OF STEAM NAVIGATION. 



[SECT. x. 



OF THE RESISTANCE OF VESSELS. 



611. The resistance of a vessel moving in a fluid increases from the com- 

 mencement of the motion, till it is equal to the moving force, and then the motion 

 becomes uniform. It is the resistance at this uniform motion only, which we have 

 to consider. 



In order to assist in the first steps of the inquiry, let us confine ourselves to 

 a prismatic vessel with flat ends, moving in the direction of its length. 



612. The resistance of such a prism would be nearly equal to the head of 

 water, which would give the water in a canal of the same length, and one and a 

 half times the section of the immersed part of the prism, the same velocity as 

 the prism. 



For let A B be that head ; then the resistance to efflux at D must be equal 

 to the resistance to motion at C, the section being the same ; otherwise the motion 

 would accelerate. But the fluid will rise at C, and fall at D, till the difference 

 be equal to the head due to the velocity of the boat ; and the efflux at D must 



FIG. 25. 



both supply a void with fluid equivalent to the velocity of the boat, and supply 

 a resistance equal to the head pressure. This will be the case when two-thirds 

 of A B is the head corresponding to the velocity. Hence, if v = the velocity, 

 A E = h, and B E = x = the head equivalent to the friction, 



_ 64 (h x) . 

 1-5 



where 64, neglecting a small fraction, is the proper coefficient for the motion of 

 a fluid when free from friction or cohesion ; consequently, 



1-5 v s 



