Pressure of Fluids. 305 



Moreover, since the magnitude of this pressure is equal to 

 the surface multiplied by the distance of the centre of gravity, 41 ^ 

 the pressure on the upright side of a vessel of the form of a par- 

 allelepiped is to the pressure on the bottom, as half the area of Fig.176. 

 the side to the area of the bottom, or as half the height of the 

 side to the length of the bottom, reckoned in the direction of a 

 perpendicular to this side. When the parallelopiped is a cube, 

 the pressure on the side is half that on the bottom, and the pres- 

 sure upon the four sides together, double that upon the bottom. 



Since the pressure of any fluid is proportional to the depth 

 below the surface, the strain upon the sides of a sluice, and the 

 banks of a canal, must increase uniformly from the top to the 

 bottom ; and, when this force is to be resisted by earth or mason- 

 ry, since the strength of the materials may be estimated in a 

 certain proportion to the weight, commonly as a third or fourth 

 part, if AB be the height of the bank or dike, and a third of its 

 density be to that of water, as AB to BC, by joining AC, this 

 line will represent the proper slope. If the bank be composed 

 of stone or brick, the base BC must be at least equal to the 

 altitude AB ; if it be of earth, BC should exceed the height AB 

 by one half. 



Let AC, BC, represent the floodgates of a canal-lock which 

 are opened by means of the extended arms AF, BF. When we Fl S- 209 

 shut the gate, AC is pressed at right angles by the water with 

 a force proportional to AC, and which, from the principle of the 

 moment of inertia, must exert a perpendicular effort at the end 



-- 2 



C, as AC. The strain thence produced in the direction AB 355. 

 will be opposed by an equal and opposite effort from the gate 

 BC. These two forces constitute the power which closes the 

 gates. If the angle ACB be very acute, the gates would close 

 feebly; if on the other hand ACB be too obtuse, the gates 

 would occasion a great strain upon the sides of the sluice. This 



strain in the direction CA is as AC, other things being the 

 same ; it is also as the width of the canal or as AD, and for 

 the reason above given, inversely as CD ; that is, the force in 

 question is as 



CD 

 Mech. 39 



