Applied Fluid Mechanics
7th Edition
ISBN: 9780133414622
Author: UNTENER
Publisher: YUZU
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Chapter 19, Problem 19.27PP
Forthe conditions shown in figs. 19.719- 19.10 0, complete the design of the duct system by specifying the sizes for all duct sections necessary to achieve a system that is balanced when it carries the flow rates shown. Compute the pressure at the fan outlet, assuming that the final outlets from the duct system are to atmospheric pressure. When an inlet duct section is shown, also complete its design and compute the pressure at the fan inlet. Note that there is no single best solution to these problems, and several design decisions must be made. It may be desirable to change certain features of the suggested system design to improve its operation or to make it simpler to achieve a balanced system.
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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 19 Solutions
Applied Fluid Mechanics
Ch. 19 - Determine the velocity of flow and the friction...Ch. 19 - Repeat Problem 19.1 O for duct diameters of 16,...Ch. 19 - Prob. 19.3PPCh. 19 - Determine the velocity of flow and the friction...Ch. 19 - Repeat Problem 19.40 for duct diameters of...Ch. 19 - Prob. 19.6PPCh. 19 - Prob. 19.7PPCh. 19 - '19.8 A branch duct for a heating system measures...Ch. 19 - Prob. 19.9PPCh. 19 - Prob. 19.10PP
Ch. 19 - A branch duct for a heating system measures 75250...Ch. 19 - Prob. 19.12PPCh. 19 - Prob. 19.13PPCh. 19 - Prob. 19.14PPCh. 19 - Repeat Problem 19.14, but use a five-piece elbowCh. 19 - Prob. 19.16PPCh. 19 - Prob. 19.17PPCh. 19 - Prob. 19.18PPCh. 19 - Prob. 19.19PPCh. 19 - Prob. 19.20PPCh. 19 - Compute the pressure drop as 0.20m3/s of air flows...Ch. 19 - Prob. 19.22PPCh. 19 - Compute the pressure drop as 0.85m3/s of air flows...Ch. 19 - A section of duct system consists of 42 ft of...Ch. 19 - A section of duct system consists of 38 ft of...Ch. 19 - The intake duct to a fan consists of intake...Ch. 19 - Forthe conditions shown in figs. 19.719- 19.10 0,...Ch. 19 - Forthe conditions shown in figs. 19.719- 19.10 0,...Ch. 19 - Prob. 19.29PPCh. 19 - Forthe conditions shown in figs. 19.719- 19.10 0,...
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