(Fig. 8.24). In this type of body there is low 

 drag, very little wake and what drag does 

 exist is largely that of skin friction. As is 

 evident from Figure 8.24, the drag coefficient 

 (C(i) of such streamlined bodies of revolution 

 is governed primarily by the length to diame- 

 ter ratio, sometimes referred to as the "fine- 

 ness" ratio and secondarily by Reynolds 

 number of the flow. 



A review of the submersible configurations 

 in Figures 8.18 and 8.19 reveals no parallels 

 to the ALBACORE hull; the closest similarity 

 being perhaps that of the DSRV. Submers- 

 ibles range between bluff (non-streamlined) 

 to somewhere approaching streamlined bod- 

 ies; the majority congregating towards the 

 lower middle or bluff end of this broad cate- 

 gory. Consequently, high form drag is preva- 

 lent. 



Skin Friction Drag 



Skin friction drag is due to the viscosity of 

 the water. Its effects are exhibited in the 

 adjacent, thin layers of fluid in contact with 

 the vehicle's surface — i.e., the boundary 

 layer. The boundary layer begins at the sur- 

 face of the submersible where the water is in 

 immediate contact with the surface and is at 

 zero velocity relative to the surface. The 

 outer edge of the boundary layer is at water- 

 stream velocity. Consequently, within this 

 layer is a velocity gradient and shearing 

 stresses produced between the thin layers 

 adjacent to each other. The skin friction drag 

 is the result of stresses produced within the 

 boundary layer. Initial flow within the 

 boundary layer is laminar (regular, continu- 

 ous movement of individual water particles 

 in a specific direction) and then abruptly 

 terminates into a transition region where 

 the flow is turbulent and the layer increases 

 in thickness. To obtain high vehicle speed, 

 the design must be towards retaining lami- 

 nar flow as long as possible, for the drag in 

 the laminar layer is much less than that 

 within the turbulent layer. 



An important factor determining the con- 

 dition of flow about a body and the relative 

 effect of fluid viscosity is the "Reynolds num- 

 ber." This number was evolved from work of 

 the Englishman Osborne Reynolds in the 

 1880's who observed that what might have 

 begun as laminar flow became abruptly tur- 



bulent when a particular value of the prod- 

 uct of the distance along a tube and the 

 velocity divided by the viscosity was reached. 

 The Reynolds number expresses in non-di- 

 mensional form a ratio between inertia 

 forces and viscous forces on the particle, and 

 the transition from the laminar to the turbu- 

 lent area occurs at a critical Reynolds num- 

 ber value. This critical Reynolds number 

 value is lowered by the effects of surface 

 imperfections and regions of increasing pres- 

 sure. In some circumstances, sufficient ki- 

 netic energy of the flow may be lost from the 

 boundary layer such that the flow separates 

 from the body and produces large pressure 

 or form drag. 



The Reynolds number can be calculated by 

 the following: 



Re = 



pVl VI 



m 



ALBACORE Type HuK 



LENGTH TO DIAMETER (FINENESS) RATIO 



Fig. 6 24 Drag coefficjent of streamline bodies of revolution 



393 



