Chapter 1.6 - Physical Systems Driven by the Flow Variable

Vocabulary flashcards covering key concepts from Chapter 1.6 notes on flow-variable driven storage systems, duality, transfer functions, impulse/step responses, and lossless vs lossy first-order dynamics.

Potential variable (voltage)

A quantity that drives current but does not itself flow; voltage is a potential variable.

Flow variable (current)

A quantity that measures how much of a substance flows per unit time; current is the flow variable.

Duality (inductor–capacitor)

Inductor and capacitor are symmetric: what the inductor does to current, the capacitor does to voltage.

Inductance (L)

Φm = L I; inductance relates magnetic flux to current in a coil.

Capacitance (C)

Q = C V; capacitance relates electric charge to voltage on capacitor plates.

Inductor voltage relation

V_L = L (di/dt); voltage across an inductor is proportional to the rate of change of current.

Capacitor current relation

i_C = C (dV/dt); current through a capacitor is proportional to the rate of change of voltage.

Energy in an inductor

E_L = (1/2) L I^2; energy stored in an inductor depends on current.

Energy in a capacitor

E_C = (1/2) C V^2; energy stored in a capacitor depends on voltage.

Series/Parallel rules (L and C)

Inductors in series add: Leq = ΣLi; capacitors in parallel add: Ceq = ΣCi.

Flow-source drive concept

Driving a circuit with a flow variable uses a current source (e.g., pumping fluid into a tank).

Gas-tank analogy

Modeling a tank-fill system with fluid head ΔH; transfer function relates flow to height; depends on ρ, A, g.

Transfer function

Ratio of output to input in the frequency domain; for first-order systems it has a first-order s-polynomial in the denominator.

Unit impulse input

I(s) = 1 for a unit impulse; used to obtain the impulse response of a system.

Unit impulse response (h(t))

Time-domain response to a unit impulse; for a passive first-order system it decays exponentially.

Natural frequency

ω_n; the system’s inherent frequency of response, related to the pole of the transfer function.

Time constant

τ; the reciprocal relation to the natural frequency (e.g., τ ≈ 1/ω_n; for RC, τ = RC).

Pole

Root of the denominator of the transfer function; determines natural frequency and stability characteristics.

Lossless vs lossy first-order systems

Lossless: constant or ramp response; lossy: exponentially decaying response.

Poiseuille’s law

Linear approximation for flow through a conduit as a function of pressure difference; used to model leaks.

Bernoulli’s equation

Nonlinear relation for fluid flow; often avoided in linear models due to nonlinearities.

Head and flow variables (gΔH and f)

Head: change in fluid height; f: volumetric flow; multiplying by g relates to power in hydraulic systems.

gΔH

Head scaled by gravity; used as a potential variable for fluid height in hydraulic/energy contexts.