38 HYDRAULICS AND ITS APPLICATIONS 



E.g. In the Monitor (U.S.N.) calculated time was 2'5 sees. 



experimental 2*7 sees. 



Froude, experimenting on ships fitted with and without bilge keels, 1 

 found that the effect of the keel is to extinguish the oscillations more 

 rapidly, but that the effect on the period of rolling is very slight, the 

 average difference produced by the addition of these keels being about 

 6 per cent. Also the extinctive effect is greater when the ship is moving 

 than when stationary. 



The effect of an increase in the metacentric height is to stiffen the 

 vessel and to diminish the period of the oscillation, while any increase in 

 its radius of gyration tends to increase the period. Too great stiffness is 

 inadvisable because of the tendency of the forces brought into play to 

 strain the vessel, and it is often advisable in the case of a cargo vessel to 

 arrange the cargo so that its heavier portions are as near to the skin of 

 the vessel as possible. This increases the radius of gyration, and thus the 

 period of rolling, without seriously affecting the stability. 



The metacentric height in the case of merchant ships varies of course 

 with the loading, but when fully loaded is usually between 1J and 4 feet. 

 For small vessels, such as tugs and torpedo boats, it varies from about 

 1 to 2 feet. 



ART. 13. STRENGTH OF PIPES AND CYLINDERS. 



This will be briefly discussed as being of great importance to the 

 hydraulic engineer. 



In a thin pipe the stress over the whole thickness of metal may be 

 taken as being sensibly uniform, and by considering a section made by a 

 diametrical plane we see that the force per unit length of pipe tending to 

 rupture it across this plane = 2 r p, where 

 > = pipe radius in inches. 

 p = internal pressure in Ibs. per square inch. 



If t = thickness of pipe in inches and/= stress per square inch 

 in metal, we have the force resisting rupture along this plane = Zft. 



.'. for equilibrium / = or t = ^~ . 



For steel or wrought-iron pipes this rule is sufficiently accurate, and 

 here the working value of/ varies from 7,500 to 8,500 Ibs. per square inch 

 for wrought iron, and 10,000 to 12,000 Ibs. per square inch for steel, 



For an investigation into the action of bilge keels see a paper by Dr. G. H. Bryan, 

 "Trans. Inst. Naval Architects," 1900. Also by G. H. Baker, Trans. Inst. Naval Architects," 



