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.
Bernoullis equation: (p/ρg) + (2V2/g) + z = c
Isentropic expansion: pvγ = c
The Attempt at a Solution
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 2015-02-05, 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.