Science Buddies: "Ask an Expert"

I am doing a science project on Water bottle Rockets. I am looking for equations that will help support my hypothesis

My hypothesis: If there is more water in a water bottle rocket Then it will have more airtime because it will have more mass to displace therefore it will have more momentum according to the conservation of momentum law.

I have done lots of research and come upon many equations but don't know what ones to use.

Please help your friend
8th grade scientist in need of help

The basic F (force)= m (mass) a (acceleration) will definitely be involved in multiple ways.
I think you missed a significant component in a pressurized bottle rocket. The gas (air) above the water in the rocket is trapped and pressurized. The amount of air and its pressure will definitely be a major part of determining what happens. The ideal gas law, P (pressure) V (volume) = n (number of moles)R (Reynolds constant) T (temperature) will also be involved. The air pressure is what pushes the water out of the rocket. If the volume of air at atmospheric pressure is less than what it takes to expel all of the water, then having more water will increase the remaining mass so the effect of the force and the resulting acceleration will be less, so the velocity obtained and the distance traveled will be less.
The shape factors in the transition to the jet area and the jet area itself will affect the Bernouli effects. The Bernouli principle and equations will also be involved.

Let me see if I can explain what Craig said in a different way.

The basic equation is F = M a. The thing that gives your rocket more air time is how high it goes. That is controlled by the acceleration. So you need to make acceleration the highest you can. Using simple algebra, you can solve the equation F=Ma for acceleration and you find that a = F / M. The F is the force of the water shooting out of bottle. The M is the mass of the bottle, which is mostly just water.

So you see, if M gets bigger, then a gets smaller. The acceleration goes down, so the rocket won't go as high. Also, if you put more water into the bottle, then you will be able to put in less air. The air creates the force. With less air, you will get less force, which will reduce acceleration even more.

It is a simple thing to demonstrate with experiments. Make several trials using different quantities of water and air pumped up to different pressures. If the weather is calm, you can time how long the rocket is in the air. If you graph air time on the x axis and mass of water on the y axis, you will be able to measure the effect. Then make a similar graph for each air pressure you choose for your experiment.

I hope this helps.

Ed Neu
Buffalo, MN

Awesome project!

Just to add on to Edneu and Craig's posts, here are some physics equations you might want to consider:

w=mg, where w=weight, m=mass, and g=acceleration due to gravity. Essentially, the weight of an object is the force of gravity that acts on it. Therefore, the greater an object's weight, the more force required to oppose the force of gravity on the object and lift it up (e.g., it's much harder to lift up a truck because it has such great mass). Therefore, while more water further pressurizes the air, it increases the bottle's mass and makes it harder for it to fly.

Also, neglecting air resistance, the time from initial to final in a parabolic trajectory is measured by t=2v/g, where v is the initial upward velocity of the rocket. Clearly, since g stays constant, in a free fall situation the time an object stays in the air entirely depends on its initial velocity. Going back to previous posts, F=ma, and the initial velocity depends on the initial acceleration.

Good luck with your project!

--Manjinder