This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Assignment 1 ( SCI 3510 Mathematical and Statistical Modelling ) (1) Prove the equation of state for variable velocity u ( x, t ) and density ρ ( x, t ). (2) Suppose that the velocity u ( x, t ) is selected as the prime variable. Find the relation between flux q ( x, t ) and velocity u ( x, t ) for Greenshields model. Then prove the identity: U max parenleftbigg ρ ρ 2 ρ max parenrightbigg = ρ max parenleftbigg u u 2 U max parenrightbigg , (3) It is officially suggested by the Transportation Department of US to keep three carlength apart from the front car for a safety drive. Show that the maximum flux reaches 3 4 q max for Greenshields model, if the principle of three carlength is obeyed. (4) Suppose the velocitydensity relation is modelled as u ( ρ ) = U max parenleftbigg 1 ρ 2 ρ 2 max parenrightbigg , Give a brief discussion with comparison to Greenshields model ( 300 words limited )....
View
Full
Document
This note was uploaded on 01/19/2012 for the course ECON 201 taught by Professor Wong during the Spring '11 term at CUHK.
 Spring '11
 wong

Click to edit the document details