462 Mr. A. Griffiths on Diffusive Convection. 



To take a definite example let 



R = 0*1 centim., 



v =0-1324, 



T=0-1, 



k =2-47 xlO" 6 , 



L =4 centim. 



Then /= 10,000, and a study of the deviation shows that it 

 is practically nil, except when r is nearly equal to R ; in which 

 case it equals 



e^ r-R) approximately. 



To make it equal to 0*001, r must equal 0*09931, and it is 

 clear that, on the assumptions made, the effect of the viscosity 

 is to produce variations in the average flow of only a fraction 

 of a per cent. With tubes of ordinary calibre, no appreciable 

 error is made if the viscosity be neglected altogether. The 

 expressions also show that the tubes would have to be very 

 narrow to affect the magnitude of the diffusive convection to 

 any appreciable extent. 



Another method of showing that very little error is made 

 by neglecting the viscosity is to obtain an expression for the 

 average velocity. 



Let V = the average velocity up the tube, then 



f R 

 V r X7rR 2 =l Zirrvbr 



12P* [^ 2 -^{f(ef^e-f^^ fR + e-^)+^}] 

 = gTU ef^ + e-'f* 



Since / is large the second term within the square brackets 

 may be neglected, and we obtain 



Y= .p 2 approximately. 



Considering the case of two tubes of equal bore, but of 

 unequal length, studied in Section III., 



let ?! = " excess of pressure " producing the flow up the 

 tube L 1# 

 P 2 = the corresponding excess (or defect) producing 

 the flow down the tube L 2 , 

 then it can be readily seen that 



P2='-2 - (Li~L 2 ) — Pi ; 

 hence , ?TL 2 2 V 2 _ ^T^-L,) _ ^TL^ 



<2* ~ " % in * 



