Applied Fluid Mechanics
7th Edition
ISBN: 9780133414622
Author: UNTENER
Publisher: YUZU
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Chapter 1, Problem 1.18PP
In an attempt at a land speed record, a car travels
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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 1 Solutions
Applied Fluid Mechanics
Ch. 1 - 1.1 Convert 1250 millimeters to meters.Ch. 1 - Convert 1600 square millimeters to square metersCh. 1 - Convert 3.65x103 cubic millimeters to cubic metersCh. 1 - Convert 2.05 square meters to square millimetersCh. 1 - Convert 0.391 cubic meters to cubic millimetersCh. 1 - Convert 55.0 gallons to cubic metersCh. 1 - An automobile is moving at 80 kilometers per hour,...Ch. 1 - Convert a length of 25.3 feet to metersCh. 1 - Convert a distance of 1.36 miles to meters.Ch. 1 - Convert a length of 3.65 inches to millimeters.
Ch. 1 - Convert a distance of 2580 feet to meters.Ch. 1 - Convert a volume of 480 cubic feet to cubic...Ch. 1 - Convert a volume of 7390 cubic centimeters to...Ch. 1 - Convert a volume of 6.35 liters to cubic nneters.Ch. 1 - Convert 6.0 feet per second to meters per secondCh. 1 - Convert 2500 cubic feet per minute to cubic meters...Ch. 1 - A car travels 0.50 km in 10.6 s. Calculate its...Ch. 1 - In an attempt at a land speed record, a car...Ch. 1 - A car travels 1000 ft in 14 s. Calculate its...Ch. 1 - In an attempt at a land speed record, a car...Ch. 1 - A body starting from rest with constant...Ch. 1 - A body starting from rest with constant...Ch. 1 - A body starting from rest with constant...Ch. 1 - A body starting from rest with constant...Ch. 1 - The formula for kinetic energy is KE=mv2, where m...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2 where m...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is where m = mass...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - Compute the pressure change required to cause a...Ch. 1 - Compute the pressure change required to cause a...Ch. 1 - Compute the pressure change required to cause a...Ch. 1 - For the conditions described in Problem 1.59...Ch. 1 - A certain hydraulic system operates at 3000 psi....Ch. 1 - A certain hydraulic system operates at 20.0 MPa....Ch. 1 - A measure of the stiffness of a linear actuator...Ch. 1 - 1.64 Repeat Problem 1.63 but change the length of...Ch. 1 - Repeat Problem 1.6319 but change the cylinder...Ch. 1 - Using the results of Problems 1.63-1.65, generate...Ch. 1 - Calculate the mass of a can of oil if it weighs...Ch. 1 - Calculate the mass of a tank of gasoline if it...Ch. 1 - '1.69 Calculate the weight of 1m3 of kerosene if...Ch. 1 - Calculate the weight of a jar of castor oil if it...Ch. 1 - Calculate the mass of 1 gal of oil if it weighs...Ch. 1 - Calculate the mass of 1ft3 of gasoline if it...Ch. 1 - Calculate the weight of 1ft3 of kerosene if it has...Ch. 1 - Calculate the weight of 1 gal of water if it has a...Ch. 1 - Assume that a man weighs 160 lb (force) Compute...Ch. 1 - In the United States, hamburger and other meats...Ch. 1 - The metric ton is 1000 kg (mass). Compute the...Ch. 1 - Convert the force found in Problem 1.77 to lb.Ch. 1 - Determine your weight in lb and N and your mass in...Ch. 1 - The specific gravity of benzene is 0.876....Ch. 1 - Air at 16 C and standard atmospheric pressure has...Ch. 1 - Carbon dioxide has a density of 1.964kg/m3 at 0 C....Ch. 1 - A certain medium lubricating oil has a specific...Ch. 1 - At 100 C mercury has a specific weight of...Ch. 1 - A cylindrical can 150 mm in diameter is filled to...Ch. 1 - Glycerin has a specific gravity of 1.258. How much...Ch. 1 - The fuel tank of an automobile holds 0.095m3. If...Ch. 1 - The density of muriatic acid is 1200 kg / m3...Ch. 1 - Liquid ammonia has a specific gravity of 0.826....Ch. 1 - Vinegar has a density of 1080 kg / m3 Calculate...Ch. 1 - Methyl alcohol has a specific gravity of 0.789....Ch. 1 - A cylindrical container is 150 mm in diameter and...Ch. 1 - A storage vessel for gasoline ( sg=0.68 ) is a...Ch. 1 - What volume of mercury (sg = 13.54) would weigh...Ch. 1 - A rock has a specific gravity of 2.32 and a volume...Ch. 1 - The specific gravity of benzene is 0.876....Ch. 1 - Air at 59 F and standard atmospheric pressure has...Ch. 1 - Carbon dioxide has a density of 0.003 81 slug/ft3...Ch. 1 - A certain medium lubricating oil has a specific...Ch. 1 - At 212F mercury has a specific weight of 834...Ch. 1 - One gallon of a certain fuel oil weighs 7.50 lb....Ch. 1 - Glycerin has a specific gravity of 1.258. How much...Ch. 1 - The fuel tank of an automobile holds 25.0 gal. If...Ch. 1 - The density of muriatic acid is 1.20 g/cm3....Ch. 1 - Liquid ammonia has a specific gravity of 0.826....Ch. 1 - Vinegar has a density of 1.08 g/cm3. Calculate its...Ch. 1 - Alcohol has a specific gravity of 0.79. Calculate...Ch. 1 - A cylindrical container has a 6.0-in diameter and...Ch. 1 - A storage vessel for gasoline (sg = 0.68) is a...Ch. 1 - How many gallons of mercury (sg = 13.54) would...Ch. 1 - A rock has a specific gravity of 2.32 and a volume...Ch. 1 - A village of 75 people desires a tank to store a...Ch. 1 - A cylindrical tank has a diameter of 38 in with...Ch. 1 - What is the required rate, in N/min, to empty a...Ch. 1 - An empty tank measuring 1.5 m by 2.5 m on the...Ch. 1 - A tank that is 2 ft in diameter and 18 in tall is...Ch. 1 - A standard pump design can be upgraded to higher...Ch. 1 - What is the annual cost to run a 2 HP system if it...Ch. 1 - Determine the displacement, in liters, for one...Ch. 1 - Determine the flow rate, in m3/hr, for another...Ch. 1 - At what speed, in rpm, does a single cylinder pump...Ch. 1 - Prob. 2CAEA
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