352 Determination of Inertia of a Sphere moving in a Fluid. 



The vertical force due to gravity was 0*950 lb., so that by 

 comparison with the equation 



,dv 



M 



dt 



F-h 



the value of M' will be seen to be 1584c lb., or 1*46 times the 

 displacement of the bodv. 



1%. 1. 



OP..O 



oiS 



o x 





















o 



x \ 













OIO 



<3 







s 



O ^v 

















O ^ 



c 



V o 







005 



^ 













X. 

















\ 



\ 









. 



(Velocity)^ 







O 'OS -to -15 '20 '25 '30 



The value of k, the coefficient of resistance, expressed in 

 gravitational units, is 2*44: for this particular case. Assuming 

 the resistance R to be proportional to the square of the 

 diameter, so that 



n=k'd 2 v 2 , 



the value of k' is 0'241, the units being feet, pounds, and 

 seconds. 



Having in view the modification of the theoretical flow 

 which may be caused by frictional resistances, the value 

 obiained for the increase' of inertia, namely 0'46 times the 

 displacement, may be considered a sufficient verification of 

 the value deduced analytically for this case. It may be 

 pointed out that any error involved in the assumption of the 

 value 2 for the index of n, whilst modifying the frictional 

 coefficient, would affect the value of the inertia obtained from 

 the experiment by a negligible amount. Although the fluid 

 was not of unlimited extent, the ratio of the dimensions of 

 the tank to those of the sphere were sufficiently large to 

 render the effect of the cylindrical walls inappreciable. 



