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Fluid inertia

The physical element called pure fluid inductor or pure fluid inertor models the inertia effects encountered in accelerating a fluid in a pipe or passage. An ideal fluid inductor is defined by the linear relation


where is the inductor pressure momentum, is the inductor pressure, is the inductor volume flow, and the constant parameter [] is the fluid inductance of the fluid inductor, also termed fluid inertance.

Figure 6.15: () Pipe segment. () Pure fluid inductor. () Pipe model.

To visualize the concept of fluid inductance, let us consider the unsteady frictionless flow of an incompressible fluid in a nonaccelerating pipe segment of length . If the pipe has constant area cross-section and the velocity of the fluid is uniform across any cross section of the pipe, we can say that every fluid particle has the same velocity and hence the same acceleration . Then the force necessary to produce an acceleration of the fluid mass in the pipe is

where is the pressure drop across the pipe segment. As [kg.m] denotes the mass density of the fluid, is the mass of all the fluid in the pipe segment. The volume flow , so that the fluid inductance of the flow in the pipe is

This relation holds only when the pipe is not being accelerated. If the pipe itself has an acceleration, additional pressure difference effect between the inlets of the pipe segment will have to be taken into account.

Fig. 6.15 gives our graphical symbol for the pure fluid inductor (or resistor). The pure inductor is associated with two variables: the inductor pressure drop and the conductor fluid flow . Polarities of these two variables are always related to the polarity of the symbol indicated by the + sign as indicated in Fig. 6.15. This means that the pressure at the + pole is assumed larger than that at the second pole. The inductor flow is considered positive if it is oriented from the + pole towards the inductor.

The symbol of the pure fluid inductor is utilized in Fig. 6.15 to model the pipe segment shown in fig Fig. 6.15. The nodes A and B represent energy interactions at the corresponding inlets of the real pipe segment. The gauge pressures and at the pipe inlets are denoted by empty-head arrows placed between the symbols for the reference pressure and the related nodes. Respecting the conductor orientation, the pressure drop corresponds to the conductor pressure , and the flow corresponds to the conductor flow . As the postulate of continuity applies to the pure inductor , or .

In actual fluid piping, significant friction effects are often present along with the inertance effects, and the inertance effect tends to predominate only when the rate of change of flow rate (fluid acceleration) is relatively large. Since flow resistance in a pipe decreases more rapidly with increasing pipe area than does inertance, it is easier for inertance effects to overshadow resistance effects in pipes of large sizes. However, when the rate of change of flow rate is large enough, significant inertance effects are sometimes observed even in fine capillary tubes.

Figure 6.16: () Two-tank system. () Dynamic model.
A fluid-flow system consisting of two interconnected tanks is shown in Fig. 6.16. The corresponding model respecting fluid-flow inertia is in Fig. 6.16.

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Herman Mann 2005-05-05