Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
8th Edition
ISBN: 9781119080701
Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein
Publisher: WILEY
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Chapter 3.6, Problem 38P
To determine
The pressure in the tank.
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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 3 Solutions
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
Ch. 3.2 - Prob. 1PCh. 3.2 - Air flows steadily along a streamline from point...Ch. 3.2 - Water flows steadily through the variable area...Ch. 3.2 - What pressure gradient along the streamline,...Ch. 3.2 - At a given location the airspeed is 20 m/s and the...Ch. 3.2 - What pressure gradient along the streamline,...Ch. 3.2 - The Bernoulli equation is valid for steady,...Ch. 3.2 - An incompressible fluid flows steadily past a...Ch. 3.2 - Consider a compressible liquid that has a constant...Ch. 3.3 - Air flows along a horizontal, curved streamline...
Ch. 3.3 - Water flows around the vertical two-dimensional...Ch. 3.3 - Water in a container and air in a tornado flow in...Ch. 3.3 - Prob. 15PCh. 3.5 - At a given point on a horizontal streamline in...Ch. 3.5 - A drop of water in a zero-g environment (as in the...Ch. 3.5 - When an airplane is flying 200 mph at 5000-ft...Ch. 3.5 - Air flows over the airfoil shown in Fig. P3.20....Ch. 3.5 - Some animals have learned to take advantage of the...Ch. 3.5 - Estimate the pressure on your hand when you hold...Ch. 3.5 - 2013 Indianapolis 500 champion Tony Kanaan holds...Ch. 3.5 - What is the minimum height for an oil (SG = 0.75)...Ch. 3.5 - Prob. 25PCh. 3.5 - A Bourdon-type pressure gage is used to measure...Ch. 3.5 - Estimate the force of a hurricane strength wind...Ch. 3.5 - A 40-mph wind blowing past your house speeds up as...Ch. 3.5 - Prob. 29PCh. 3.6 - Prob. 30PCh. 3.6 - Estimate the pressure needed at the pumper truck...Ch. 3.6 - The tank shown in Fig. P3.32 contains air at...Ch. 3.6 - Water flows from the faucet on the first floor of...Ch. 3.6 - Prob. 34PCh. 3.6 - Prob. 35PCh. 3.6 - Streams of water from two tanks impinge upon each...Ch. 3.6 - Several holes are punched into a tin can as shown...Ch. 3.6 - Water flows from a pressurized tank, through a...Ch. 3.6 - Prob. 39PCh. 3.6 - Prob. 41PCh. 3.6 - Figure P3.42 shows a tube for siphoning water from...Ch. 3.6 - For the pipe enlargement shown in Fig. P3.43, the...Ch. 3.6 - A fire hose nozzle has a diameter of in. According...Ch. 3.6 - Water flowing from the 0.75-in.-diameter outlet...Ch. 3.6 - Prob. 46PCh. 3.6 - Prob. 47PCh. 3.6 - Prob. 48PCh. 3.6 - The pressure and average velocity at point A in...Ch. 3.6 - Water (assumed inviscid and incompressible) flows...Ch. 3.6 - Prob. 51PCh. 3.6 - Prob. 52PCh. 3.6 - Prob. 53PCh. 3.6 - Prob. 54PCh. 3.6 - Prob. 55PCh. 3.6 - Prob. 56PCh. 3.6 - Water (assumed frictionless and incompressible)...Ch. 3.6 - Prob. 58PCh. 3.6 - Water flows through the pipe contraction shown in...Ch. 3.6 - Prob. 60PCh. 3.6 - Prob. 61PCh. 3.6 - Prob. 62PCh. 3.6 - Prob. 63PCh. 3.6 - Prob. 64PCh. 3.6 - The circular stream of water from a faucet is...Ch. 3.6 - Water is siphoned from the tank shown in Fig....Ch. 3.6 - Prob. 67PCh. 3.6 - Prob. 68PCh. 3.6 - Water is siphoned from the tank shown in Fig....Ch. 3.6 - Prob. 70PCh. 3.6 - Water exits a pipe as a free jet and flows to a...Ch. 3.6 - Water flows steadily from a large, closed tank as...Ch. 3.6 - Prob. 73PCh. 3.6 - Prob. 74PCh. 3.6 - Prob. 75PCh. 3.6 - Prob. 76PCh. 3.6 - Prob. 77PCh. 3.6 - Prob. 78PCh. 3.6 - Prob. 79PCh. 3.6 - Air is drawn into a small open-circuit wing tunnel...Ch. 3.6 - Prob. 81PCh. 3.6 - Water flows steadily from the large open tank...Ch. 3.6 - Prob. 83PCh. 3.6 - Prob. 84PCh. 3.6 - Prob. 85PCh. 3.6 - Prob. 86PCh. 3.6 - Prob. 87PCh. 3.6 - Prob. 88PCh. 3.6 - Prob. 89PCh. 3.6 - Prob. 90PCh. 3.6 - Prob. 91PCh. 3.6 - Prob. 92PCh. 3.6 - Prob. 93PCh. 3.6 - Prob. 94PCh. 3.6 - Prob. 95PCh. 3.6 - Prob. 96PCh. 3.6 - Prob. 97PCh. 3.6 - Prob. 98PCh. 3.6 - Prob. 99PCh. 3.6 - Determine the flowrate through the submerged...Ch. 3.6 - The water clock (clepsydra) shown in Fig. P3.101...Ch. 3.6 - Prob. 102PCh. 3.6 - Prob. 105PCh. 3.6 - Prob. 106PCh. 3.6 - Prob. 107PCh. 3.6 - Prob. 109PCh. 3.6 - Prob. 110PCh. 3.6 - Water flows through the branching pipe shown in...Ch. 3.6 - Prob. 112PCh. 3.6 - Prob. 113PCh. 3.6 - Prob. 114PCh. 3.6 - Prob. 115PCh. 3.6 - Prob. 116PCh. 3.6 - Prob. 117PCh. 3.6 - Prob. 118PCh. 3.6 - Prob. 119PCh. 3.6 - Prob. 120PCh. 3.6 - Prob. 121PCh. 3.6 - Prob. 122PCh. 3.6 - Prob. 123PCh. 3.6 - Water flows in a rectangular channel that is 2.0 m...Ch. 3.6 - Prob. 125PCh. 3.6 - A Venturi meter with a minimum diameter of 3 in....Ch. 3.6 - Prob. 127PCh. 3.6 - Prob. 128PCh. 3.6 - What diameter orifice hole, d, is needed if under...Ch. 3.6 - A weir (see Video V10.13) of trapezoidal cross...Ch. 3.6 - Prob. 131PCh. 3.6 - Water flows under the inclined sluice gate shown...Ch. 3.7 - Water flows in a vertical pipe of 0.15-m diameter...Ch. 3.7 - Prob. 134PCh. 3.7 - Draw the energy line and hydraulic grade line for...Ch. 3.8 - Prob. 137PCh. 3.8 - Prob. 138P
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