Concept explainers
The following ODEs have been proposed as a model of an epidemic:
where
(a) If a single infectious individual enters the city at
(b) Suppose that after recovery, there is a loss of immunity that causes recovered individuals to become susceptible. This reinfection mechanism can be computed as rR, where r 5 the reinfection rate. Modify the model to include this mechanism and repeat the computations in (a) using
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Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The stress profile shown below is applied to six different biological materials: Log Time (s] The mechanical behavior of each of the materials can be modeled as a Voigt body. In response to o,= 20 Pa applied to each of the six materials, the following responses are obtained: 2 of Maferial 6 Material 5 0.12 0.10 Material 4 0.08 Material 3 0.06 0.04 Material 2 0.02 Material 1 (a) Which of the materials has the highest Young's Modulus (E)? Why? Log Time (s) (b) Using strain value of 0.06, estimate the coefficient of viscosity (n) for Material 6. Stress (kPa) Strainarrow_forward۳۸% ۱۰:۲۱ ص docs.google.com/forms 10 نقاط Resolve the 300 N into two components at the u and v axis 300N 20 70° Fu = 109.1 N, Fv= 244.5 N O Fu = 300.2 N, Fv= 217.5 N O Fu = 154.1 N, Fv= 219.3 N O Fu = 203.2 N, Fv= 267.7 N Oarrow_forwardQ8): To find how much heat is required to bring a kettle of water to its boiling point, you are asked to calculate the specific heat of water at 61°C. The specific heat of water is given as a function of time in Table below. Temperature, T Specific heat, C₂ (°C) J kg-°C 22 42 52 82 100 4181 4179 4186 4199 4217 Determine the value of the specific heat at 7=61°C using the direct T method of interpolation and a third order polynomial. Find the absolute relative approximate error for the third order polynomial approximation (Lagrange Method).arrow_forward
- The following diagram illustrates measurements that 145.0 L 0 d. Q Joom ма 8-42.00 で how equal to I'm in Thermal conductivity. materi di L M Heat Flow ? b. 3.24 kW N 0 d २ R I. thermal Resistance 17 a. 0.80 KW b. none OF c. 9.25 KIKW d. 1.08 e. K| kw 0.68 44.12 KW 37.5 KW M R 1.0m the above d mall a. decrease b. unchanged c. increase the walls side is exposed to temperatures of 5000 upper while its lower siche is exposed to unidirectional heat flow in Assume steady state, radiation and Convectim heat effects. 20°C. y direction Neglect none of IF antract reere tance heat N S 1.0m op the above a row of bricks, an taking thicknees Bricks k (kw/m-k) Flow? 0.50 0.25 0-50 0-80 0.4⁰ 0.50 0.25 0.50 • not neglighe, what happen to overall d. inereact then decrease e increase / decrease depending on value of Contact resistancearrow_forwardYou are the mechanical engineer supervising the layout of a piping system. In a certain portion of the pipe, the specifications are as follows: length of pipe is 10m, inside diameter of 30cm, outside diameter of 30.5cm, maximum allowable speed of 15m/s and a coefficient of 0.003456. If the uncertainties are 0.02mm for length, 0.8mm for the diameters and 0.1mm/s for the velocity, what loss of head will be imminent in this pipe? In the piping system above, what is the uncertainty in computed head loss contributed by the velocity of the pipe?arrow_forwardYou are the mechanical engineer supervising the layout of a piping system. In a certain portion of the pipe, the specifications are as follows: length of pipe is 10m, inside diameter of 30cm, outside diameter of 30.5cm, maximum allowable speed of 15m/s and a coefficient of 0.003456. If the uncertainties are 0.02mm for length, 0.8mm for the diameters and 0.1mm/s for the velocity, what loss of head will be imminent in this pipe? With all the above uncertainties, what is the total uncertainty in the head loss?arrow_forward
- A closed thermodynamic system consists of a fixed amount of substance (i.e. mass) in which no substance can flow across the boundary, but energy can. For a closed themodynamic system we cannot add energy to the system, via substance (E ) (1.e. matter which contains energy is not allowed across the boundary) Across the Boundaries E° = No Q = = Yes W mass NO CLOSED = Yes SY STEM m = constant | energy YES Figure 1.1. If the substance inside the thermodynamic system shown in figure 1.1. (i.e. piston cylinder device) is air, is the system a Fixed closed system Moveable closed system A. В.arrow_forwardYou are the mechanical engineer supervising the layout of a piping system. In a certain portion of the pipe, the specifications are as follows: length of pipe is 10m, inside diameter of 30cm, outside diameter of 30.5cm, maximum allowable speed of 15m/s and a coefficient of 0.003456. If the uncertainties are 0.02mm for length, 0.8mm for the diameters and 0.1mm/s for the velocity, what loss of head will be imminent in this pipe?arrow_forwardGive True or False for the following: 1.In liquids and gases, heat transmission is caused by conduction and convection 2.The surface geometry is the important factor in convection heat transfer 3. The heat transfer by conduction from heated surface to the adjacent layer of fluid, 4. The heat transfer is increased in the fin when &> 1 5.The unit of the thermal diffusivity is m²/s 6. Temperature change between the materials interfaces is attributed to the thermal contact resistance 7. A material that has a low heat capacity will have a large thermal diffusivity. 8. Heat conduction flowing from one side to other depends directly on thickness 9.Fin efficiency is the ratio of the fin heat dissipation with that of no fin 10.The critical radius is represented the ratio of the convicted heat transfer to the thermal conductivityarrow_forward
- 100 80 60 40 20 0.002 0.004 0.006 0.008 0.01 0.012 Strain, in/in. FIGURE P1.17 1.18 Use Problem 1.17 to graphically determine the following: a. Modulus of resilience b. Toughness Hint: The toughness (u) can be determined by calculating the area under the stress-strain curve u = de where & is the strain at fracture. The preceding integral can be approxi- mated numerically by using a trapezoidal integration technique: u, = Eu, = o, + o e, - 6) %3D c. If the specimen is loaded to 40 ksi only and the lateral strain was found to be -0.00057 in./in., what is Poisson's ratio of this metal? d. If the specimen is loaded to 70 ksi only and then unloaded, what is the permanent strain? Stress, ksiarrow_forwardTwo kinds of bacteria are found in a sample of tainted food. It is found that the population size of type 1, N1 and of type 2, N2 satisfy the equation dN/dt=-0.1/N1 dN/dt30.7/N2 N1 is equal to 1000 at time equal to zero, while N2 is equal to 30 at time equal to zero. Then the population sizes are equal N1 = N2 at what time? (4 decimal places)arrow_forwardStudent A B D H Number 201780130 2 1 7 8 1 3 Evaluate the following variables and use them as given in the following problems. 200 if I is even, 250 if I is odd (D + G)*10 (H + I/2, if in case the result is zero, use 3 (A +C + E)*2 (P + M)*20 H + 5 M Q %3D 50(E + G + 1) II II || || || |||| ZNPORXarrow_forward
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