what does this unit actually mean?

For the discussion of math. Duh.

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sippawitz
Posts: 25
Joined: Tue Oct 20, 2009 10:09 pm UTC

what does this unit actually mean?

I'm looking at some atmospheric dispersion modelling and I came across the Briggs Equation to calculate the rise of a bouyant plume.

wiki article
http://en.wikipedia.org/wiki/Atmospheric_dispersion_modeling#The_Briggs_plume_rise_equations

The bouyancy factor is given in m^4 s^-3

I've been assured by a colleague that a deep understanding of this isn't entirely necessary, as it is taken into account when we measure the stack velocity and the temperature, and calculated in the magic black box. However, my curiousity is piqued as to how this is unit is derived.

masher
Posts: 821
Joined: Tue Oct 23, 2007 11:07 pm UTC
Location: Melbourne, Australia

Re: what does this unit actually mean?

http://www.cwr.uwa.edu.au/services/mode ... e/ch8.html

Says that that the buoyancy factor given in your link has the same units as the buoyancy flux.

There are also references for the equations they give.

Still working on its derivation.

Edit: Derivation is not being done by me. I've forgotten too much fluid physics, and I really need to do other stuff...

.

Edit:
Just got the book (Fischer).

The buoyancy flux is given by the product of the density ratio of the received and discharged fluids, g (9.8m/s/s) and Q.

Q is the volume flux of the fluid, which is given as the product of the cross sectional area of the fluid flow and it's velocity.

So, by dimensional analysis, B = L^2 * L.T^-1 * L.T^-2 = L^4.T^-3.

Don't know why, but it is.

sippawitz
Posts: 25
Joined: Tue Oct 20, 2009 10:09 pm UTC

Re: what does this unit actually mean?

Cheers mate, i'll try my best to figure out what you just wrote

thanks for taking the time. tis 'preciated.