EDDY FORMATION 71 



Also for continuity we have 



^ _i_ ^ _j_ ?Jf? n 

 a^~ l ~a 2 /" t "a *~ u 



8 , d v , d iv 



.'. u - -- \- u x -- f- it - = 0. 



9 x ^y 02 



Adding this to the right-hand side of the above equation, this becomes 

 du du dv \ 9 % dw 



\ 9 (u u) 8 (u v) , 8 (u w) ,<>u 



~ p \ dx ~~3y ~ry t~8 j 



So that the equation may be written 



f ?i 3 



p x + {"8^ to* ~ p u u ) + a^ ^ ~ p w r) 



8 v 1 8 



+ 8 (1 - P u w) I = P ^ 



the left-hand side of this equation expressing the force producing the 

 acceleration ^, in the direction X. Taking this to be the direction 



of mean flow in a tube, and neglecting the external force p X, and 

 (Pxx puu), which simply marks the variation in the direction of flow, 

 we are left with two terms which represent the variations in directions at 

 right-angles to this. Since these involve the shear on parallel layers of 

 the fluid, it is probable that the conditions involving steady or sinuous 

 motion depend in some definite manner on these terms, and since, in a 

 'parallel tube, terms in y and z are similar and symmetrical if the effect 

 of gravity be neglected, we may consider any one of these, and note how 

 any variation in this may affect the conditions of flow. 



Considering the term ^ (p yx p v u}, substituting from equation (8), 



tS 



p. 60, this may be written 



8 / 8 v ' 8 u 



The first of these terms involves the coefficient of viscosity //, and is of 



the nature ^ X - - = -f-, while the second is of the nature p V*. 

 space L 



It was inferred then, that since the relative value of these terms probably 

 determines the critical velocity, the latter will depend on the relation 



P VL' 



Putting 7, = ^- where d is the diameter of pipe, experiments were 



