RESISTANCE OF SUBMERGED PLANES 



387 



momentum in the direction of motion, and hence the pressure on the 

 front of the plane, is less than - .At only one point, i.e., the centre 



t/ 



of the plane, is the momentum actually destroyed, and here the pressure 



W v 2 

 intensity amounts to -~ > the nea( ^ corresponding to the velocity of 



flow. Immediately after passing the plane the motion becomes sinuous, 

 eddies are formed, 1 and since 



FIG. 175. 



the energy of eddy produc- 

 tion has to be supplied in the 

 form of extra work done on 

 the plate, this directly in- 

 creases the resistance to mo- 

 tion. In other words, while 

 the pressure on the front of 

 the plane is unaffected, that 

 on the rear face is reduced 

 by this eddy production, and 

 since the resistance to motion 

 is equal to the difference of 

 pressure on the two faces, 

 this is increased. Plates of 

 different shapes have different effects as regards eddy production, the cir- 

 cular shape giving least resistance for a given area, while generally the 

 resistance increases slightly with the ratio of the length of periphery 

 to the area of the plane. Also it would appear that as the size of plate 

 increases, the proportional effect of the eddy production increases slightly. 

 Experiments show that for the normal motion of a submerged plane 

 through still water, where the boundaries are so remote as not to affect 



the resistance, this is given by k - - Ibs., where k is a coefficient 



/ 



depending on the size and shape of the plate, and diminishing slightly as 

 the speed increases. 



With a circular plate, k varies from about '560 in a plate of 1 inch 

 diameter to "650 with a diameter of 3 inches and "720 with a diameter of 

 6 inches, afterwards increasing slightly with the diameter. Dubuat and 

 Duchemin obtained a mean value of "717 for a plate 1 foot square moving 

 through still water, k being '50 for the front of the plate and '217 for the 



See Art. 15, p. 47. 



C 



