EFFECT OF TRANSLATION OF AXES 



A point fixed in the body is selected as the origin of a moving system of coordinates; 

 the axes remain parallel to a second system which is fixed in space (see Figure 1). The posi- 

 tion vector of any point of space with 

 respect to the stationary system is 

 designated by r and with respect to 

 the moving system by r^. , The posi- 

 tion vector of the moving origin is r^, 

 and its velocity is v^. The following 

 relations hold; 





y-yo = y,, 



z ~ z ^^ z. 



[2] 



Figure 1 



where the subscript m refers to the moving system. 



The velocity of a fluid particle with respect to the moving origin is related to its abso- 

 lute velocity by 



'Im = 'I - ^o 



where q^ is the relative velocity and q is the absolute velocity. Since v^ is a function of time 

 only, it satisfies the identity 



where 



Therefore 



or, since 



we have 



o m^ o m' 



v_ = \ -i— + i -i_ + k -^ 



5a;, 



^yn 



dz. 



dx„ dy„ dz„ 

 dx dy dz 



V„ = V 



