Pressure and temperature of water boiling in a heated container with a small hole

[InteroperabilityFix]

I'm trying to build a mathematical model of something like Heron's Aeolipile:

http://en.wikipedia.org/wiki/Aeolipile

I'd like to know, based on a known heat flux, the pressure and temperature attained in the container.
I assume as water boils, the control volume loses mass and energy, the pressure and temperature of the vapors will stabilize.

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[racookpe1978]

Only if the rate of boiling equals the vent rate through the 2 nozzles. The pipes are very, very short. Best just approximate them as a two opposite "nozzle loss" = boiling pressure above atmosphere.

Hint, you will find you need very, very small nozzles to create enough backpressure to spin the sphere. try a welding store = look for oxy-acetylene nozzles you can adopt. Get as good a bearings as you can afford!

Reality check. Go to your stove tonight. Put a pot of water on the stove and apply heat. Put a lid on the pot, then "seal" it with a little water around the rim. The lid will lift and surge up and down as the boiling pressure (1/100 of an atmosphere or so) lifts the lid against gravity. that is the amount of "force' available to roate the theoretical sphere against friction of the bearing holding up the (heavy) pot of water.

 

[EdStainless]

The one that I built (44 years ago) was two small cans hanging from a cross member.
The center of the cross member rested on a pivot.
We put very hot water in the cans, they had tiny holes punched in the caps (from the inside) and faced opposite directions.
Then we used wire to hold wads of cotton under the cans, soaked them with alcohol and lit them.
It took a while to get the factors correct but we did get it to spin nicely for a while.

It was a very practical lesson in friction, force, heat transfer and general mechanics.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[crshears]

Umm, er, the OP is building a mathematical model, not a mechanical one...

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[gruntguru]

You will need to model the system with an adjustable nozzle diameter to match the mass flow of steam across the system boundary to the rate of water converted to steam at each selected saturation pressure. (I assume you want to analyse the system at a range of different pressures)

Assuming a well insulated boiler, efficiency should increase with pressure. hfg reduces as pressure increases as will boiling rate for a givven heat flux. Of course nozzle velocity and therefore thrust also increases with pressure.

je suis charlie