These average values (for one cycle) can be found from figures 11 and 12 for 



use in equation (24). 



du 



In practice, both U and— are unknown, and knowing C,v, is of little use. 



The errors in neglecting the acceleration term can be large, even at large values 



U T 



of i^eriod parameter. Take the typical case of -- — ^ 200 T = 10 seconds 



a 



U^ = 10 centimeters per second, d = 0.51 centimeter. Extrapolating figures 11 

 and 12, Cq = 1.2, and Cf^ = 2.6. Substituting these values into equation (24), 



F = 0.54-— + 0.31 UlL/l (25) 



dt 



Let U = sin coi. Values of F from the above equation are plotted in figure 21, 

 first using only the velocity term and then using both terras. The force curve 

 using both terms is what a real current meter would actually detect. Therefore 

 by using this force curve and solving for U in equation (24), where the accelera- 

 tion term is neglected, the indicated velocity can be plotted (fig. 22). The true 

 velocity, U = sin co(, is also plotted for comparison. The large errors are obvious 



i! T 



from the curves. Making- 



larger, by making d smaller, probably will not 



change the values of C^, and Cp . This is a reasonable assumption for Cq until 

 the critical Reynolds number is reached. The assumption for C^ may not be valid 

 although the curve in figure 12 appears asymptotic for large-period parameter 

 values. The ratio of the velocity term to the acceleration term varies as 



"7 in equation (24). By making d smaller, the acceleration term could be made 



less significant. Making d several times smaller, less than 0.51 centimeter, would 

 reduce the forces to such a level that they would be hard to measure. 



0.1 0.2 0.3 0.4 



0.5 



t/T 



0.6 U.7 0.8 0.9 1.0 



Figure 21. Drag force current meter example. 



33 



