process I just couldn't help myself trying to get in over my head in the modeling. [/QUOTE]
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Modeling a Bottle Rocket: Analyzing the Maximum Altitude
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