and 



*e 



^P =^"^1 r^p sin a dx [2] 





 where r is the radius from the axis to the body surface, 



a is the angle between the tangent to the meridian profile and the axis of the body, 



X is the arc length along the meridian profile, and 



x^ is the total arc length of the body from nose to tail. 



The sum of the two drags then constitutes the total viscous drag D or 



^=^/^^P [3] 



The alternate procedure involving the velocity profile of the wake, which is better 

 suited to the methods of this report, is to determine the total drag, without need of resolution 

 into skin-friction and pressure drag, by considering the net rate of loss of momentum of the 

 flow of the entire stream. The analytical procedure is to apply the momentum theorem of 

 hydrodynamics to a control surface enclosing a region about the body with dimensions suf- 

 ficiently large to have substantially undisturbed free- stream pressure p^ at its periphery. The 

 total drag of the body which is the net rate of loss of momentum in the axial direction is then 

 given by 



D = 27Tp \ u{u^ -u)Tdr 



[4] 

 



where U^ is the velocity of the incoming undisturbed stream ahead of the body, 



u is the velocity in the wake far downstream, 



r is the radial distance from the axis, and 



p is the mass density of the fluid. 

 In terms of the momentum area of the wake far downstream 



ft , r J^(l-JL\rdr 



[5] 







the drag is 



D =2ttp UJ Q.^ [6] 



The drag coefficient Cq based on some appropriate reference area A is 



Cjj = ^ = iiLik [71 



ipt/2^ ^ 



2 ~ 

 Inasmuch as the momentum area of the wake fi^ is the final stage of the development 

 of the boundary-layer flow from its inception on the nose of the body, it is necessary to cal- 



