Fluid statics#Hydrostatic pressure

The hydrostatic paradox (also Pascal's paradox by Blaise Pascal ), the apparent paradox, that the hydrostatic pressure that results in a liquid in a vessel at the bottom of the vessel, although depends on the filling level of the liquid, but not of the shape of the vessel and thus the amount of liquid. The physical basis of the hydrostatic pressure. It is calculated as:

With:

Explanation

In all vessels with the same level acting in the same height, the same fluid pressure on the bottom of the vessel, regardless of the base and the vessel geometry. As a consequence arises in communicating vessels, the same level one, regardless of the tube geometry.

Communicating Vessels: In all tubes the liquid is the same level, although distinguish the quantities of liquid strong.

A stationary fluid in a uniform gravitational field, neglecting the capillary hydrostatic pressure only by the depth below the liquid surface is subject. If the water level is different in different ascending branches of the communicating vessels, the liquid would not be in balance in them. In this case, the liquid flowing in the cross-connections to ( in the presence of friction), a balance is established. Thereafter, the liquid is equally high in all branches. The air pressure has not taken into account, since in all areas of communicating tubes it is the same in a very good approximation.

In a vessel with liquid, the forces caused by the fluid and the opposing forces of the vessel wall pick up. This balance of forces can be used to illustrate how the various forces acting, although at the same depth throughout, there is the same hydrostatic pressure. At an interface between the liquid and the vessel, the liquid is at each point, as well as in the interior of the liquid, at a certain hydrostatic pressure depending on the depth below the liquid level. This causes a force on each surface element, which is perpendicular to the sheet and to the outside. As long as the vessel wall is intact, it causes a back pressure which removes the force of the hydrostatic pressure. Breaking at a location in the vessel, there is at a hydrostatic pressure greater than zero, an opening occurs at this point of the liquid and is accelerated by the forces due to the pressure difference. As a result, the injected liquid away from the opening, depending on the position of the opening and upwardly. After emerging from the orifice is no hydrostatic pressure acts more on the fluid and, consequently, no force due to the hydrostatic pressure

Explanation of the effect in communicating tubes

The hopper and cylinder unfold on their bottom surfaces each the opposing force from the weight of the overlying water ( blue) plus the force due to air pressure (green).

The opposing force of the water, the cross tube ( brown) is the same for all bottom surfaces of the now composite tubes. This is equivalent to saying that the water pressure at the same level has the same amount.

The forces on the edge of the hopper act on the vessel shell and this defies the load with an equally large force ( magenta ), otherwise would break the shell. Similarly, the envelope of the cone must counteract the forces that are only weakened due to the smaller amount of water and the consequent lower weight and not canceled.

On the right two sealed tubes you can clearly see that the force on the shell and the same opposing force of the shell depend on the height. Locks to the funnel in the height of the water level with a wafer-thin lid, it can not break. Substituting this cover but something deeper and removes the water lying above it, to break this, because he can not build the necessary counterforce.

Application

• A water tower is a reservoir that is placed higher than the water consumers. The difference in height causes the water pressure at the delivery points.
• The water level gauge is an ideal instrument for measuring height differences in distant places. The operating principle is based on the communicating vessels: The water level is the same in both vertically arranged ends of a hose.
• When Artesian wells occurs at a well hole, the water itself upwards.
• All hydraulic equipment