HYDROSTATICS 345 



Pascal's Law. The pressure per unit of area exerted anywhere 

 on a mass of liquid is transmitted undiminished in all directions; 

 and any surface in contact with the liquid will be subjected to this 

 pressure in a direction at right angles to the surface. 



PRESSURE OF LIQUIDS ON SURFACES 



General Principles. The pressure of a liquid on any surface 

 immersed in it is equal to the weight of a column of the liquid 

 whose base is the surface pressed and whose height is the per- 

 pendicular depth of the center of gravity of the surface below 

 the level of the liquid. The pressure thus exerted is not depen- 

 dent on the shape or size of the vessel containing the liquid, 

 nor on the form of the surface, whether it be flat or curved; nor 

 on the position of the surface, whether it be vertical, horizontal, 

 or inclined. The pressure is normal to the immersed surface. 



Let, in the accompanying illustrations, the depth of water in 

 each dam be 12 ft. Consider a portion of the embankment or 

 wall 1 ft. long. Then in Fig. 1 the area of the immersed sur- 

 face is 12 sq. ft.; the distance of the center of gravity of the 

 surface from the level of the water is 6 ft., and assuming the 

 weight of water as 62.5 Ib. per cu. ft., the total pressure on 

 the surface AB is 12X6X62.5 = 4,500 Ib. In Figs. 2 and 3 

 the walls, being inclined, expose a greater surface to pressure, 

 say 18 ft. from A to B. Then the total pressure is 1SX1X 

 6X62.5 = 6.750 Ib. These pressures may be considered as 

 forces acting, in each case, normally to the surface AB. The 

 point of application C of the resultant pressure on the wall, 

 called the center of pressure, is not at the center of gravity of 

 the submerged area, but at one-third of the distance AB from 

 the bottom; so that in each case CB=\ AB. 



In Fig. 1 the resultant pressure is horizontal, producing an 

 overturning moment about the outer toe, and also tending to 

 slide the wall along its base. In Figs. 2 and 3 the resultant 

 pressure may be resolved into two components, one horizontal 

 and the other vertical. The horizontal component in both 

 cases is the same as the total pressure in Fig. 1, whereas in 

 Fig. 2, the vertical component tends to counteract the effect of 

 the horizontal component, and in Fig. 3, it tends to lift the wall. 



