### Author Topic: derivation of a PDE describing traffic flow  (Read 1838 times)

#### Shaghayegh A

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##### derivation of a PDE describing traffic flow
« on: September 25, 2016, 03:41:49 PM »
In example 8 of chapter 2.1 where we derive a PDE describing traffic flow, how do we derive $Ï_t+vÏ_x=0\;(6)$ from $p_t+q_x=0\;(3)\;?$

It seems that $q_x$ some how equals $vp_x=[c(\rho)+ c' (\rho)\rho] \;p_x=c(p) \frac{\partial p}{\partial x}+\frac{d c(p)}{p} p \frac{\partial p}{\partial x}$? Can someone please explain how we get equation (6)? Thanks

#### Victor Ivrii

You plug $q= q(\rho)$ into $\rho_t + q_x=0$