V„ = linear regression rate of fuel surface, ft. /sec. 

 F 



= bulk density of fuel bed 



Pbd'Vp V p^ 



^RE yd VP d V ^p ^* (10) 



The quantity V ^b represents the gas velocity, V , at the surface of the fuel, and 



Vp is the same a's^the Vl used by Hottel. Multiplying the regression rate of the 

 surface by the ratio of fuel density to gas density provides the value of the gas 

 velocity at the surface. This means that liquid-pool fires and solid-fuel fires should 

 correlate. 



BULK DENSITY OF FUEL BED 



We noted a similarity between equation 6 and the equation published by Thomas and 

 Law (1965). The equations are equivalent in concept except that o^^A/p^ is replaced by 

 1/p^ (bulk density of the fuel bed). These two quantities are approximately equal; 

 the exact relation can be determined by considering the properties of the fuel particle 

 and fuel bed. The porosity of a fuel bed, X, is defined as: 



^1 - ^2 



a 2 



where: \ = porosity, ft.^/ft.2 



a = fuel particle surface area-to-volume ratio, ft.^/ft.^ 

 a ^ 



Vl = fuel bed volume, ft.^ 

 V2 = fuel particles volume, ft.^ 

 Rearranging this equation we have: 



a A + 1 = V1/V2 (12) 



The volumes of the fuel bed, V^, and the fuel particles, V2 , are proportional to the 

 respective densities: 



Vl = W^/p^ and V2 = W^/p^ 



where is the weight of the fuel. Combining these terms and substituting into 

 equation 12, the result is: 



a A -, 



3- -L 



a A + 1 = p^/p, or 1/p, = + — . (13) 



a '^f'^b b p^ p^ 



This relation exists for fuel beds made up of a single size of fuel. In more complex 

 fuel beds, the bulk density provides a gross estimate; whereas appraising by size 

 classes, variation of particle density, and proportion of each size class provides a 

 more accurate estimate. For the present, we are considering only homogeneous beds of 

 a single fuel. 



FLAME AND BURNING CHARACTERISTICS 



Information that would enable us to predict flame size or burning rates from a 

 given fuel complex is not yet available; hence, it is difficult to estimate rates of 



5 



