RESISTANCE OF SHIPS 



395 



of flow this latter equation reduces to 



(p. 68). 



d s ~ li 2 



The first two of these equations show that lines of equal pressure cut the 

 stream lines at right angles. If then in Fig. 179, A and C, as also B and D, 

 are points of equal pressure on two adjacent stream lines A B and C D, 

 over which the mean velocities are u -f- S u and u, the corresponding values 

 of B s for equal values of S p are A B and C D, so that 



A B _ _u_ 



CD ~ u + Sn 



But the centre of curvature of the stream lines is at the point of inter- 

 section of A C and B D produced, so that -~-j = 



u r -4- 8r 



u + u ~~ r 

 and, neglecting small quantities of the second order, this reduces to 



which is identical with equation (2) above. 



Wave production is a very complicated phenomenon, and depends in 

 magnitude and in form largely on the form and speed of the boat. In 



general it may be taken that the motion ^^____ . _^^^ 



is accompanied by the formation of bow / 



and stern waves, and by a fall of the 



water surface amidships (Fig. 180). 



The fact that outward stream-line flow 



must commence in front of the bows, 



and that the head necessary to produce 



this can only be obtained by a relative 



elevation of the surface level, accounts 



for the bow wave, while the reduction 



in velocity of the accompanying stream 



at the stern and the consequent increase 



in pressure accounts for the stern wave. 1 



Also the increased velocity amidships is 



+ct 



IB 



r 



Fie*. 179. 



accompanied by a diminution in pressure, and accounts for the lowering 

 of the surface level at this point. With a wholly submerged body the 

 displacements produced on the surrounding mass of water are identical in 



1 For an article on the changes of level around a vessel, see the Engineer, vol. 63, p. 252. 



