EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 28, Problem 22P
Population-growth dynamics are important in a variety of planning studies for areas such as transportation and water-resource engineering. One of the simplest models of such growth incorporates the assumption that the rate of change of the population p is proportional to the existing population at any time t:
where
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
HW4
EX1:
An automobile moving over a rough road (Fig. 1.64) can be modeled considering
(a) weight of the car body, passengers, seats, front wheels, and rear wheels; (b) elasticity of
tires (suspension), main springs, and seats; and (c) damping of the seats, shock absorbers,
and tires. Develop three mathematical models of the system using a gradual refinement in the
modeling process.
FIGURE 1.64 An automobile moving on a
rough road.
EX2
1.5* The consequences of a head-on collision of two automobiles can be studied by considering
the impact of the automobile on a barrier, as shown in Fig. 1.65. Construct a mathematical
model by considering the masses of the automobile body, engine, transmission, and suspen-
sion and the elasticity of the bumpers, radiator, sheet metal body, driveline, and engine
mounts.
FIGURE 1.65 An automobile colliding with a barrier.
Drag and Drop the correct answers in the blanks.
A mass mis hanging from the end of a vertical spring that has a
spring constant k. The equilibrium position of the mass, yo, is
The total potential energy of the mass when it
is displaced by s from the equilibrium position is given by
Y.
is zero
+ U(s) = ks
+ positive
* negative
1
1
ks+
21
+ U(s)
ks² +
mgyo
%3D
U(s)
mgyo
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.
Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 28 - 8.1 Perform the first computation in Sec. 28.1,...Ch. 28 - 28.2 Perform the second computation in Sec. 28.1,...Ch. 28 - A mass balance for a chemical in a completely...Ch. 28 - 28.4 If, calculate the outflow concentration of a...Ch. 28 - 28.5 Seawater with a concentration of 8000 g/m3...Ch. 28 - 28.6 A spherical ice cube (an “ice sphere”) that...Ch. 28 - The following equations define the concentrations...Ch. 28 - 28.8 Compound A diffuses through a 4-cm-long tube...Ch. 28 - In the investigation of a homicide or accidental...Ch. 28 - The reaction AB takes place in two reactors in...
Ch. 28 - An on is other malbatchre actor can be described...Ch. 28 - The following system is a classic example of stiff...Ch. 28 - 28.13 A biofilm with a thickness grows on the...Ch. 28 - 28.14 The following differential equation...Ch. 28 - Prob. 15PCh. 28 - 28.16 Bacteria growing in a batch reactor utilize...Ch. 28 - 28.17 Perform the same computation for the...Ch. 28 - Perform the same computation for the Lorenz...Ch. 28 - The following equation can be used to model the...Ch. 28 - Perform the same computation as in Prob. 28.19,...Ch. 28 - 28.21 An environmental engineer is interested in...Ch. 28 - 28.22 Population-growth dynamics are important in...Ch. 28 - 28.23 Although the model in Prob. 28.22 works...Ch. 28 - 28.25 A cable is hanging from two supports at A...Ch. 28 - 28.26 The basic differential equation of the...Ch. 28 - 28.27 The basic differential equation of the...Ch. 28 - A pond drains through a pipe, as shown in Fig....Ch. 28 - 28.29 Engineers and scientists use mass-spring...Ch. 28 - Under a number of simplifying assumptions, the...Ch. 28 - 28.31 In Prob. 28.30, a linearized groundwater...Ch. 28 - The Lotka-Volterra equations described in Sec....Ch. 28 - The growth of floating, unicellular algae below a...Ch. 28 - 28.34 The following ODEs have been proposed as a...Ch. 28 - 28.35 Perform the same computation as in the first...Ch. 28 - Solve the ODE in the first part of Sec. 8.3 from...Ch. 28 - 28.37 For a simple RL circuit, Kirchhoff’s voltage...Ch. 28 - In contrast to Prob. 28.37, real resistors may not...Ch. 28 - 28.39 Develop an eigenvalue problem for an LC...Ch. 28 - 28.40 Just as Fourier’s law and the heat balance...Ch. 28 - 28.41 Perform the same computation as in Sec....Ch. 28 - 28.42 The rate of cooling of a body can be...Ch. 28 - The rate of heat flow (conduction) between two...Ch. 28 - Repeat the falling parachutist problem (Example...Ch. 28 - 28.45 Suppose that, after falling for 13 s, the...Ch. 28 - 28.46 The following ordinary differential equation...Ch. 28 - 28.47 A forced damped spring-mass system (Fig....Ch. 28 - 28.48 The temperature distribution in a tapered...Ch. 28 - 28.49 The dynamics of a forced spring-mass-damper...Ch. 28 - The differential equation for the velocity of a...Ch. 28 - 28.51 Two masses are attached to a wall by linear...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
(a) Show that (x) = x2 is an explicit solution to xdydx = 2y on the interval (, ). (b) Show that (x) = ex x is...
Fundamentals of Differential Equations (9th Edition)
Analytic Functions. Find fz=ux,y+ivx,y with u or v as given. Check by the Cauchy Reimann equations for analyti...
Advanced Engineering Mathematics
|4.2| = ?
Basic Technical Mathematics
Is there a relationship between wine consumption and deaths from heart disease? The table gives data from 19 de...
College Algebra Essentials (5th Edition)
The equation of the line y=1.2x−4.2 in rectangular coordinate system.
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- The following table lists temperatures and specific volumes of water vapor at two pressures: p = 1.0 MPa p = 1.5 MPa T (°C) v(m³/kg) T (°C) v(m³/kg) 200 0.2060 200 0.1325 0.1483 0.1627 0.2275 240 280 240 280 0.2480 Data encountered in solving problems often do not fall exactly on the grid of values provided by property tables, and linear interpolation between adjacent table entries becomes necessary. Using the data provided here, estimate i. the specific volume at T = 240 °C, p = 1.25 MPa, in m³/kg the temperature at p = 1.5 MPa, v = 0.1555 m³/kg, in °C the specific volume at T = 220 °C, p = 1.4 MPa, in m³/kg ii. iii. 11.arrow_forwardQ: The flow through bridge opening is a function of hydraulic properties, fluid characteristics and channel geometries as follows: fi(ht, ho, B, Va, ha,hu, p,H,g) = 0 Where h, is the bridge deck thickness, h, is the bridge deck height, B is the bridge opening, Va is the downstream velocity, ha is the downstream water level, hu is the upstream water level, p is the mass density, u is the water dynamic viscosity and g is the gravitational acceleration. Use Buckingham n theorem to express the dimensionless terms through the abovementioned variables.arrow_forwardGiven: Consider an adiabatic steam turbine operating at steady-flow conditions. The known operating conditions are: Inlet conditions Exit (outlet) conditions Pressure (MPa) Temperature (°C) Velocity (m/s) Steam quality Mass flow rate (kg/s) Elevation (height) (m) 10 450 0.010 80.01 50.01 91.9 % 12.01 9.0 9.0 Required: Draw clear and consistent schematic for the problem representing the inlet and exit (outlet) conditions and label your schematic with the given conditions. Analyze the problem systematically using step-by-step CV energy and mass analyses, justify the equations, state your assumptions, and determine the following (circle your final answers): (a) The specific enthalpy values at inlet and exit of the turbine. (b) The mass flow rate of steam at exit. (c) The specific heat transfer. (d) The rate of change in the kinetic energy of the steam between inlet and exit. (e) The power output generated by the turbine. (f) The specific work output. (g) The specific volumes at inlet and…arrow_forward
- You have two toys with two different shapes; one is shaped like a solid cylinder and the other like a solid sphere. The two toys have the same volume (V(cylinder) = V(sphere)) and same radius (R(cylinder)=R(sphere)). They both generate the same total heat (q(cylinder)=q(sphere)) and are made from the same material (k(cylinder)=k(sphere)). a) Determine whether the sphere toy or the cylinder toy has the higher heat flux anywhere in the toy b) Calculate the ratio of the maximum heat fluxes between them Hint: Assume the ends of the cylinder toy to be perfectly insulated.arrow_forwardA system consisting of a power cycle and a heat pump cycle, each operating between hot and cold reservoirs whose temperature are 500 K and 300 K, respectively. All energy transfers are positive in the directions of the arrows. The accompanying table provides two sets of steady-state data, in kW. For each set of data, determine if the system is operating in accord with the first and second laws of thermodynamics. Power cycle QHQc W cycle (a) 60 40 20 (b) 120 80 40 Heat pump cycle QHQ'cW'cycle 60 20 80 20 80 100 Power cycle- Hot reservoir, TH= 500 K O'H J Qc o'c Cold reservoir, Te= 300 K W cycle Heat pumparrow_forward3G 4G 9:1V docs.google.com/forms :D Mechanics / صباحي *مطلوب Untitled Section F1 F2 a F3 B. d b C F4 D Consider the following values: - F5 a = 13 m; b = 8 m; c = 10 m; d = 5 m; F1 = 3 kN; F2 = 11 kN; F3 = 2 kN; F4 = 20 kN; F5 = 2 kN; a = 30° , 0 = 60° B = 30° 1] What is the resultant moment of the five forces acting on the rod about point A? a) 19.2 kN.m b) 32.7 kN.m c) 44.6 kN.m d) 29.8 kN.m e) 14.1 kN.m f) 21.3 kN.m 2] What is the resultant moment of the five forces acting on the rod about point B? a) 98.8 kN.m b) 23.7 kN.m c) 81.6 kN.m d) 65.6 kN.m e) 91.1 kN.m f) 74.2 kN.m 3] What is the resultant moment of the five forces acting on the rod about point C? a) 125.7 kN.m b) 111.1 kN.m c) 74.6 kN.m d) 109.4 kN.m e) 24.1 kN.m f) 65.3 kN.m 4] What is the resultant moment of the five forces acting on the rod about point D? a) 17.8 kN.m b) 88.7 kN.m c) 10.6 kN.m d) 59.5 kN.m e) 29.1 kN.m f) 70.1 kN.m 5] What is the moment of the force F2 about point E? Activate V ) 21.3 kN.m Go to Setting…arrow_forward
- Thermodynamics Answer the following problem with complete solutions. Write legibly A gas goes through the following thermodynamic processes: A to B: constant-temperature compression; B to C: constant-volume cooling; C to A: constant-pressure expansion. The pressure and volume at state C are 1.4 bars and 0.028 m^3, respectively. The net work during the C-to-A process is 10.5 kJ. What net work is derived from one complete A-B-C cycle?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_forwardQ\. The first law of thermodynamics involves three main components, if we know the behavior of two components, estimate the behavior of the third component. ( Conclusion ) : a. If heat is added to the system, then the internal energy of the system increases. ..... .. b. If heat leaves the system, then the internal energy of the system decreases .... c. If the work is done by the system, then the internal energy of the system decreases ... ....... d. If the work is done on the system, then the internal energy of the system increases.. .......arrow_forward
- within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of A gas three processes: Process 1-2: Constant volume, V = 0.06 m², U2 - U, = 40.4 kJ Process 2-3: Expansion with PV = constant, U3 - U2= 0 Process 3-1: Constant pressure, P =3 bar, W31 = (-20) kJ There are no significant changes in kinetic or potential energy. %3D Identify the process on a sketch of p-V diagram plotted for the cycle. Formulate the expression for heat transfer for process 2-3 and process 3-1. (Hint: Apply first law of thermodynamics for closed systems) (a) (b) (c) Solve to find the net-work for the cycle and heat transfer for the process 2-3 and Heat transfer for process 3-1, in kJ Identify if the above system executes a power cycle or a refrigeration cycle. Give (d) reason.arrow_forward1. Use total differential to estimate the change: in calculating the value of f (x, y, z) = 3x?yz³ when (x, y, z) change from A (-1, 2, 1) to B (-0.998, 2.003, 0.999). in the volume, V, of a pyramid with square base when its height, h, is increased from 2 to 2.2m and its base dimension, x, is decreased from 1 to 0.9 m. The volume (a) (b) of pyramid is given by V = x²h. 3arrow_forward3. Laws on Conservation. Using the energy model sketched below plus concepts of energy conservation, consider the impact of a dirty war on the global energy. To start, assume that the impact of this war has created an atmosphere that absorbs 75% of the incoming sunlight, while the albedo is reduced to nearly 20%. Let's assume that Earth's ability to reflect incoming solar radiation is negligible. The Earth's surface radiates 240 W/m2, all of which is absorbed by the atmosphere. Assuming that Earth can be modeled as a blackbody emitter and incoming/outgoing energy as shown in the schematic, find the following quantities: a) The "nuclear winter" temperature [°C] of the surface of the Earth b) X, the rate [W/m²] at which radiation is emitted from the atmosphere to space c) Y, the rate [W/m²] of absorption of short-wavelength solar radiation at the Earth's surface d) Z, the rate [W/m2] at which the atmosphere radiates energy to the Earth's surface Incoming 342 W/m² Reflected to space X…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY