# hydrostatics

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## hydrostatics:

see mechanics**mechanics,**

branch of physics concerned with motion and the forces that tend to cause it; it includes study of the mechanical properties of matter, such as density, elasticity, and viscosity.

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## Hydrostatics

The study of liquids at rest. In the absence of motion, there are no shear stresses; the internal state of stress at any point is determined by pressure alone. Hence, the pressure at a point is the same in all directions. Pressure acts normally to all boundary surfaces. For equilibrium under gravity, regardless of the shape of the containing vessel, the pressure is uniform over any horizontal cross section. Pressure varies with height or depth. Two different reference levels are used in measuring pressure. For many engineering purposes, gage pressure is used with pressure measured relative to atmospheric pressure as zero. For most scientific purposes, pressure is referred to true zero. Normal atmospheric pressure at sea level caused by the weight of the air above is approximately 101 kilopascals or 14.7 pounds per square inch absolute.

The buoyant force is the force exerted vertically upward by a fluid on a body wholly or partly immersed in it. Its magnitude is equal to the weight of the fluid displaced by the body. This value is also the vertical component of the fluid pressure force acting upward against the bottom of the body minus the fluid pressure force component (if any) acting vertically downward against the top of the body. If this buoyant force equals the weight of the body, the body will remain at the given level. If it exceeds the weight of the body, the latter will rise, and vice versa. The buoyant force as a single magnitude acts vertically upward through the center of buoyancy which is the center of gravity of the displaced fluid. *See* Archimedes' principle

Pressure applied to a confined liquid is transmitted with equal intensity throughout the liquid and by it to all surfaces of the confining vessel or piping. Hence, a small force applied to a small area of a confined liquid can create a large force against a large area. If the small and large areas are pistons, the device may be a hydraulic press or jack. Because the transmitting liquid is practically incompressible and its volume virtually constant, the linear movement of the large piston will be to that of the small piston in inverse proportion to their areas. The principle of multiplying a force by means of liquid pressure applies also to hydraulic brakes, power steering, control systems, and the like; the actuating force may be a pump instead of a small piston.

## Hydrostatics

a branch of fluid mechanics that studies the equilibrium of a fluid and the effect of a fluid that is at rest on a body immersed in it. One of the principal tasks of hydrostatics is the study of the distribution of pressure in a fluid. When this is known, it is possible to calculate, on the basis of the laws of hydrostatics, the forces exerted by a fluid at rest on a body immersed in it, as for example, a submarine, on the walls and bottom of a container, on the wall of a dam, and so on. In particular, the conditions for the flotation of bodies on the surface of or within a fluid can be deduced, and the conditions under which floating bodies will have stability can be ascertained, a very important consideration in shipbuilding. The laws of hydrostatics, especially Pascal’s law, serve as the basis for the operation of the hydraulic press, the hydraulic accumulator, the fluid manometer, the siphon, and many other machines and instruments.

If a heavy fluid at rest has a free surface where the external pressure is equal to p_{o} at all points, then the pressure of the fluid at a depth *h* is equal to

*p* = *p*_{o} + *ρgh*

that is, the pressure at a depth *h* is equal to the external pressure added to the weight of a column of the fluid having a height *h* and a base area equal to 1 (ρ is the density of the fluid and *g* is the acceleration of gravity). The properties of pressure expressed by this formula are used in such hydrostatic machines as the hydraulic press and the hydraulic accumulator.

One of the basic laws of hydrostatics is Archimedes’ principle, which determines the magnitude of buoyant force acting on a body immersed in a fluid or gas. A case frequently encountered is that in which the fluid is moving together with the container so that the fluid is at rest with respect to the container. From the laws of hydrostatics it is possible to determine the shape of the fluid’s surface in such a container, for instance, when it is rotating. Since the fluid’s surface must always be in such a state that the sum of all the forces acting on the particles of the fluid, other than the pressure forces, are normal to the surface, the surface of a fluid in a cylindrical container that is rotating uniformly around its vertical axis assumes the shape of a paraboloid of revolution. The same thing happens in the oceans—the surface of the water is not an exact sphere but is somewhat flattened toward the poles. The flattening of the earth itself toward the poles is to some degree due to this fact. Thus, the laws of hydrostatics, which make it possible to determine the shape of the surface of a uniformly rotating fluid, are important in cosmogony.

### REFERENCES

*Elementarnyi uchebnikfiziki*, 6th ed., vol. 1. Edited by G. S. Lands-berg. Moscow, 1968.

Khaikin, S. E.

*Fizicheskie osnovy mekhaniki*. Moscow, 1962. Chapter 15.