Applied Fluid Mechanics: Global Edition
7th Edition
ISBN: 9781292019611
Author: Robert Mott
Publisher: Pearson Higher Education
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Chapter 11, Problem 11.43PP
Figure 11.32 shows a pipe delivering water to the putting green on a golf course. The pressure in the main is at
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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 11 Solutions
Applied Fluid Mechanics: Global Edition
Ch. 11 - Water at 10C flows from a large reservoir at the...Ch. 11 - For the system shown in Fig. 11.14, kerosene (...Ch. 11 - Figure 11.15 shows a portion of a hydraulic...Ch. 11 - Figure 11.16 shows part of a large hydraulic...Ch. 11 - Oil is flowing at the rate of 0.015m3/s in the...Ch. 11 - For the system shown in Fig. 11.18, calculate the...Ch. 11 - A liquid refrigerant flows through the system,...Ch. 11 - Water at 100F is flowing in a 4-in Schedule 80...Ch. 11 - A hydraulic oil is flowing in a drawn steel...Ch. 11 - In a processing plant, ethylene glycol at 77F is...
Ch. 11 - Water at 15C is flowing downward in a vertical...Ch. 11 - Turpentine at 77F is flowing from A to B in a 3...Ch. 11 - ]11.13 A device designed to allow cleaning of...Ch. 11 - Kerosene at 25C is flowing in the system shown in...Ch. 11 - Water at 40C is flowing from A to B through the...Ch. 11 - Oil with a specific gravity of 0.93 and a dynamic...Ch. 11 - Determine the required size of new Schedule 80...Ch. 11 - What size of standard hydraulic copper tube from...Ch. 11 - Water at 60F is to flow by gravity between two...Ch. 11 - The tank shown in Fig. 11.24 is to be drained to a...Ch. 11 - Figure 11.25 depicts gasoline flowing from a...Ch. 11 - For the system in Fig. 11.26, compute the pressure...Ch. 11 - For the system in Fig. 11.26, compute the total...Ch. 11 - For the system in Fig. 11.26 specify the size of...Ch. 11 - A manufacturer of spray nozzles specifies that the...Ch. 11 - Specify the size of new Schedule 40 steel pipe...Ch. 11 - Refer to Fig. 11.27. Water at 80C is being pumped...Ch. 11 - For the system shown in Fig. 11.27 and analyzed in...Ch. 11 - In a water pollution control project, the polluted...Ch. 11 - Repeat Problem 11.29, but use a 3-in Schedule 40...Ch. 11 - Water at 10C is being delivered to a tank on the...Ch. 11 - If the pressure at point A in Fig. 11.29 is 300...Ch. 11 - Change the design of the system in Fig. 11.29 to...Ch. 11 - It is desired to deliver 250 gal/min of ethyl...Ch. 11 - For the system shown in Fig. 11.30, compute the...Ch. 11 - Repeat Problem 11.35, but consider the valve to be...Ch. 11 - Repeat Problem 11.35, but consider the valve to be...Ch. 11 - Figure 11.31 depicts a DN 100 Schedule 40 steel...Ch. 11 - Repeat Problem 11.38 but replace the globe valve...Ch. 11 - Repeat Problem 11.38 but use a DN 125 Schedule 40...Ch. 11 - Repeat Problem 11.38, but replace the globe valve...Ch. 11 - It is desired to drive a small,...Ch. 11 - Figure 11.32 shows a pipe delivering water to the...Ch. 11 - Repeat Problem 11.43, except consider that there...Ch. 11 - A sump pump in a commercial building sits in a...Ch. 11 - For the system designed in Problem 11.45, compute...Ch. 11 - Figure 11.33 shows a part of a chemical processing...Ch. 11 - For the system described in Problem 11.47, and...Ch. 11 - For the system described in Problem 11.47, and...Ch. 11 - For the system described in Problem 11.47, and...Ch. 11 - Analyze the system shown in Fig. 11.11 with...Ch. 11 - Create a program or a spreadsheet for analyzing...Ch. 11 - Create a program or a spreadsheet for determining...
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