0195136047.pdf

1.5 ANALOGY BETWEEN ELECTRICAL AND OTHER NONELECTRICPHYSICAL SYSTEMS 51

TABLE 1.5.1Mechanical-Electrical Analogs

Mathematical Force–Current Force–Voltage

Quantity Unit Symbol Relation Analog Analog

Force N f(t) ··· i(t) v(t)

Velocity m/s u(t) ··· v(t) i(t)

Mass kg f=Mdudt CL

(Newton’s law)

f

B

Cm =

M

f

u

1

K

u

u

f

Compliance m/N f=C^1 m

∫

udt L C

(=1/stiffness) (Hooke’s law)

Viscous friction N·s/m f=Bu G= 1 /R R

or damping

Pipe

Water

tank h

Flow out Fo

Flow in Fi

Figure 1.5.1Simple hydraulic system.

TABLE 1.5.2Analogy Between Electrical and Hydraulic Systems

Quantity Hydraulic System Electrical System

Flow Output flow rateFo Currenti

Potential Fluid levelh Voltagev

Resistance Fluid resistanceR Electrical resistanceR

Energy storage element Fluid storage parameterA CapacitanceC

Volume of fluid (or charge) V=Ah q=Cv

Next, let us consider heat flow from an enclosure with a heating system to the outside of

the enclosure, depending upon the temperature differenceTbetween the inside and outside of

the enclosure. The heat capacity of the enclosure is analogous to capacitance, in the sense that

the enclosure retains part of the heat produced by the heating system. One can then infer the

analogy between electrical and thermal systems given in Table 1.5.3.

The heat flow, per Newton’s law of cooling in a very simplified form, can be considered to be

proportional to the rate of change of temperature with respect to distance. An approximate linear

relationship between heat flow and change in temperature can be expressed as