FLUID PRESSURE. As a result of the reaction of the containing walls on a liquid or a gas there is always a 'pressure' at each point throughout the fluid, i.e. there is a force acting over any surface immersed in the fluid; the munerieal value of the pressure over apy area is by defini tion the force per square centimeter, and the `pressure at a point' is the limiting value of the force acting on any surface at that point divided by the area of the surface, as the area is sup posed to be taken smaller and smaller until it becomes practically a point. This pressure. due to the reaction of the walls. is the same for all points in the fluid. There is also an additional pressure at each point of a fluid on the surface of the earth owing to the fact that any horizontal plane passing through that point has to support the weight of the column of fluid vertically above it. If the area of this plane is A; the vertical height above it .to the top of the fluid, h; the average density of the fluid, p : the aeeel eration due to gravity of a falling body, g ; the upward force will be phy.i, and, therefore, the pressure is rah. These two pressures are the only ones which affect our senses or produce mechanical effects in general; but there is also, of course. at any point in a liquid what may be called 'cohesion,' or pressure due to the action of the molecules on each other. Some idea of the magnitude of this may be obtained by separating the molecules, e.g. by boiling the liquid. It is greatly affected by dissolving substances in the liquid. The pressure against any surface im mersed in a fluid at rest is always at right angles to it, otherwise there would be produced a flow ing owing to the component of the pressure along the surface. Further, the pressure at any point in a fluid at rest is the same in all directions, because, if it were greater in one direction than in another. the fluid would flow. Therefore the pressure at any point in a fluid at rest is the sum of the pressure due to the reaction of the walls, P. and that due to gravity. pgh. As noted
above. the former is the same for all points in the fluid. As a consequence. if a fluid is in closed in a cylinder into which fit two pistons of different areas, .1, and ..1„, the forces which must Ise applied to these pistons from without to pre vent the fluid from pressing them outward are PA, and P.1,—mnitting any action of gravity. Therefore, if A, is small compared with the tee on the former piston is small compared with the balancing force on the latter; so a small force may produce a large one. In a liquid which is almost incompressible, l' may be very great ; and so the force produced may be enormous; hut. in a gas, which is easily compressed, P is never very large: and so the force produced is small. (This principle is that of the hydrostatic press. See HYDRAULIC PRESS.) The total pressure, i.e. P pgh, at all points in the same horizontal level in any one fluid, regardless of the shape or size of the containing vessel. is the same; for imagine a vessel with a horizontal bottom. all points of the fluid along this must have the same pressure. otherwise the fluid would flow; the pressure at any point at a level h mntimeters above this bottom plane is less than that at the bottom by an amount pgh flic same for all points in the plane. II, now, portions of the vessel are imagined removed, so as to leave a vessel of any shape, the pressure at the various points remains nnalre,ted. The slire on any portion of the containing walls va ries with the depth; so the thrust outward on this portion is the resultant of a series of par allel forces, increasing from top to bottom; the point of application of this resultant is called the 'centre of pressure.' If the wall is a vertical rectangle. the centre of the pressure. dile to grav ity, for a liquid. is at a distance one-third the height from the bottom. etc.