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 V^{2}+ 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 | edit source]
- F= force
- m = Mass
- a = acceleration
- T = Time
Transportation[edit | edit source]
- q = flow
- k = density
- v = velocity
Electricity[edit | edit source]
- V= Voltage
- I = Current
- R = Resistance
- G = Conductance = 1 / Resistance
Water[edit | edit source]
- P = hydrostatic pressure
- ρ = fluid density =mV = mass *volume
- g = acceleration due to gravity
- h = height
- c= constant
- A = area