Applied Fluid Mechanics
7th Edition
ISBN: 9780133414622
Author: UNTENER
Publisher: YUZU
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Textbook Question
Chapter 2, Problem 2.59PP
Convert a viscosity measurement of
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 2 Solutions
Applied Fluid Mechanics
Ch. 2 - Define shear stress as it applies to a moving...Ch. 2 - Define velocity gradient.Ch. 2 - State the mathematical definition for dynamic...Ch. 2 - Which would have the greater dynamic viscosity, a...Ch. 2 - State the standard units for dynamic viscosity in...Ch. 2 - State the standard units for dynamic viscosity in...Ch. 2 - State the equivalent units for poise in terms of...Ch. 2 - Why are the units of poise and centipoise...Ch. 2 - State the mathematical definition for kinematic...Ch. 2 - State the standard units for kinematic viscosity...
Ch. 2 - State the standard units for kinematic viscosity...Ch. 2 - State the equivalent units for stoke in terms of...Ch. 2 - Why are the units of stoke and centistoke...Ch. 2 - Define a Newtonian fluid.Ch. 2 - Define a non-Newtonian fluid.Ch. 2 - Give five examples of Newtonian fluids.Ch. 2 - Give four examples of the types of fluids that are...Ch. 2 - Appendix D iS gives dynamic viscosity for a...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D iS gives dynamic viscosity for a...Ch. 2 - Appendix D iS gives dynamic viscosity for a...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - If you want to choose a fluid that exhibits a...Ch. 2 - Which type of viscosity measurement method uses...Ch. 2 - In the rotating-drum viscometer, describe how the...Ch. 2 - In the rotating-drum viscometer, describe how the...Ch. 2 - What measurements must be taken to determine...Ch. 2 - Define the term terminal velocity as it applies to...Ch. 2 - What measurements must be taken to determine...Ch. 2 - Describe the basic features of the Saybolt...Ch. 2 - Are the results of the Saybolt viscometer tests...Ch. 2 - Does the Saybolt viscometer produce data related...Ch. 2 - Which type of viscometer is prescribed by SAE for...Ch. 2 - Describe the difference between an SAE 20 oil and...Ch. 2 - What grades of SAE oil are suitable for...Ch. 2 - What grades of SAE oil are suitable for...Ch. 2 - If you were asked to check the viscosity of an oil...Ch. 2 - If you were asked to check the viscosity of an oil...Ch. 2 - Prob. 2.53PPCh. 2 - The viscosity of a lubricating oil is given as 500...Ch. 2 - Using the data from Table 2.5. report the minimum,...Ch. 2 - Convert a dynamic viscosity measurement of 4500 cP...Ch. 2 - Convert a kinematic viscosity measurement of 5.6...Ch. 2 - The viscosity of an oil is given as 80 SUS at...Ch. 2 - Convert a viscosity measurement of 6.5x103 Pa.s...Ch. 2 - An oil container indicates that it has a viscosity...Ch. 2 - In a falling-ball viscometer, a steel ball 1.6 mm...Ch. 2 - A capillary tube viscometer similar to that shown...Ch. 2 - In a falling-ball viscometer, a steel ball with a...Ch. 2 - A capillary type viscometer similar to that shown...Ch. 2 - A fluid has a kinematic viscosity of 15.0 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 55.3 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 188 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 244 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 153mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 205mm2/s at...Ch. 2 - An oil is tested using a Saybolt viscometer and...Ch. 2 - An oil is tested using a Saybolt viscometer and...Ch. 2 - Prob. 2.73PPCh. 2 - Prob. 2.74PPCh. 2 - An oil is tested using a Saybolt viscometer and...Ch. 2 - Prob. 2.76PPCh. 2 - Convert all of the kinematic viscosity data in...Ch. 2 - Use a spreadsheet to display the values of...
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