Then the formulas may be taken to refer to a cylinder of radius a moving with its axis 

 distant h - r/2 from a rigid parallel wall; a/h is to be assumed small. See Figure 162. 



Figure 162 — Slender cylinder moving 

 near a wall. See Section 95(B). 



The cylinder has a velocity V inclined at an angle /3 to the positive a;-axis, which is drawn 

 perpendicularly away from the wall. The kinetic energy per unit length is half of T^ as 

 given by Equation [95c] or 





[95g] 



Let the components of the acceleration of the cylinder be denoted by x and y. Then in 

 Equation [95e, f] • 



a-j = - x^ = - X, y^ = y\ = y, x^=-V cos /3, y^ = 7 sin ^; 



and the component of force A on unit length of the cylinder, taken positive away from the 

 wall, and the component Y^ taken parallel to it and toward positive /S are, from Equations 

 [95e,f], 



np a'* V 



9 / oM .. 

 Aj = - TT^pa'' I 1 + I X 



cos 2 ^, 



npa-^V^ 

 y + sin 2 /S. 



[95h] 



[95i] 



240 



