Investigate the relationship between pressure, when you are standing up barefooted.

Question

Consider, M people (aka pax) who want to travel by car from O to D. They all start working at D at Q (e.g., Q=8am). If a person departs at time t, assume the time needed to go from O to D is given by c(t)=A+Bx(t), where x(t) is the flow of people departing at time t [car/unit of time]. In addition, a is the penalty for being early at work (E(t) is how early the person arrived when departing at time t), and ẞ is the penalty for being late at work (L(t) is how late the person arrived when departing at time t). Assume 0 < a < 1 < ß. Further assume the departure time choice problem under the equilibrium conditions. Prove that the arrival time of people who depart when most of the M people start their trips is equal to Q.

Answer 1

Question

Chapter 10, Problem 6P

(a)

To determine

Investigate the relationship between pressure, when you are standing up barefooted.

(b)

To determine

Investigate the relationship between pressure, when you are lying on your back.

(c)

To determine

Investigate the relationship between pressure, when you are sitting on a tall chair with your feet off the ground and the chair.

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Consider, M people (aka pax) who want to travel by car from O to D. They all start working at D at Q (e.g., Q=8am). If a person departs at time t, assume the time needed to go from O to D is given by c(t)=A+Bx(t), where x(t) is the flow of people departing at time t [car/unit of time]. In addition, a is the penalty for being early at work (E(t) is how early the person arrived when departing at time t), and ẞ is the penalty for being late at work (L(t) is how late the person arrived when departing at time t). Assume 0 < a < 1 < ß. Further assume the departure time choice problem under the equilibrium conditions. Prove that the arrival time of people who depart when most of the M people start their trips is equal to Q.

1. Plot the SWRC (suction vs. volumetric water content) from the van Genuchten (1980) model for the following “base-case” parameters (assume m = 1-1/nvG): alpha vG = 0.35 kPa-1, nvG = 2.2,Delta res = 0.02, and delta S = delta sat = 0.45. These values are approximately representative of a sand.Perform a sensitivity analysis on each of the base case parameters (i.e., vary each by ±10% while holding the other three constant) to determine their relative effects on the SWRC. For example, how would a change in s alter the curve if the other base case parameters stay the same? In your answer, provide 4 plots for the parametric evaluation of each parameter as well as a brief qualitative explanation for each plot (for example, when investigating the effect of alpha vG, show the base-case curve and the curves with different values of alpha vG on the same plot). Be sure that suction is plotted on a logarithmic scale. Also, discuss how theparameters of the van Genuchten SWRC model might differ…

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