Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259877827
Author: CENGEL
Publisher: MCG
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Chapter 10, Problem 64P
To determine
The sketch of equipotential curves.
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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 10 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 10 - Discuss how nondimensalizsionalization of the...Ch. 10 - Prob. 2CPCh. 10 - Expalain the difference between an “exact”...Ch. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - A box fan sits on the floor of a very large room...Ch. 10 - Prob. 9PCh. 10 - Prob. 10P
Ch. 10 - Prob. 11PCh. 10 - In Example 9-18 we solved the Navier-Stekes...Ch. 10 - Prob. 13PCh. 10 - A flow field is simulated by a computational fluid...Ch. 10 - In Chap. 9(Example 9-15), we generated an “exact”...Ch. 10 - Prob. 16CPCh. 10 - Prob. 17CPCh. 10 - A person drops 3 aluminum balls of diameters 2 mm,...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Consider again the slipper-pad bearing of Prob....Ch. 10 - Consider again the slipper the slipper-pad bearing...Ch. 10 - Prob. 30PCh. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - Prob. 34EPCh. 10 - Discuss what happens when oil temperature...Ch. 10 - Prob. 36PCh. 10 - Prob. 38PCh. 10 - Prob. 39CPCh. 10 - Prob. 40CPCh. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Prob. 47PCh. 10 - Prob. 48PCh. 10 -
Ch. 10 - Prob. 50CPCh. 10 - Consider the flow field produced by a hair dayer...Ch. 10 - In an irrotational region of flow, the velocity...Ch. 10 -
Ch. 10 - Prob. 54CPCh. 10 - Prob. 55PCh. 10 - Prob. 56PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 58PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 60PCh. 10 - Consider a steady, two-dimensional,...Ch. 10 -
Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - In an irrotational region of flow, we wtite the...Ch. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Water at atmospheric pressure and temperature...Ch. 10 - The stream function for steady, incompressible,...Ch. 10 -
Ch. 10 - We usually think of boundary layers as occurring...Ch. 10 - Prob. 73CPCh. 10 - Prob. 74CPCh. 10 - Prob. 75CPCh. 10 - Prob. 76CPCh. 10 - Prob. 77CPCh. 10 - Prob. 78CPCh. 10 - Prob. 79CPCh. 10 - Prob. 80CPCh. 10 - Prob. 81CPCh. 10 -
Ch. 10 - On a hot day (T=30C) , a truck moves along the...Ch. 10 - A boat moves through water (T=40F) .18.0 mi/h. A...Ch. 10 - Air flows parallel to a speed limit sign along the...Ch. 10 - Air flows through the test section of a small wind...Ch. 10 - Prob. 87EPCh. 10 - Consider the Blasius solution for a laminar flat...Ch. 10 - Prob. 89PCh. 10 - A laminar flow wind tunnel has a test is 30cm in...Ch. 10 - Repeat the calculation of Prob. 10-90, except for...Ch. 10 - Prob. 92PCh. 10 - Prob. 93EPCh. 10 - Prob. 94EPCh. 10 - In order to avoid boundary laver interference,...Ch. 10 - The stramwise velocity component of steady,...Ch. 10 - For the linear approximation of Prob. 10-97, use...Ch. 10 - Prob. 99PCh. 10 - One dimension of a rectangular fiat place is twice...Ch. 10 - Prob. 101PCh. 10 - Prob. 102PCh. 10 - Prob. 103PCh. 10 - Static pressure P is measured at two locations...Ch. 10 - Prob. 105PCh. 10 - For each statement, choose whether the statement...Ch. 10 - Prob. 107PCh. 10 - Calculate the nine components of the viscous...Ch. 10 - In this chapter, we discuss the line vortex (Fig....Ch. 10 - Calculate the nine components of the viscous...Ch. 10 - Prob. 111PCh. 10 - The streamwise velocity component of a steady...Ch. 10 - For the sine wave approximation of Prob. 10-112,...Ch. 10 - Prob. 115PCh. 10 - Suppose the vertical pipe of prob. 10-115 is now...Ch. 10 - Which choice is not a scaling parameter used to o...Ch. 10 - Prob. 118PCh. 10 - Which dimensionless parameter does not appear m...Ch. 10 - Prob. 120PCh. 10 - Prob. 121PCh. 10 - Prob. 122PCh. 10 - Prob. 123PCh. 10 - Prob. 124PCh. 10 - Prob. 125PCh. 10 - Prob. 126PCh. 10 - Prob. 127PCh. 10 - Prob. 128PCh. 10 - Prob. 129PCh. 10 - Prob. 130PCh. 10 - Prob. 131PCh. 10 - Prob. 132PCh. 10 - Prob. 133PCh. 10 - Prob. 134PCh. 10 - Prob. 135PCh. 10 - Prob. 136PCh. 10 - Prob. 137PCh. 10 - Prob. 138P
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