6. Symmet-rical Lenses: See Figure E-1. These lenses are two intersecting or 

 separated spheres: 



— 1 — -I 1 1 1 1 1 1 



— ( 



►=^^ 



i 







•— i 



^ 



©* t (?j- H ' 













B 



1 1 1 1 1 1 1 1 













R 



The abscissa is the ratio of B/R. The motion is in the direction shown. 



7. Two Parallel Rectangular and Square Plates: See Figure E-1. The abscissa 

 is the ratio of spacing between two plates to width, where the spacing is 

 measured from center to center of the plates. The ratio of length to width 

 of the plates are over 17 to 1. The motion is in a direction parallel to the 

 thickness of the plates. 



For all of the oscillatory motion cases the experiments were conducted at low 

 velocities and high accelerations. Thus the total resistance force to the moving 

 object is largely due to the added mass which is dependent on the acceleration. At 

 higher velocities, the total resistance force is due to a velocity-dependent drag term 

 as well as to the added mass term. That part of the resistance to motion due to viscous 

 and form drag and that part due to added mass are difficult to separate. Stelson and 

 Mavls° and Silberman' realized the difficulties. From experiments on a sphere the 

 measured added mass increased by approximately 1% above the values obtained from 

 ideal fluid theory. Thus it was concluded that viscosity did not seriously affect the 

 experimental values for the added mass. 



A recent method (Zienkiewicz and NathlO) of measuring the added mass is 

 worth mentioning here. Using an electric analogy method, the virtual mass as well 

 as the pressure distribution around a rigid body accelerating in an incompressible 

 fluid can be determined. In the following table, the results are compared with the 

 known added mass coefficients obtained from other sources. Agreement is excellent. 



Object 



Added Mass Coefficient 



Obtained by 

 ZienkiewiczlO 



From Indicated Source 



Infinitely long vertical plate 

 Infinitely long cylinder 

 Thin circular disc 

 Cube 



1.03 

 0.98 

 0.61 

 0.62 



1.04 (RiabouchinskylO) 

 1.00 (H. Lambll) 

 0.636 (H. Lambll) 

 0.67 (Stelson6) 



74 



