Fundamentals of Transportation/Analogs

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Transportation networks have analogs with network processes in other systems, such as water networks, structures, and electrical networks. Some of the relationships are outlined below.


' Transportation Water: Hydrostatics Structures Electrical
Node Conservation Law Flow (q) Current (Kirchoff’s Current Law)
Fundamental Law q = kv P = ρgh F=δ (mv)/ δ (T) V=IR
k = q/v F= v δ (m)/ δ (T) V=I/G
v=q/k Bernoulli’s Equation: Ohm’s Law on resistor
Constant=p+1/2ρ V2+ ρgh
P=F/A (area)
F=ma
Analogs flow (q) Pressure (P*A) δm/δT Current (I)
density (k) Density (ρ) Force (F) Voltage (V)
velocity (v) velocity (v) velocity Conductance (G)
Equilibrium Conditions Wardrop (time equal on used pairs in parallel) Sum of horizontal (and sum of vertical) forces on a structure = 0, sum of moments = 0. Voltage drop across two components in parallel are equal

Structures[edit]

  • F= force
  • m = Mass
  • a = acceleration
  • T = Time

Transportation[edit]

  • q = flow
  • k = density
  • v = velocity

Electricity[edit]

  • V= Voltage
  • I = Current
  • R = Resistance
  • G = Conductance = 1 / Resistance

Water[edit]

  • P = hydrostatic pressure
  • ρ = fluid density =mV = mass *volume
  • g = acceleration due to gravity
  • h = height
  • c= constant
  • A = area