Need Help With Project. Similar to a sprinkler.

[ewildes3]

What I'm making is kind of like a sprinkler or Aeolipile. I have a 2 blade propeller that I'd like to boost with an air tank(s). It has to go from 100rpm to 300rpm via a nozzle at the tips of blades. I'm trying to determine the minimum pressure and volume requirements for a tank of air that can do this.

I calculated that I needed a total torque of 1629.06N*m to go from 100 to 300rpm in 2 seconds (the amount of time isn't set in stone) but I've been stuck on the fluids aspect of this problem for a couple days now. I'm sure I'm making this harder than it needs to be by thinking so long on it. I'm just not confident in my assumptions.

All I want is an equation I can use to calculate the tangential force acting on the blade due to the flow of air from a tank at some pressure and volume through some pipe and out a 90 degree nozzle.

I'd very much appreciate your help and advice.

[Timelord]

Your problem cries out for an empirical solution because of the chaotic nature of the gas flow. Nozzle efficiencies and pressure drops thru the piping makes this a difficult problem to establish precise boundary conditions for. It would probably would be simpler to construct your device and hook it to a welding tank of nitrogen with a regulator. Vary the pressure to establish this requirement and put a flow meter in the line to calculate the required volume of your tank. It would also be easy (if your design allowed) to vary the nozzle diameter and optimize it against the input pressure by experimentation.

just say'n,

Timelord

[JAlberts]

While ultimately you will end up having to do some prototype testing, I think the below attached MS Excel calculation will help you get to a reasonable starting point before you start your prototyping. While there are several elements to your design this calculation, as you can see, will give you a general idea of the nozzle inlet air pressure and air consumption rate based upon your required torque.
In addition to the nozzle and tank sizing, you will also need to determine the piping size required between your tank outlet and the nozzle(s) to deliver the correct pressure to the nozzle(s) and that is a bit more complex; however, once you have done the required pressure and flow volume determination, I have access to a piping flow loss program that I use to give you a bit of help with the piping sizing. Please be aware of the limitations of this program as it is only valid for "air" service and for converging nozzles with critical flow ie an inlet/outlet pressure ratio > = 2:1.
To see the basis of this calculation, I suggest you go to the: http://en.wikipedia.org/wiki/Rocket_engine_nozzle website, if you haven't already done so. What the attached calculation does is provide the m dot mass flow and sonic nozzle velocity necessary to solve the basic thrust equation given in that reference.

[JAlberts]

I attempted to post this yesterday but it seem to be lost in Ethernet so here it is again. While ultimately you will end up having to do some prototype testing, I think the below attached MS Excel calculation will help you get to a reasonable starting point before you start your prototyping. While there are several elements to your design this calculation, as you can see, will give you a general idea of the nozzle inlet air pressure and air consumption rate based upon your required torque. In addition to the nozzle and tank sizing, you will also need to determine the piping size required between your tank outlet and the nozzle(s) to deliver the correct pressure to the nozzle(s) and that is a bit more complex; however, once you have done the required pressure and flow volume determination, I have access to a piping flow loss program that I use to give you a bit of help with the piping sizing. Please be aware of the limitations of this program as it is only valid for "air" service and for converging nozzles with critical flow ie an inlet/outlet pressure ratio > = 2:1. To see the basis of this calculation, I suggest you go to the: http://en.wikipedia.org/wiki/Rocket_engine_nozzle website, if you haven't already done so. What the attached calculation does is provide the m dot mass flow and sonic nozzle velocity necessary to solve the basic thrust equation given in that reference.

[ewildes3]

Thank for your help so far. My research has led me to this thread:

http://www.physicsforums.com/showthread.php?t=694656

Is the equation for mass flow rate, shown here, appropriate? Because by combining that with the general thrust equation here:

https://www.grc.nasa.gov/www/k-12/airplane/thrsteq.html

I get a minimum tank pressure of 894.49kpa to produce a force of 381.78N, the force I need to sustain for 2s. That's doable with some medium sized carbon fiber tanks I've found online but when I looked at the work aspect of the problem I confused myself. According to W=PV, even a small tank at the standard 4500psi is capable of producing enough work to achieve my acceleration. This confuses me because these small tanks can't house the 230gal of air that would be expelled by my rig when powered by 89449kpa for 2s.

[ewildes3]

I finally got around to using your excel file. It yielded almost the same results! ^_^ thanks alot for the help.