FLU 



xdx 



U V ' gx 



Cor. If any pressure be exerted on the surface of the fluid, and h' = 

 the height of a column of the fluid which would exert the same pressure, 



, = . 



Ex. 1. If equal hemispheres are emptied by orifices in the vertex and 

 base, time in the first case : time in last : ; 7 : 12 ; the actual time in the 



first case being ~^-= =, and in the latter 



lo a *j o a j & 



2. In paraboloids, the times are as 1 : 2. 



3. In cones, the times are as 3 I 8. 



4. In a sphere, time of emptying upper half '. time of emptying 

 ^ lower : ; 8 ^ 7 : 7. 



5. To determine the time in which a cylinder will empty itself into 



a vacuum, its upper surface being exposed to the pressure of 

 the atmosphere. 



Let h = height of the vessel, and h 1 = the height of a column of iluid, 

 equal to the weight of the atmosphere. Then by Cor. Art. 5. 



6. If upon the altitude of a fluid in a vessel as diameter we describe a 

 | circle, the horizontal space described by the fluid from a perpendicular 

 orifice at any point in the diameter equals twice the ordinate of the $ 

 circle drawn from that point, and .*. varies as sin. 0, where 6 the arc 

 of a circle, whose diameter is the depth of the fluid, and versed sine the 

 depth of the orifice. 



7. In jets d'eau, the differences between the heights of the jets and of 

 the reservoirs, are as the squares of the heights of the jets themselves, 

 i.e. if H and H' be the heights of two reservoirs, h and h' the heights of 

 the actual jets, 



H h : H' /j':: h* : h*. 



FLUIDS, resistance of.f Vince y Bland.) 



The resistance to a body moving in a fluid arises from the inertia, the 

 tenacity, and the friction of the fluid. But the resistance here consider- 

 ed is that arising solely from the inertia of the fluid. The following ar- 

 ticles are also deduced upon an hypothesis which cannot obtain in real 

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