412 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 11, NO. 17 



ture difference between the metal and air flowing past it. The nu- 

 merical values of q were found to agree very well with values com- 

 puted from a formula given by vStanton and Lanchester: 



CpRf 



q. = 



V 



and by Lees / m V '' 



Rf = pV- [0.0765 \V^) + 0.0009] 



the comparison being made for radiator cores with smooth round and 

 square and hexagonal air tubes, nearly all direct cooling surface. 

 The formulas given were originally stated for long circular cylindrical 

 tubes with smooth walls, Cp being specific heat of air at constant pres- 

 sure, V the velocity of the air through the tube, p its density, and 

 M its viscosity. Rj is the surface friction, or force per unit surface be- 

 tween the air stream and walls of the tube, and D is tube diameter. 

 The above formulas m.ay be combined into a single expression 

 (making some reductions not given here in detail), so as to compute 

 heat dissipation of a core from its dimensions, and for simple type 

 regular cellular cores it seems highly probable that results will be 

 reliable within 10 per cent. 



// = MCpT (1 - e"""') 

 .., = ^ [o.047l(^^J"'V 0.0009] 



H = heat dissipated, units of power per unit frontal area of core, 

 M — mass of air per unit time per unit frontal area, 

 Cp = specific heat of air at constant pressure, 

 T = temperature difference water and air entering core. 

 Any consistent set of units whatever may be used for the above 

 four quantities, but care must be exercised to avoid any inconsis- 

 tencies; i.e., the heat units for H and Q must match, the mass units 

 for M and Cp, the area unit for H and M, etc. The same is true for 

 the following sets of quantities, although the units for these need 

 not be the same as the first set. 



Xi = depth of radiator core, in same units as f, 

 r = hydraulic radius of air tube (quotient of area by perimeter) , 

 M = mass of air per unit time per unit frontal area, 

 p. = viscosity of air in a unit consistent with M and r, 

 a = free area of core ; the ratio of the total cross section of the tubes 

 to the frontal area. (Being a ratio it is independent of units.) 



