Fundamentals of Transportation/Analogs

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

StructuresEdit

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

TransportationEdit

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

ElectricityEdit

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

WaterEdit

  • P = hydrostatic pressure
  • ρ = fluid density =mV = mass *volume
  • g = acceleration due to gravity
  • h = height
  • c= constant
  • A = area
Last modified on 24 July 2008, at 20:02