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In fluid mechanics, inertance is a measure of the pressure difference in a fluid required to cause a unit change in the rate of change of volumetric flow-rate with time. The base SI units of inertance are kg m −4 or Pa s 2 m −3 and the usual symbol is I.
Δp is the pressure difference between the two ends, L is the length of pipe, μ is the dynamic viscosity, Q is the volumetric flow rate, R is the pipe radius, A is the cross-sectional area of pipe. The equation does not hold close to the pipe entrance. [8]: 3 The equation fails in the limit of low viscosity, wide and/or short pipe.
A relatively simple version [1] of the vertical fluid pressure variation is simply that the pressure difference between two elevations is the product of elevation change, gravity, and density. The equation is as follows: =, where P is pressure, ρ is density, g is acceleration of gravity, and; h is height.
p is the pressure; V is the volume; n is the amount of substance of gas (moles) R is the gas constant, 8.314 J·K −1 mol −1; T is the absolute temperature; To simplify, a volume of gas may be expressed as the volume it would have in standard conditions for temperature and pressure, which are 0 °C (32 °F) and 100 kPa. [2]
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
A pressure prism is a way of visually describing the variation of hydrostatic pressure within a volume of fluid. When variables of fluid density , depth, gravity , and other forces such as atmospheric pressure are charted, the resulting figure somewhat resembles a prism .
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.
This pressure difference arises from a change in fluid velocity that produces velocity head, which is a term of the Bernoulli equation that is zero when there is no bulk motion of the fluid. In the picture on the right, the pressure differential is entirely due to the change in velocity head of the fluid, but it can be measured as a pressure ...