Variable mass calculation of thrust for a water rocket

  • #1
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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) + (2V2/g) + z = c

Isentropic expansion: pvγ = c

The Attempt at a Solution


[/B]
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%202015-02-05%2C%203%2050%2055%20PM.jpg?dl=0
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.
 

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Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
Welcome to PF;
this is something that is normally done by taking a small dm ejected in time dt, and working out the dp that results.
 

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