FLUID SYSTEMS
Gases and liquids are collectively referred to as fluids. Fluid systems are used in many in- dustrial as well as commercial applications. For example, liquid level control is a well-known application of liquid systems. Similarly, gas systems are used in robotics and in industrial movement control applications.
In this section, we shall look at the models of simple liquid systems (or hydraulic systems).
2.4.1 Hydraulic Systems
The basic elements of hydraulic systems are resistance, capacitance and inertance (see Fig- ure 2.21). These elements are similar to their electrical equivalents of resistance, capacitance and inductance. Similarly, electrical current is equivalent to volume flow rate, and the potential difference in electrical circuits is similar to pressure difference in hydraulic systems.
Hydraulic resistance
Hydraulic resistance occurs whenever there is a pressure difference, such as liquid flowing from a pipe of one diameter to to one of a different diameter. If the pressures at either side of a hydraulic resistance are p1 and p2, then the hydraulic resistance R is defined as
Hydraulic capacitance
Hydraulic capacitance is a measure of the energy storage in a hydraulic system. An example of hydraulic capacitance is a tank which stores energy in the form of potential energy. Consider the tank shown in Figure 2.21(b). If q1 and q2 are the inflow and outflow, respectively, and V is the volume of the fluid inside the tank, we can write
Hydraulic inertance
Hydraulic inertance is similar to the inductance in electrical systems and is derived from the inertia force required to accelerate fluid in a pipe.
Let p1 − p2 be the pressure drop that we want to accelerate in a cross-sectional area of A, where m is the fluid mass and v is the fluid velocity. Applying Newton’s second law, we can write
Example 2.12
Figure 2.22 shows a liquid level system where liquid enters a tank at the rate of qi and leaves at the rate of qo through an orifice. Derive the mathematical model for the system, showing the relationship between the height h of the liquid and the input flow rate qi .
Example 2.13
Figure 2.24 shows a two-tank liquid level system where liquid enters the first tank at the rate of qi and then flows to the second tank at the rate of q1 through an orifice R1. Water then leaves
