Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259877827
Author: CENGEL
Publisher: MCG
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Chapter 6, Problem 72P
To determine
(a)
The engine thrust prior to insertion of thrust reverse.
To determine
(b)
The braking force required.
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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 6 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 6 - Express Newton’s second law of motion for rotating...Ch. 6 - Express Newton’s first, second, and third laws.Ch. 6 - Is momentum a vector? If so, in what direction...Ch. 6 - Express the conservation of momentum principle....Ch. 6 - How do surface forces arise in the momentum...Ch. 6 - Explain the importance of the Reynolds transport...Ch. 6 - What is the importance of the momentum-flux...Ch. 6 - Write the momentum equation for steady...Ch. 6 - In the application of the momentum equation,...Ch. 6 - Two firefighters are fighting a fire with...
Ch. 6 - A rocket in space (no friction or resistance to...Ch. 6 - Describe in terms of momentum and airflow how a...Ch. 6 - Does it take more, equal, or less power for a...Ch. 6 - In a given location, would a helicopter require...Ch. 6 - Describe body forces and surface forces, and...Ch. 6 - A constant-velocity horizontal water jet from a...Ch. 6 - A horizontal water jet of constant velocity V from...Ch. 6 - A horizontal water jet from a nozzle of constant...Ch. 6 - A 2.5-cm-diameter horizontal water jet with a...Ch. 6 - A 90 elbow in a horizontal pipe is used to direct...Ch. 6 - Repeat Prob. 6-20 for the case of another...Ch. 6 - A horizontal water jet impinges against a vertical...Ch. 6 - Water enters a 7-cm-diameter pipe steadily with a...Ch. 6 - A reducing elbow in a horizontal pipe is used to...Ch. 6 - Repeat Prob. 6-24 for the case of = 125°.Ch. 6 - A 100-ft3/s water jet is moving in the positive...Ch. 6 - Reconsider Prob. 6-26E. Using appropriate...Ch. 6 - Commercially available large wind turbines have...Ch. 6 - A fan with 24-in-diameter blades moves 2000 cfm...Ch. 6 - A 3-in-diameter horizontal jet of water, with...Ch. 6 - Firefighters are holding a nozzle at the end of a...Ch. 6 - A 5-cm-diameter horizontal jet of water with a...Ch. 6 - Prob. 33PCh. 6 - A 3-in-diameter horizontal water jet having a...Ch. 6 - An unloaded helicopter of mass 12,000 kg hovers at...Ch. 6 - Prob. 36PCh. 6 - Water is flowing through a 10-cm-diameter water...Ch. 6 - Water flowing in a horizontal 25-cm-diameter pipe...Ch. 6 - Prob. 39PCh. 6 - Water enters a centrifugal pump axially at...Ch. 6 - An incompressible fluid of density and viscosity ...Ch. 6 - Consider the curved duct of Prob. 6-41, except...Ch. 6 - As a follow-up to Prob. 6-41, it turns out that...Ch. 6 - Prob. 44PCh. 6 - The weight of a water tank open to the atmosphere...Ch. 6 - A sluice gate, which controls flow rate in a...Ch. 6 - A room is to be ventilated using a centrifugal...Ch. 6 - How is the angular momentum equation obtained from...Ch. 6 - Prob. 49CPCh. 6 - Prob. 50CPCh. 6 - Prob. 51CPCh. 6 - A large lawn sprinkler with two identical arms is...Ch. 6 - Prob. 53EPCh. 6 - The impeller of a centrifugal pump has inner and...Ch. 6 - Water is flowing through a 15-cm-diameter pipe...Ch. 6 - Prob. 56PCh. 6 - Repeat Prob. 6-56 for a water flow rate of 60 L/s.Ch. 6 - Prob. 58PCh. 6 - Water enters the impeller of a centrifugal pump...Ch. 6 - A lawn sprinkler with three identical antis is...Ch. 6 - Prob. 62PCh. 6 - The impeller of a centrifugal blower has a radius...Ch. 6 - An 8-cm-diameter horizontal water jet having a...Ch. 6 - Water flowing steadily at a rate of 0.16 m3/s is...Ch. 6 - Repeat Prob. 6-66 by taking into consideration the...Ch. 6 - A 16-cm diameter horizontal water jet with a speed...Ch. 6 - Water enters vertically and steadily at a rate of...Ch. 6 - Repeal Prob. 6-69 for the case of unequal anus-the...Ch. 6 - Prob. 71PCh. 6 - Prob. 72PCh. 6 - A spacecraft cruising in space at a constant...Ch. 6 - A 60-kg ice skater is standing on ice with ice...Ch. 6 - A 5-cm-diameter horizontal jet of water, with...Ch. 6 - Water is flowing into and discharging from a pipe...Ch. 6 - Indiana Jones needs So ascend a 10-m-high...Ch. 6 - Prob. 79EPCh. 6 - A walnut with a mass of 50 g requires a force of...Ch. 6 - Prob. 81PCh. 6 - Prob. 82PCh. 6 - A horizontal water jet of constant velocity V...Ch. 6 - Show that the force exerted by a liquid jet on a...Ch. 6 - Prob. 85PCh. 6 - Prob. 86PCh. 6 - Water enters a mixed flow pump axially at a rate...Ch. 6 - Prob. 88PCh. 6 - Water enters a two-armed lawn sprinkler along the...Ch. 6 - Prob. 91PCh. 6 - Prob. 92PCh. 6 - Prob. 93PCh. 6 - Prob. 94PCh. 6 - A water jet strikes a moving plate at velocity...Ch. 6 - Water flows at mass flow rate m through a 90°...Ch. 6 - Prob. 97PCh. 6 - Water shoots out of a Iar2e tank sitting a cart...Ch. 6 - Prob. 99PCh. 6 - Prob. 100PCh. 6 - Prob. 101PCh. 6 - Consider water flow through a horizontal, short...Ch. 6 - Consider water flow through a horizontal. short...Ch. 6 - Prob. 104PCh. 6 - Prob. 105PCh. 6 - Prob. 106PCh. 6 - The velocity of wind at a wind turbine is measured...Ch. 6 - The ve1ocity of wind at a wind turbine is measured...Ch. 6 - Prob. 109PCh. 6 - Prob. 110PCh. 6 - Prob. 111PCh. 6 - Consider the impeller of a centrifugal pump with a...Ch. 6 - Prob. 113PCh. 6 - Prob. 114P
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