386 



HYDRAULICS AND ITS APPLICATIONS 



while the loss of energy expressed as a fraction of ^-, experienced with 

 the best value of m is as follows. 



ART. 111. RESISTANCE OF SUBMERGED PLANE SURFACES. 



If an entirely submerged plane surface be moved normally or obliquely 

 with uniform velocity through still water, the resistance to motion 

 depends slightly on frictional resistances, but to a much larger extent on 

 the change of momentum produced in the surrounding water during the 

 passage of the plane, and on the eddy production in the rear of the plane. 



Normal Motion of a Plane through* Still Water. 



Here, in front of the plane, stream line motion is set up, and if a be 

 the area of the plate, and v its velocity, a column of water of sectional 

 area a and of length v feet, is transferred from front to rear of the plane 

 per second. The effect of this in producing resistance, may be seen by 

 considering the flow of a steady stream past such a submerged plane. 

 As before, up to the plane the motion is steady, and the stream line 

 formation is as indicated in Fig. 175. 1 The plane, therefore, affects the 

 momentum in a direction normal to its plane, of a mass of water of 

 volume a v cubic feet, per second. Since the velocity of the mass in this 

 direction is initially v feet per second, if it were possible to destroy the 

 whole of its momentum the total pressure on the front of the plane would 



From a consideration of the stream line formation, it is, 



, Wav 2 ,, 

 be - - Ibs. 



however, clear that it is only those stream lines at and near the centre of 

 the plane which are actually diverted at right angles to their normal 

 direction, the outer layers being diverted through a smaller angle 

 depending on their distance from the centre, so that the change of 



1 From a paper by Professor Hcle Shaw, " Trans. Inst. Naval Architects," 1898, vol. 85. 



