or

where is the inductor pressure momentum, is the inductor pressure, is the inductor volume flow, and the constant parameter [Pa.sm] is the

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

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.

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.