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Homework Statement
I am trying to derive the formula for time varying thrust given that I know the initial mass/volume of water in a water rocket. Knowns will include initial pressure, initial volume of water, and nozzle cross sectional area.
Homework Equations
Bernoullis equation: (p/ρg) + (2V^{2}/g) + z = c
Isentropic expansion: pv^{γ} = c
The Attempt at a Solution
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I derived the formula for the exit velocity of the water from the nozzle using the Bernoullis equation,
https://www.dropbox.com/s/gnatjasgb2fjx5i/Photo%2020150205%2C%203%2050%2055%20PM.jpg?dl=0
https://www.dropbox.com/s/gnatjasgb2fjx5i/Photo 20150205, 3 50 55 PM.jpg?dl=0
I know that I am supposed to derive a differential equation for the velocity and pressure but I cant seem to setup the equation using the isentropic flow formula.
any help will be appreciated. thank you.
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