Speed of Hot air Rising

faisal_durr · February 11, 2011, 06:16

Hi guys, Im carrying out salt bath experiments. My case consists of a hot plume rising in an empty room. Can anyone tell me what formula to use to find out the speed of the hot plume rising? Thanks.

chrisjcoffey · February 11, 2011, 08:41

The centre-line velocity in the buoyant plume behaves like

W~B^(1/3)z^(-1/2),

where B is the buoyancy flux and z the vertical coordinate.

The classic paper "Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234, 1–23." provides derivations of the velocity in a buoyant plume. Alternatively, the book "Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic Press, Inc." provides a good derivation from a dimensional analysis view point.

February 11, 2011, 06:16	Speed of Hot air Rising	#1
faisal_durr Member Faisal Durrani Join Date: Nov 2009 Location: England Posts: 62 Rep Power: 16	Hi guys, Im carrying out salt bath experiments. My case consists of a hot plume rising in an empty room. Can anyone tell me what formula to use to find out the speed of the hot plume rising? Thanks.

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February 11, 2011, 08:41		#2
chrisjcoffey New Member Chris Coffey Join Date: May 2010 Location: UK Posts: 1 Rep Power: 0	The centre-line velocity in the buoyant plume behaves like W~B^(1/3)z^(-1/2), where B is the buoyancy flux and z the vertical coordinate. The classic paper "Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234, 1–23." provides derivations of the velocity in a buoyant plume. Alternatively, the book "Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic Press, Inc." provides a good derivation from a dimensional analysis view point.