Chapter 18, Problem 2RQ

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.

P15.45 WP A stainless steel pipe (Figure P15.45) with an outside diameter of 2.375 in. and a wall thickness of 0.109 in. is subjected to a bending moment M = 50 lb ft and an internal pressure of 180 psi. Determine the absolute maximum shear stress on the outer surface of the pipe. M FIGURE P15.45 M

10.72 What power must the pump supply to the system to pump the oil from the lower reservoir to the upper reservoir at a rate of 0.3 m³/s? Sketch the HGL and the EGL for the system. p=940 kg/m³ v = 10-5 m²/s Elevation 100 m Elevation 112 m L= 150 m Oil Steel pipe D = 30 cm Problem 10.72

L / 83° 28° $75°E M 202° Q2: The scanning process was completed from point J to point N. The direction of the straight line was LM and the angles of deviation are shown in the figure below. Find the direction of the remaining sides? N

Q3: The scanning process was completed from point F to point G. The direction of the line Fl and the angles of deviation and interior are shown in the figure below. Find the direction of the remaining sides? Azimn = 60° F 52° 52° 72° R= 572.958/D ° T-R tan(A/2) • LC 2R sin (A/2) • E-R (sec(A/2)-1) • M-R (1-cos (A/2)) L= 10 A/D •C=2R sin(2D/2) • d=Dc/10 c' 2R sin (d/2) • Y= √√R2-X2-K • K= R2- K=R-M G H معادلات :مفيدة

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Q1/ The specific gravity of the soil is 1.41 percentage of water content by weight at field capacity and wilting point are 15% and 7% respectively calculate the equivalent moisture content as equivalent depth for 1.2m root zone : 1. at permanent wilting point 2. at field capacity 3. for ready available water