Concept explainers
The Lotka-Volterra equations described in Sec. 28.2 have been refined to include additional factors that impact predator-prey dynamics. For example, over and above predation, prey population can be limited by other factors such as space. Space limitation can be incorporated into the model as a carrying capacity (recall the logistic model described in Prob. 28.16) as in
where
(a) Employ a very large value of
(b) Compare (a) with the more realistic carrying capacity of
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Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- A generic property is being transported through a fluid of constant cross-sectional area at steady-state. The concentration of the property, T, at point 1, is 0.015 / unit volume. The concentration of the property, I, at point 2 is 0.0075 / unit volume. Points 1 and 2 are 2 m apart. The constituitive property, 8, however, is not constant.... Rather it is a function of T according to: 8 = 0.15 + 1.65 I a.) Derive an integrated form of the equation for steady-state flux, yarrow_forward1. In the test-firing of a missile, there are some events that are known to cause the missile to fail to reach its target. These events are listed below, together with their approximate probabilities of occurrence during a flight: Event Probability (A1) Cloud reflection (A2) Precipitation (A3) Target evasion (A4) Electronic countermeasure 0.0001 0.005 0.002 0.04 The probabilities of failure if these events occur are: F F G) = 0.3; P| G) = 0.01; P | 이-)= 0.005; P = 0.0002 Use Bayes' theorem (Eq. 2.10) to calculate the probability of each of these events being the cause in the event of a missile failing to reach its target. Bayes' theorem: P(B|A) * P(A) P(A|B) = P(B)arrow_forwardWe are using simple exponential smoothing to predictmonthly electric shaver sales at Hook’s Drug Store. At theend of October 2006, our forecast for December 2006 saleswas 40. In November 50 shavers were sold, and duringDecember 45 shavers were sold. Suppose a 0.50. At theend of December, 2006, what is our prediction for the totalnumber of shavers that will be sold during March and Aprilof 2007?arrow_forward
- Cars arrive at a service station according to Poisson's distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 min. At steady state, the average waiting time in the queue is (a) 10 min (b) 20 min (c) 25 min (d) 50 minarrow_forward1. The observed and model simulated average daily flow in month flow at the outlet of a river catchment during a given period is presented as follows. Predicted flow Observed flow 0.25 0.30 0.70 0.73 0.80 0.87 0.71 0.90 0.71 0.65 1.60 1.45 0.90 0.70 0.71 0.61 0.24 0.22 1.00 0.64 0.81 1.00 1.05 0.90 0.46 0.48 0.27 0.23 0.80 0.24 0.32 0.42 0.80 0.89 (i) Evaluate the model performance based on any two computed statistical measures of performance of your choice. (ii) Explain possible reasons for model performance observed in (i) above. (Hint: Refer to reading material provided on model evaluation by Moriasi et al., 2007)arrow_forwardQ1/ Three reactors linked by pipes. As indicated, the rate of transfer of chemicals through each pipe is equal to a flow rate (Q, m³/s) multiplied by the concentration of the reactor from which the flow originates (C, mg/m³). In steady state, develop mass balance equations for the reactors, and solve the three simultaneous linear algebraic equations for their concentrations by Gauss-elimination method with partial pivoting. 400 mg/s 221%2 Q1301 1241 2 Q23c₂ 3 licz 200 mg/s 233 = 120 13 = 40 12 = 80 23 = 60 21 = 20arrow_forward
- An object is shot upward from the ground with an initial velocity of 640 ft/sec, and experiencés a constant deceleration of 32 ft/sec² due to gravity as well as a deceleration of (v(t) / 10) ft/sec due to air resistance, where v(t) is the object's velocity in ft/sec. (a) Set up and solve an initial-value problem to determine the object's velocity v(t) at time t. (b) At what time does the object reach its highest point?arrow_forwardis a mass hanging by a spring under the influence of gravity. The force due to gravity, Fg, is acting in the negative-y direction. The dynamic variable is y. On the left, the system is shown without spring deflection. On the right, at the beginning of an experiment, the mass is pushed upward (positive-y direction) by an amount y₁. The gravitational constant g, is 9.81 m/s². No Deflection m k Fg = mg Initial Condition m k Fg = mg Figure 3: System schematic for Problem 4. Yi 8 Your tasks: A Write down, in terms of the variables given, the total potential energy stored in the system when it is held in the initial condition, relative to the system with no deflection. B Write down an expression for the total energy H as the sum of potential and kinetic energy in terms of y, y, yi and element parameters. Will H change as the mass moves? C After the system is released, it will start to move. Write down an expression for the kinetic energy of the system, T, in terms of position, y, the initial…arrow_forward2. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT C3Q(t)- a(T – T) dt %3D | where T is the slab temperature in °R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/ºR, Ts = 530°R and a = 5x10-8 Btu/h-°R*. %3D %3D %3D (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.arrow_forward
- yo 9:1V i %A LO äbä 20 A ladder 13 ft long is leaning against a wall. The bottom of the ladder is being pulled away from the wall at the constant rate of 6 ft/min. How fast is the top of the ladder moving down the wall when the bottom of the * ?ladder is5 ft from the wall 13 y 6 ft/min 2.5 3.5arrow_forward4. Referring to the property table below for saturated liquid, using linear interpolation to determine the following values: a. Pat T = 94°C b. U at P = 0.4285 bar C. vat U= 315.67 kJ/kg Internal Energy, Specific Volume, v x 10 (m*/kg) U ("C) (bar) (kJ/kg) 0.3858 1.0259 313.90 75 80 0.4739 1.0291 334.86 85 0.5783 1.0325 355.84 90 0.7014 1.0360 376.85 95 0.8455 1.0397 397.88 100 1.014 1.0435 418.94arrow_forwardQ.5. Power (P) of an internal combustion engine can be calculated via formula given below: 2nNT %3D 60 Whereas; T and N is engine torque and engine speed, respectively. For T and N the values below were obtained during measurements: T=250 5 Nm N=2000 21 rpm Make error analysis with commonsense basisarrow_forward
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