Applied Fluid Mechanics: Global Edition
7th Edition
ISBN: 9781292019611
Author: Robert Mott
Publisher: Pearson Higher Education
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Chapter 11, Problem 11.9PP
A hydraulic oil is flowing in a drawn steel hydraulic tube with an OD of
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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
B
y(t)
100 L
y(0) = 20 kg
2 L/min
1 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t > 0:
Analytically (hand calculations)
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.
www.m
k₁ = 3
(y₁ = 0).
m₁ = 1
k2=2
(y₂ = 0)
|m₂ = 1
Y2
y 2
System in
static
equilibrium
(Net change in
spring length
=32-31)
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)
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)
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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