By adopting a similar purely empirical approach the analysis of the data 

 obtained in these tests revealed that the more suitable length scale to 

 be used with f^Cy) was the parameter a g D. The forms that most closely 

 approximated the experimental data were 



- -£= x 10 3 

 f , (y) = e for two-dimensional roughness 



and _ 1211 



f 1 (y) = _5 e for three-dimensional roughness. 



It is understood that we do not claim that these expressions describe the 

 real physical model; on the other hand we believe that the flow field 

 described by these equations cannot be very much different than the 

 actual one since a considerable amount of data was used in their deriva- 

 tion. The implication is that the calculated values by means of these 

 functions will be as close to reality as the form of equation (3-15) 

 permits . 



In the determination of the function f2(y) the characteristic length 



for all conditions of roughness seemed to be the parameter — of the 



P 

 laminar case. The phase angle seemed to increase as a power function 

 with distance. The empirical relationships obtained as the results of 

 these tests are the following: 



1/3 

 f 2 (y) = 1.55 (gy) Smooth wall 



and 



2/3 

 f ? (y) = .5 (gy) Two or three-dimensional 



rough wall . 



The phase angle was measured by two different methods; in the first it 

 was obtained directly from the velocity measurement record. The time at 

 which the flow was changing direction was registered on the time scale 

 of the velocity record while the time of change in direction of the plate 

 motion was recorded by another needle of the oscillograph. The time 

 interval between these two changes of direction after having been aver- 

 aged out for a number of periods gave the desired phase angle. In the 

 second method the record of the change of flow direction was obtained 

 visually; through a thin brass tube a dye streak was introduced into the 

 flow; the change of direction of the streak at any level was observed 

 and it was recorded by means of a push button arrangement; the motion 

 of the plate was recorded as above. This method is more accurate be- 

 cause the equipment it employs is very simple; but on the other hand it 

 is subject more to personal bias. The two methods were checked against 

 each other in tests with smooth wall and the good agreement of the re- 

 sults was a proof that either one may be used with equal confidence. The 

 first method has been used to measure the phase shift in the smooth case 



B-3 



