F L U 



4. The thickness of pipes to convey water is as - ; where h is the 



height of the head of water, d the diameter of the pipe, and c the cohe- 

 sion of a bar of the same material as the pipe, and an inch square. In the 

 same metal, thickness varies as h d. This result obviously only gives the 

 proportional thickness : to determine the actual thickness, we must have 

 a series of experiments on which to found our computation. But these 

 do not appear to have been carried on upon a sufficiently large scale to 

 inspire us with any confidence in the results. In fact, the thickness of 

 pipes is generally determined in practice by experiment, or rather by 

 imitating, as near as circumstances will allow, some other work of a 

 similar kind. 



Should we, however, suppose, with Dr Gregory, that a pipe of cast 

 iron 15 inches diameter, and f of an inch thick, will be strong enough for 

 a head of water of 600 feet ; and a pipe of oak of the same diameter, and 

 two inches thick, would sustain a head of 180 feet, we should have for 



any other head h and diameter d t thickness of cast iron pipes = 19non 



and thickness of oak pipes =~ jor/y 

 For the pressure of fluids against dykes see Dyke. 



FLUIDS discharge of y through very small apertures in the bottom or 

 sides of vessels. ( Fince, Bland, Play fair.) 



1. The velocity at the aperture is equal to that acquired in falling free- 

 ly through | the altitude of the fluid above the orifice, and the velocity at 

 the vena contracta equal to that acquired in falling through the whole 

 height. 



Cor. 1. Hence if h = height of the fluid above the orifice, g32% feet, 

 the velocity at the orifice = Vg- h t and velocity at the vena contracta 



Cor. 2. If any pressure be exerted on the surface of the fluid, the ve- 

 locity of the issuing fluid will be increased. Thus when water is pro- 

 jected into a vacuum, as the pressure of the atmosphere is equal to that 

 of a column of water of 34 feet, v = ^2g. (h -f 34). And in general, if 

 h' be the height of the column of fluid, which would exert the same pres* 

 sure as is applied at the upper surface, 



Cor. 3. It is found by experiment that the section of the vena eontrac- 

 116 



