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This is also called the regime of high vacuum, or even ultra-high vacuum. This is opposed to viscous flow encountered at higher pressures. [1] The presence of free molecular flow can be calculated, at least in estimation, with the Knudsen number (Kn). [2] If Kn > 10, the system is in free molecular flow, [3] also known as Knudsen flow. [4]
The equation to calculate the pressure inside a fluid in equilibrium is: + = where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:
If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved.
The pressure force pushing the liquid through the tube is the change in pressure multiplied by the area: F = −A Δp. This force is in the direction of the motion of the liquid. The negative sign comes from the conventional way we define Δp = p end − p top < 0. Viscosity effects will pull from the faster lamina immediately closer to the ...
Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant. Therefore, when the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved.
In 1934, Georges Lemaître used an unusual perfect-fluid equation of state to interpret the cosmological constant as due to vacuum energy. In 1948, the Casimir effect provided an experimental method for a verification of the existence of vacuum energy; in 1955, however, Evgeny Lifshitz offered a different origin for the Casimir effect.
This difference in pressure causes the upward buoyancy force. The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known. The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is in contact with the fluid:
When the pressure in one part of a physical system is reduced relative to another, the fluid or gas in the higher pressure region will exert a force relative to the region of lowered pressure, referred to as pressure-gradient force. If all gas or fluid is removed the result is a perfect vacuum in which the pressure is zero.