Thermodynamics: Open system: outlet but no inlet

[Paul245]

Hi There

I'm wokring on a miniature steam car ~0.7kg. I've decided that I would like to investigate the feasibility of propelling the car with a steam jet. So I found a couple of equations that work on the velocity of the exhaust. Equation 1) De Laval nozzel equation for the velocity of the steam at the nozzel outlet, and 2) Ideal Rocket equation which takes the steam velocity from equation (1) to give the change in velocity of the car.

Using these two equations I was able to get an estimate of acceleration and velocity of the car given fueled mass of car, and internal and external boiler pressure. Anyway, I believe that the figures are possible and that finally they depend only on the mass flow rate, which depends on the nozzell size and boiler pressure.

I'm having difficulty finding the right way to determine boiler pressure given that it has a single outlet and amount of heat input. Any advice would be much appreciated.

 

[Nick Bruno]

this question seems somewhat vague. can you be more specific?

 

[Paul245]

Hi

Thanks for your response. Say there's a boiler with a single outlet. It contains a volume of water at room temperature. Then transfer some heat so that the water evaporates and pressure increases. What is the best way to determine, pressure inside the boiler and the speed of the steam exiting the boiler?

 

[Nick Bruno]

Hi Paul,

In order to solve this problem I believe you would use the first law of thermodynamics or the law of enthalpy:

H = U + pV

where H = the internal enthalpy, U = the internal energy, p = the pressure and V = the volume.

When you divide this equation by the internal mass, you have units of J/kg or energy per mass also known as specific energy (i think).

As you know the internal energy (because this will most likley be the amount of heat you input into the system in Joules thru resistance heating or whatever means) all you have to do is find the pressure since volume is constant.

Now, for moist air pressure can be kind of tricky, so I would suggest looking up a gas constant for moist air and using the equation

p = nRT/V ; where n = moles of a gas, R = the gas constant, T = temperature, and V = volume.

Once you have a value for enthalpy, H, you will have units of
J/kg = N/m/kg = kg*m/s^2/m/kg

or kg^2/s^2.

As you notice once you take the square root of this value you will have a mass flow rate of kg/s.

mass flow rate, or mdot = rho*velocity*Area

where rho = the density of the moving mass, velocity is the flux through the control surface, and area is the area of the control surface or exiting pipe area.

With this you should be able to find the velocity and pressures you are looking for. They may be off, because of some assumptions, but without getting too technical, you will probably get a resonable estimation.

Once the system is at steady state you can calculate thrust by T = mdot*v where m is the mass of steam/air mix exiting and v is the velocity it is exiting.

 

[Nick Bruno]

looking at this again, i suggest you look into psychrometrics