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 



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

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

 integrate with respect to & between the limits 0_ and TT. The result is _. 

 m dvi/dt, 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 &amp;lt;f) and *fy the terms ur cos 6 and ur sin 6, respectively, 

 we get 



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 



4 log* (1). 



