132 



WELLS'S NATURAL PHILOSOPHY. 



How is the 

 pressure of a 

 liquid exerted 

 laterally ? 



Fig 



How may the 

 pressure upon 

 the side of a 

 vessel of water 

 be calculated ? 



298. As liquids transmit pressure equally in 

 all directions, this pressure will act sideways 

 as well as downward, and the pressure at any 

 115^ point upon the side of a vessel con- 

 taining a liquid, will be in propor- 

 tion to the perpendicular depth of 

 that point below the surface. 



Fig. 115 represents a vessel of water with 

 orifices at the side, at different distances fi'oro 

 the surface. The water will flow out with a 

 force proportionate to the pressure of the water 

 at these several points, and tliis pressure is 

 proportionate to the depth below the surface. 

 Thus, at a the water will flow out with the 

 least force, because the pressure is least at that 



point. At 6 and c the force and pressure will be greater, because they are 



situated at a greater depth below the surface. 



299. To find the pressure upon the side of a 

 vessel containing water, multiply the area of 

 the side by one half its whole depth below the 

 surface, and this product again by the weight 



of a cubic foot of water. 



Suppose A C, Fig. IIG, to represent the section of the 

 side of a canal, or a vessel filled with water, and let the 

 whole depth, AC, be 10 feet: then at the middle point, 

 B, the depth, A B, will be 5 feet. Now the pressure at 

 C is produced by a column of water whose depth is 10 

 feet, but the pressure at B is produced by a column 

 whose depth is 5 feet, which is the average between tho 

 pressure at the surface and at the bottom, or the average of the entire pressure 

 upon the side. Hence the total pressure upon the side of a vessel containing 

 water will be equal to the weight of a column of water whose base is equal to 

 the area of that side, and whose height is equal to one half the depth of the 

 liquid in the vessel, or, in other words, to the depth of the middle point of the 

 side below the surface. 



As the pressure upon the sides of a reservou* containing wa- 

 ter increases with the depth, the walls of embankments, dams, 

 canals, etc., are made broader or thicker at the bottom than 

 at the top (as in Fig. 114). For the same reason, in order to 

 render a cistern equally strong throughout, more hoops should 

 be placed near the bottom than at the top. 



If a surface equal to the side of a vessel containing liquid were laid upon 

 the bottom, then the pressure upon the surface would be double the actual 



Why should 

 nu embankment 

 be made strong- 

 er at ttie bot- 

 tom than at the 

 top? 



