Would you not just apply a Galilean transformation to a Boltzmann distribution? It's odd, I was wondering precisely this thing about 90 seconds ago, how thermal distributions change under symmetries of either Euclidean or Lorentzian space-time. Weird....
Thus the conclusion, "coincidence is never coincidental". Erm, I don't appear to be able to post a link, so this is a text address of a site at Virginia U, that has lectures and animations for gas statistics and kinetics (read the entropy lectures, if you already have the intro stuff covered): http: //galileo.phys.virginia.edu/classes/152.mf1i.spring02/HeatIndex.htm"] which, coincidentally, I've been looking at (the 252 stuff which is the next part and covers relativity and stuff).
thanks for the reply alphanumeric and noodler. I have read the note but where do i should began? everything seems so basic and fundamentals. actually i need to determine the velocity of air at certain distance from the rectangular duct opening, let say 4meter from the rectangular duct opening. It is sudden expansion of air from rectangular duct. the outlet air velocity of the rectangular duct is 10 m/s and the dimension of the duct is 52cm X 55cm. I already got one equation, but it is not for rectangular duct, it is only for long and narrow slit of rectangular duct.It has no input of both width and height for my rectangular duct. here is the pic i95.photobucket.com/albums/l130/sp3d2/rectangularjetequation.jpg"]
Ok, I don't think the outlet being square is going to have much effect on the airstream, especially 4m away from it. You need a pressure/density relation for the flow of air, relative to distance from the outlet. This needs to relate to its velocity, and the viscosity of the medium. You have a cross section for the outflow = 55x52 cm. Do you have a grip on statistical velocity distribution for a gas?
4 meter is the example. I would like to know more than that. I did learn transport phenomena. I checked the transport phenomena book by lightfoot&bird but the velocity distribution in that book dont have a relationship with the dimension of duct as it is for small circular tube only. mine is a bigger dimension of duct, not tube. but thats ok, now im using a circular jet equation and replaced the the hydraulic diameter to transform the rectangular area to circular area to make thins easier as you said being square is not much different. im using this equation for rectangular duct i95.photobucket.com/albums/l130/sp3d2/circularjet.jpg"] i hope its correct Please Register or Log in to view the hidden image!
Just to clarify, are you trying to compute the macroscopic motion of the air or the Boltzman-like distribution of the individual air particles? For instace, if you blast air through a hole in a wall it speads out in a conic jet, which interacts with the air or if there's no air it'll reduce in density. The shape of the jet depends on things like densities, temperatures, pressures and if you're just doing vaguely armwaving things you can just use a bit of calculus to work out the density of the jet at any particular place given it's spreading shape. If you're doing something more precise, including turbulence (ie something like this dynamic) then you'll want a supercomputer and a grasp of Navier-Stokes equations. Or are you trying to work out the Boltzman distribution for a column of gas particles (each with velocity \(\mathbf{v}_{i}\))which is moving at a constant velocity, \(\mathbf{V}\), relative to your frame? In that case you'd need to work out the distribution you get when you redo the Boltzmann distribution derivation but with \(\mathbf{v}_{i} \to \mathbf{v}_{i} + \mathbf{V}\). There should be a way of cutting to the answer quicker using simple Galilean transformations but it doens't instantly spring to mind unfortunately (it's been too many years since I did stat. mech.)
I am trying to compute the macroscopic motion of the air. To monitor movement of every particle is not necessary. The duct opening is at the bottom of curing oven. The ducting upwards 30 degree from the base of oven. The oven is 1.78m (width) x 25m (lentgh) x 3.6m (height). It will interacts with air that is readily in the oven. The temperature of hot air is 110 celcius and assume the condition within the oven is atmospheric pressure. Assume the air inside the oven already at 110celcius. From this picture you can see the condition of the duct i95.photobucket.com/albums/l130/sp3d2/CurrentandNewdesignofoven.jpg"] I just wish to have an equation so that i can determine the axial and radial velocity of air from the coming from the duct at numerous location inside the oven. Guess i need to master navier stokes first. Please Register or Log in to view the hidden image!
I think there's a shortcut, you just need to consider continuity, and Bernoulli's theorem. Energy (internal potential and kinetic) is conserved; momentum is conserved. You can apply an approximation. The compressibility of a gas (rather than a liquid) and temperature changes are involved. You have a volume flow which is 'static', so you can assume there's a finite volume element dV (moving through the cross-section A which you know) This might be useful: http: //en.wikipedia.org/wiki/Incompressible_fluid_flow ... check any links to compressible flow in that page; note that an actual liquid will be affected by gravity (Bernoulli's eqn is for horizontal flow) moreso than a gas. "Fluids" correspond to liquids and gases (and particulate solids, like sand). Please Register or Log in to view the hidden image!
i see. so my case is compressible flow because temperature change as air moves forward from the duct opening. that means the density is going to be different. thanks to noodler and alpha. Please Register or Log in to view the hidden image! let me study continuity, bernoulli and compressible flow first Please Register or Log in to view the hidden image!
