68-69] MOTION OF A CIRCULAR CYLINDER. 87 



Since, also, <? 2 = u 2 a 4 /r 4 , the pressure at any point of the cylindrical surface 

 (r=a) is 



jt>=pfa^cos0 + u 2 cos 20 -i 



The resultant force on unit length of the cylinder is evidently parallel to 

 the initial line = 0; to find its amount we multiply by -add. cos 6 and 

 integrate with respect to 6 between the limits 0_ and IT. The result is 

 m'da./de t as before. 



If in the above example we impress on the fluid and the 

 cylinder a velocity u we have the case of a current flowing 

 with the general velocity u past a fixed cylindrical obstacle. 

 Adding to < and ty the terms ur cos and ur sin 0, respectively, 

 we get 



/ a 2 \ / a 2 \ 



9 = u [r-\ cos 0, ilr = u I r ) sin .... (7). 



\ r / \ r / 



If no extraneous forces act, and if u be constant, the resultant force 

 on the cylinder is zero. 



69. To render the formula (1) of Art. 67 capable of repre- 

 senting any case of irrotational motion in the space between two 

 concentric circles, we must add to the right-hand side the term 



Alogz (1). 



