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Homework Help: Variable mass calculation of thrust for a water rocket

  1. Feb 5, 2015 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    Bernoullis equation: (p/ρg) + (2V2/g) + z = c

    Isentropic expansion: pvγ = c

    3. 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.

    Attached Files:

  2. jcsd
  3. Feb 5, 2015 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    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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