Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 9, Problem 123P
A block slides down along, straight inclined wall at speed V,riding on a thin film of oil of thickness h (Fig. 9-121). The weight of the block is W. and its surface area In contact with the oil film is A. Suppose V i s measured, and W, A. angle a. and viscosity ?? are also known. Oil film thickness h i s not known. (a) Generate an exact analytical expression for h as a function of the known parameters V, A, W, a, and
FIGURE P9-121
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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 9 Solutions
Fluid Mechanics Fundamentals And Applications
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Ch. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 14PCh. 9 - Prob. 15PCh. 9 - Prob. 16PCh. 9 - Prob. 17PCh. 9 - Alex is measuring the time-averaged velocity...Ch. 9 - Let vector c be given G=4xziy2i+yzkand let V be...Ch. 9 - The product rule can be applied to the divergence...Ch. 9 - In this chapter we derive the continuity equation...Ch. 9 - Prob. 22PCh. 9 - Repeat Example 9-1(gas compressed in a cylinder by...Ch. 9 - The compressible from of the continuity equation...Ch. 9 - In Example 9-6 we derive the equation for...Ch. 9 - Verify that the spiraling line vortex/sink flow in...Ch. 9 - Verify that the steady; two-dimensional,...Ch. 9 - Prob. 28PCh. 9 - Consider steady flow of water through an...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - The u velocity component of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - Prob. 34PCh. 9 - The u velocity component of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - Two velocity components of a steady,...Ch. 9 - Prob. 39CPCh. 9 - In CFD lingo, the stream function is often called...Ch. 9 - Prob. 41CPCh. 9 - What is significant about curves of constant...Ch. 9 - Prob. 43PCh. 9 - Prob. 44PCh. 9 - Prob. 46PCh. 9 - As a follow-up to Prob. 9-45, calculate the volume...Ch. 9 - Consider the Couette flow of Fig.9-45. For the...Ch. 9 - Prob. 49PCh. 9 - AS a follow-up to Prob. 9-48, calculate the volume...Ch. 9 - Consider the channel flow of Fig. 9-45. The fluid...Ch. 9 - In the field of air pollution control, one often...Ch. 9 - Suppose the suction applied to the sampling...Ch. 9 - Prob. 54PCh. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 57PCh. 9 - Prob. 58PCh. 9 - Prob. 60PCh. 9 - Prob. 61PCh. 9 - Prob. 62PCh. 9 - Prob. 63PCh. 9 - Prob. 64EPCh. 9 - Prob. 65PCh. 9 - Prob. 66EPCh. 9 - Flow separates at a shap corner along a wall and...Ch. 9 - Prob. 69PCh. 9 - Prob. 70EPCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Prob. 76PCh. 9 - Prob. 77PCh. 9 - Prob. 78CPCh. 9 - What are constitutive equations, and to the fluid...Ch. 9 - An airplane flies at constant velocity Vairplane...Ch. 9 - Wht in the main distionction between Newtormine...Ch. 9 - Define or describe each type of fluid: (a)...Ch. 9 - The general cool volume from of linearmomentum...Ch. 9 - Consider liquid in a cylindrical tank. Both the...Ch. 9 - Prob. 85PCh. 9 - Engine oil at T=60C is forced to flow between two...Ch. 9 - Consider the steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider steady, two-dimensional, incompressible...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider steady, incompressible, parallel, laminar...Ch. 9 - Prob. 92PCh. 9 - Prob. 93PCh. 9 - Prob. 94PCh. 9 - The first viscous terms in -comonent of the...Ch. 9 - An incompressible Newtonian liquid is confined...Ch. 9 - Prob. 97PCh. 9 - Prob. 98PCh. 9 - Prob. 99PCh. 9 - Prob. 100PCh. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Consider again the pipe annulus sketched in Fig...Ch. 9 - Repeat Prob. 9-99 except swap the stationary and...Ch. 9 - Consider a modified form of Couette flow in which...Ch. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Prob. 106PCh. 9 - Prob. 107PCh. 9 - Prob. 108CPCh. 9 - Prob. 109CPCh. 9 - Prob. 110CPCh. 9 - Prob. 111CPCh. 9 - Discuss the relationship between volumetric strain...Ch. 9 - Prob. 113PCh. 9 - Prob. 114PCh. 9 - Prob. 116PCh. 9 - Prob. 117PCh. 9 - Prob. 118PCh. 9 - Prob. 119PCh. 9 - For each of the listed equation, write down the...Ch. 9 - Prob. 121PCh. 9 - Prob. 122PCh. 9 - A block slides down along, straight inclined wall...Ch. 9 - Look up the definition of Poisson’s equation in...Ch. 9 - Water flows down a long, straight, inclined pipe...Ch. 9 - Prob. 127PCh. 9 - Prob. 128PCh. 9 - The Navier-Stokes equation is also known as (a)...Ch. 9 - Which choice is the genera1 differential equation...Ch. 9 - Which choice is the differential , incompressible,...Ch. 9 - A steady velocity field is given by...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - Prob. 135PCh. 9 - Prob. 136PCh. 9 - Which choice is not correct regarding the...Ch. 9 - In thud flow analyses, which boundary condition...
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