incompressible

Examples of incompressible in the following topics:

• Variation of Pressure With Depth

  • Note that the following discussion and expressions pertain only to incompressible fluids at static equilibrium.
  • The pressure exerted by a static liquid depends only on the depth, density of the liquid, and the acceleration due to gravity. gives the expression for pressure as a function of depth within an incompressible, static liquid as well as the derivation of this equation from the definition of pressure as a measure of energy per unit volume (ρ is the density of the gas, g is the acceleration due to gravity, and h is the depth within the liquid).
  • Equation 3 assumes that the gas is incompressible and that the pressure is hydrostatic.
  • This equation gives the expression for pressure as a function of depth within an incompressible, static liquid as well as the derivation of this equation from the definition of pressure as a measure of energy per unit volume (ρ is the density of the gas, g is the acceleration due to gravity, and h is the depth within the liquid).

• Torricelli's Law

  • This relationship applies for an "ideal" fluid (inviscid and incompressible) and results from an exchange of potential energy,

• Poiseuille's Equation and Viscosity

  • Laminar flow is often encountered in common hydraulic systems, such as where fluid flow is through an enclosed, rigid pipe; the fluid is incompressible, has constant viscosity, and the Reynolds number is below this lower critical threshold value.
  • Considering laminar flow of a constant density, incompressible fluid such as for a Newtonian fluid traveling in a pipe, with a Reynolds number below the upper limit level for fully laminar flow, the pressure difference between two points along the pipe can be found from the volumetric flow rate, or vice versa.
  • This equation is valid for laminar flow of incompressible fluids only, and may be used to determine a number of properties in the hydraulic system, if the others are known or can be measured.

• Gravity Waves and Rayleigh-Taylor Instability

  • Let's assume that both fluids are incompressible and the flow is irrotational, so we can define
  • Because the fluids are assumed to be incompressible, we have $\nabla^2 \phi=0$ and the boundary condition gives $\partial \phi/\partial z=0$ at $\phi$ and similarly for lower fluid, so we have

• Flow Rate and the Equation of Continuity

  • The equation of continuity applies to any incompressible fluid.

• Application of Bernoulli's Equation: Pressure and Speed

  • Bernoulli's equation states that for an incompressible and inviscid fluid, the total mechanical energy of the fluid is constant .

• Van der Waals Equation

  • It correctly predicts a mostly incompressible liquid phase, but the oscillations in the phase transition zone do not fit experimental data.

• Pascal's Principle

  • As, by Pascal's Law, a change in pressure is linearly proportional to a change in height within an incompressible, static liquid of constant density, doubling the height between the two points of reference will double the change of pressure, while halving the height between the two points will half the change in pressure.

• B.12 Chapter 12

  • For the classical result with an incompressible fluid we have $w=P/\rho$.