# The approximate values of density for a flame with respect to heights

I'm aware that the difference in density with respect to height is low, but I'm in need of the values for a project: in which I explain that the continuity equation of fluid dynamics will work well for gases as an approximation since the density difference is not high for different heights of a flame.

p.s: the project is a video explaining the tapering of flame. I also would like to know if showing the values of temperature incase I can't get the values for density would be acceptable.

The approximate values of density for a flame with respect to heights

I'm aware that the difference in density with respect to height is low, but I'm in need of the values for a project: in which I explain that the continuity equation of fluid dynamics will work well for gases as an approximation since the density difference is not high for different heights of a flame.

Check out: "Jet flame heights, lift-off distances, and mean flame surface density for extensive ranges of fuels and flow rates", (DOI link: https://doi.org/10.1016/J.COMBUSTFLAME.2015.09.009) by Derek Bradley, Philip H. Gaskell, Xiaojun Gu, and Adriana Palacios for formulas to make these calculations:

"The correlations are based on a vast experimental data base, covering 880 flame heights. They encompass pool fires and flares, as well as choked and unchoked jet flames of CH$_4$, C$_2$H$_2$, C$_2$H$_4$, C$_3$H$_8$, C$_4$H$_{10}$ and H$_2$, over a wide range of conditions. Supply pressures range from 0.06 to 90 MPa, discharge diameters from 4·10$^{-4}$ to 1.32 m, and flame heights from 0.08 to 110 m.".

See also: "The size of flames from natural fires", (11 October 2007) by P.H.Thomas. Origonal paper: Source: Fire Safety Science Digital Archive. "This paper discusses one of the least studied features of natural fires - the length of the turbulent flames rising from the burning fuel.".

An answer about backpressure: Why does exit pressure matches back pressure in a converging diverging nozzle?

PS: The project is a video explaining the tapering of flame.

Here's a great video from NASA: "NASA’s new High Dynamic Range Camera Records Rocket Test", not much tapering in that view but it's shot in HDR and shows the turbulence of the burning.