1. Analogy Between Engineering Systemsx
Displacement
(m)
Velocity
(m/s)
Acceleration
(m/s2) m
Mass
(kg) k
Spring Constant
(N/m) c
Damping Constant
(Ns/m) f
Force
(N) θ
Angular Dispalement
(rad)
Angular Velocity
(rad/s)
Angular Acceleration
(rad/s2) IG
Mass moment of inertia
(kg-m2) Kr
Rotational spring constant
(Nm/rad) Cr
Rotational damping constant
Nm/(rad/s) M
Moment
(Nm) q
Charge
(Coulomb)
Current
(Amper) L
Inductance
(Henry)
1/C
C:Capacitance
(Farad) R
Resistance
(Ohm) V
Voltage
(Volt) Vf
Volume
(m3) Qf
Flow Rate
(m3/s) If
Fluid Inertance
(kg/m4)
1/Cf
Cf:Fluid Capacitance Rf
Flow Resistance P
Pressure
(N/m2) Ht
Heat Energy
(Joule) Qt
Heat Flow Rate
(J/s)
1/Ct
Ct:Thermal Capacitance Rt
Thermal Resistance T
Temperature
(oC)

2. Fluid Inertance in a Pipe:Vf
Volume
(m3) Qf
Flow Rate
(m3/s) If
Fluid Inertia
(kg/m4)
1/Cf
Cf:Flow Capacitance Rf
Flow Resistance P
Pressure
(N/m2)
D.Rowell & D.N.Wormley, System Dynamics:An Introduction, Prentice Hall, 1997
Fluid Inertance in a Pipe:
If:Fluid inertia, ρ: Density (kg/m3), L: Length (m),
A: Cross section area of the pipe (m2)
Fluid Capacitance:
Cf: Fluid capacitance, At:Cross section are of the tank,
g=9.81 m/s2

3. Resistance in a Laminar flow:
Rf:Resistance, µ:Viscosity, L:Pipe length, d:Pipe diameter
Reynold’s Number=
In a laminar flow, Reynold’s Number <2000
Equivalent Electric Circuits of Flow Systems: R L C
Fluid inertia,L

4. Equivalent Electric Circuits of Flow Systems: Flow Elec. pn Vn1
pk1
Qk1 pa
Flow System: 2 3 4 Q3 A 5 Q5
Rn Rn
In Ln Qn
Cn Cn h C2 R3 L3 R4 L4 - + V4 A
Equivalent Electric Circuit: R2 L2 C1 R5 L5 - Va +
Vk1 R1 L1

5. Ct:Thermal Capacitance
ANOLOGY BETWEEN THERMAL AND ELECTRICAL SYSTEMS Ht
Heat Energy
(Joule) Qt
Heat Flow Rate
(J/s)
1/Ct
Ct:Thermal Capacitance Rt
Thermal Resistance T
Temperature
(oC)
D.Rowell & D.N.Wormley, System Dynamics:An Introduction, Prentice Hall, 1997
Thermal capacitance:
Ct=mCp Ct: Thermal Capacitance, Cp: Specific Heat, m: Mass
Thermal resistance in heat conduction:
Rt:Resistance, ρc:Thermal conductivity, A:Cross section area, L:Length

6. Q1a Ta Input Ta 1 Q1a Qk1 Q12 2 Q2a o Input 1 Qk1 Q12 2 o C1 C1 R1a
Thermal isolation 1 o
Qk1 2 Ta
Q1a
Q12
Input
(Outdoor temperature) 1 o
Qk1 2 Ta
Q1a
Q12
Input
(Outdoor temperature)
Q2a
R12
R1a C1 Va C2
R12
R1a C1 Va C2
R2a

7. Equivalent Electric Circuit
Thermal System:
Thermal Electrical Qn
Q2a
Q1a Ta
Rn Rn 2 o
Qk2 1 o
Qk1
Cn Cn
Tn Vn TB
QB2
TB is a
constant- temperature
room.
Q1B
QBa
Qk1, Qk2, TB
Inputs: VB
Equivalent Electric Circuit - + VB
RB2
RBa
R1B
R1a C1 Va
R2a C2

8. Examples:
Fluid:
Mechanical: R L C
Thermal: