Pressure of a fluid in equilibrium
Debido a la naturaleza fundamental de los fluidos, un fluido no puede permanecer en reposo en presencia de un esfuerzo cortante. Sin embargo, los fluidos pueden ejercer presión normal a cualquier superficie de contacto. Si se considera un punto del fluido como un cubo infinitesimalmente pequeño, se deduce de los principios del equilibrio que la presión en cada lado de esta unidad de fluido debe ser igual. Si no fuera así, el fluido se movería en la dirección de la fuerza resultante. Así, la presión") sobre un fluido en reposo es isótropa; es decir, actúa con igual magnitud en todas las direcciones. Esta característica permite a los fluidos transmitir la fuerza a través de la longitud de tuberías o tubos; es decir, una fuerza aplicada a un fluido en una tubería se transmite, a través del fluido, al otro extremo de la tubería. Este principio fue formulado por primera vez, de forma ligeramente ampliada, por Blaise Pascal, y actualmente se denomina ley de Pascal.
En términos de Mecánica clásica, la presión de un fluido incompresible en estado de equilibrio se puede expresar mediante la siguiente fórmula:[5].
donde P es la presión, ρ es la densidad del fluido, g es la aceleración de la
gravedad y h es la altura.
hydrostatic pressure
In a fluid at rest, all friction and inertia stresses disappear and the stress state of the system is called hydrostatic. When this condition is applied to the Navier-Stokes equations, the pressure gradient becomes a function of the body forces alone. For a barotropic fluid") in a conservative force field such as a gravitational force field, the pressure exerted by a fluid in equilibrium becomes a function of the force exerted by gravity.
Hydrostatic pressure can be determined from a control volume analysis of an infinitesimally small cube of fluid. Since pressure is defined as the force exerted on a test area (, with : pressure, : force normal to area, : area), and the only force acting on any such small cube of fluid is the weight of the column of fluid above it, the hydrostatic pressure can be calculated according to the following formula:.
where.
• - is the hydrostatic pressure (Pa),.
• - is the density of the fluid (kg/m),.
• - is the gravitational acceleration (m/s),.
• - is the test area (m),.
• - is the height (parallel to the direction of gravity) of the test area (m),.
• - is the height of the zero pressure reference point") (m).
For water and other fluids, this integral can be significantly simplified for many practical applications, based on the following two assumptions. Since many liquids can be considered incompressible"), a good reasonable estimate can be made by assuming a constant density throughout the liquid. The same assumption cannot be made in a gaseous medium. Furthermore, since the height of the liquid column between and is usually reasonably small compared to the radius of the Earth, the variation of can be neglected. Under these circumstances, the integral is simplified in the formula.
where is the height of the liquid column between the test volume and the zero pressure reference point. This formula is often called Stevin's law.[6][7] Note that this reference point must be at or below the surface of the liquid. Otherwise, you have to divide the integral into two (or more) terms with the constant and . For example, absolute pressure") compared to vacuum is.
where is the total height of the liquid column above the test zone to the surface, and is the atmospheric pressure, that is, the pressure calculated from the remaining integral over the air column from the liquid surface to infinity. This can be easily visualized using a pressure prism.
Hydrostatic pressure has been used in food preservation in a process called pascalization.[8].
Buoyancy
Any body of arbitrary shape that is immersed, partially or completely, in a fluid will experience the action of a net force in the direction opposite to the local pressure gradient. If this pressure gradient comes from gravity, the net force is produced in the opposite vertical direction to that of the gravitational force. This vertical force is called the buoyant or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Mathematically,.
where is the density of the fluid, is the acceleration due to gravity, and is the volume of fluid directly above the curved surface.[9] In the case of a ship, for example, its weight is balanced by the pressure forces of the water around it, allowing it to float. If the boat is loaded more, it would sink further into the water - displacing more water and thus receiving a greater buoyant force to balance the increased weight.
The discovery of the principle of buoyancy is attributed to Archimedes.
Medicine
In medicine, hydrostatic pressure in blood vessels is the pressure of blood against the wall. It is the opposite force to oncotic pressure.
atmospheric pressure
Statistical Mechanics shows that, for a pure ideal gas of constant temperature in a gravitational field, T, its pressure, p will vary with height, h, as.
where.
• - is the acceleration due to gravity.
• - is the absolute temperature.
• - is the Boltzmann constant.
• - is the mass of a single gas molecule.
• - is the pressure.
• - is the height.
This is known as the barometric formula, and can be derived by assuming that the pressure is hydrostatic.
If there are several types of molecules in the gas, the partial pressure of each type will be given by this equation. Under most conditions, the distribution of each gas species is independent of the other species.