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Water/Air Rocket

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to determine the exit velocity and thrust of a water rocket as a function of time. The total rocket volume is .002m^3 (2 liter coke bottle) and 1kg of water and air initially at .35MPa. Therefore the initial volume of water is .001m^3 and the volume of air is .001m^3 as well.

    T = 298K
    Vol_tot = Vol_water + Vol_air (only unknown is M_air where Vol_air = M_air*R_air*T/(P_air))

    therefore Vol_water = .001m^3 = Vol_air

    I have calculated the initial velocity and exit area to be 22.36m/s and 2.38E-5 m^2 respectively.

    2. Relevant equations

    3. The attempt at a solution

    I am assuming isentropic expansion of air.

    I started by using the Bernouilli equation Po = Pe + 1/2 * rho_water * Ue^2 (where Po is the total air pressure, Pe is assumed to be equal to the ambient air pressure (constant .1MPa)). The Po will change as a function of time, as will the exit velocity (Ue).

    I started by trying Po(t) = Mair*Rair*T/(Vol_air(t)) = Pe + 1/2 * rho_water*Ue^2

    where Vol_air(t) = Vol_tot - Vol_water(t)

    and Vol_water(t) = Vol_water_initial - dVol_water(t)

    and dVol_water(t) = dm(t)/rho_water = mdot*dt/rho_water = Ue*Ae*dt

    Po(t) = Mair*Rair*T/(Vol_tot - (Vol_water_initial + (U_final*t_final - V_initial*t_initial)*Ae))
    = Pe + 1/2*rho_water *V_initial^2

    I solved this equation for V_final and used matlab to get a Velocity vs Time graph and I can tell it's wrong. It seems that there should be an exponential term in there somewhere.

    Any help is greatly appreciated. Thanks!

    ( I was thinking about doing dPo/dt = d (const/Vol)/dt, however I'm unsure about the volume/time relationship)
  2. jcsd
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