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6 Hierarchical Component Models
Fig. 6.3 Main elements of the hydraulic system
rate in the system, and the potential difference in the electrical circuits is similar to
the pressure difference in hydraulic systems.
Hydraulic capacity is a measure of energy conservation in a hydraulic system. An
example of a hydraulic reservoir is a reservoir in which potential energy is stored.
Consider the tank shown in Fig. 6.3b. If q 1 and q 2 are the inflowing and outflowing
flows, respectively, and V is the volume of fluid inside the reservoir, then we can
write the differential equation
q 1 − q 2 =
dV
dt
= A
dh
dt
Here, A is the area of the base of the tank, and h is the height of the liquid column
in the tank. The pressure difference at the upper and lower levels of the tank is
determined by the expression:
p = P 1 − P 2 = hρg
where the expression for the height of the liquid level is given by:
h =
p
ρg
Substituting the expression for the height in the differential equation, we finally
obtain:
q 1 − q 2 =
A
ρg
d p
dt
= C
d p
dt
where C =
A
ρg
is the hydraulic capacity.
Modeling and computational Experiment 2
Let us go back to the original differential equation and rewrite it as:
dh
dt
=
q 1 − q 2
A