446 Lieut.-Col. A. R. Richardson on Stream-line 



Equations (2) and (11) show that ! dz \ increases very 

 rapidly except when w is small, so that the parts of the 

 stream-line ^=0 with the greatest curvature lie near 

 the corner B. It is in this neighbourhood that an eddy 

 may be formed, owing to viscous action, if c be sufficiently 

 large. 



A closer approximation to the observed motion will result 

 if a more complicated expression is used ; e. g., 



€ - «0-T-£ + ^ 1/2 -T ( 6 + w l/2j2 + • • • + ( 6+ W ll-I\n + ' ' ' 



would result in several turning values on i/r = 0. 



Within the limits stated above one of the constants may be 

 taken a function of the time, and so the effect of disturbing 

 an existing motion may be traced out, e. g. increasing or 

 decreasing the velocity of the plate. 



In addition to indicating the manner in which an existing 

 motion may break up, due to viscosity, these solutions give 

 possible stream-line shapes for the afterbody of a plate 

 such that, for a particular velocity q — e~% there will be 

 very little turbulent motion in rear. 



They also show that the pressure may be expected to 

 change sign at some point on the underside of the plate, 

 and that the maximum velocity on the underside is greater 

 than that on the upperside. 



VI. Calculation of the resistance in a particular case. 

 Let c be small compared with (6 — 1). 



Jo >/ 1 — w 



fl J)— s/ w 



C'B = 1 div = 2b — 7r/2 approximately. 



Jo vl—io 



Pressure on CB = P . CB-f \p ( \l-f)^ m dcj> 



Jo "9 



Pressure on C'B= Pq.C'B-^ f (^-c/>) </</>„ 



Jo ^y / 



