# CO2 powered water rocketry

by sigma
Tags: powered, rocketry, water
 P: 22 Heya. Let's say I want to build a water rocket and I want to pressurise it with a 12 or 16 g CO2 canister used for powering airguns. I want to calculate the optimal size of the pressure tank, and I want to predict the thrust of this device at various nozzle diameters. So here's the principle: CO2 is sprayed from the canister into the top of a water-filled tank. The water tank has got a hole of some sort in the bottom where water is ejected to produce thrust. The main problem I assume is to determine the pressure in the tank. The flow (and thus the thrust) is sort of proportional to the pressure. Any Ideas? //Cheers
 Emeritus Sci Advisor PF Gold P: 10,427 This is actually a very difficult problem to answer from first principles, because the size and shape of the opening at the bottom of the tank has a LOT to do with the rate at which water leaves the tank. If you know that number, the rest of the design is just kinematics. Ideally, you want there to be just enough water in the tank. If there's too much, you're pushing all its wasted mass all through the launch. If there's too little, some of your pressurized gas will escape at the end, and you'll be wasting your CO2 resources. The best thing I could tell you to do is build the nozzle, strap it to a table, and do some experiments. - Warren
 P: 22 Really? Can't I assume that the thrust from the motor is the pressuere in the tank multiplied by the nozzle area, and then add a correction factor for friction/turbulence loss. Then calculate mass flow from this. How do i know what pressure I need to design the tank for? How do I know how big the tank should be? / J.
 Emeritus Sci Advisor PF Gold P: 1,817 CO2 powered water rocketry No, your thrust is (ignoring the pressure correction) mass flow*flow velocity. To calculate both of those, you need to rely on thermodynamic principles, and water cannot be dealt with as an ideal gas.
 P: 22 Ok. I see. I've done some research and found that I can use this expression: p + rho * g * h + 1/2 rho * v^2 = constant at any point in the water. p: pressure rho: water density h: water height v: flow velocity I understand this is some variant of Bernoullis' law, or a statement of conservation of energy. This with some geometric conditions and the assumption that water is incompressible would calculate thrust at any pressure. Now for the CO2: All I Know is that p*V^k = constant for an ideal gas. k is ratio of specific heats or something that I can probably find in a table, V volume of gas. (Is there a corresponding expression for temperature?) This can't be true if the amount of CO2 is not constant, remember the CO2 is injected into the tank as the water is expelled. I could assume that CO2 would vaporize just below critical pressure. But from my experience the CO2 will get really cold and that would lower pressure according to the ideal gas law. Also critical pressure will be lower at lower temperatures. How do I account for this? /cheers