1. Consider a hydraulic system with a feedback loop shown in Fig. 1. The hydraulic system has a
first pump with prescribed pressure Psi (t) on the left and a second pump with prescribed flow
rate Qs2(t) on the right. The first pump drives the fluid into a first tank with capacitance C1,
a first long pipe with inertance /1 and resistance Ri, and a second long pipe with inertance
12 and resistance R2. The first pump drives the fluid into a second tank with capacitance C2,
an elbow with resistance R3, and a pressure relief valve with resistance R4. Moreover, the
first long pipe connects with the second tank. The second long pipe connects the elbow via
a third tank with capacitance C3 to form the feedback loop. The hydraulic system has three
nodes A, B, and C right at each tank. Answer the following questions.
B
P (t)
I , R
es? (t )
?
RA
C3
RA
On (t )
I, , R,
C
R3
Figure 1: A hydraulic system
Figure 2: An incomplete linear
with a feedback loop
graph of the system in
Fig. 1
(a) Figure 2 shows an incomplete linear graph of the hydraulic system illustrated in Fig. 1.
Complete Fig. 2.
(b) The pressure pp at node B is 1.3 atm and the pressure drop of the elbow from node B
to node C is pra is 0.1 atm. What is the pressure at the bottom of the third tank with
capacitance C3?
(c) The flow rate into the first tank is 3 m3/s. The flow rate into the first long pipe (i.e.,
from node A to node B) is 2 m3/s. The flow rate back through the second long pipe
(i.e., from node B back to node A) is 4 m3/s. What is the flow rate through the first
pump with prescribed pressure Psi?
(d) If the flow rate into the first pipe is Q1, = 2 coswt, where w is a driving frequency, what
is the pressure drop induced by the inertance of the fluid in the first pipe?
(e) A plant manager wants to estimate the fluid height h3 in the third tank, but the manager
cannot see the actual height. Engineer A proposes to measure the pressure pos at the
bottom of the third tank and use pc; to estimate 3. Engineer B proposes to measure
the flow rate QR3 through the elbow and use QR; to estimate h3. Who is right and why?