Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Textbook Question
Chapter 2, Problem 2.2PP
Define velocity gradient.
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2. Express the following complex numbers in rectangular form.
(a) z₁ = 2еjл/6
(b) Z2=-3e-jπ/4
(c) Z3 =
√√√3e-j³/4
(d) z4 = − j³
A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be
fixed supports. The beam was originally designed to withstand a triangular distributed load, however,
the loading condition has been revised and can be approximated by a cosine function as shown in the
figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can
assume that the bending rigidity (El) is constant.
wwo cos
2L
x
A
B
Figure 3: Built in beam with a varying distributed load
In order to do this, you will:
a. Solve the reaction forces and moments at point A and B.
Hint: you may find it convenient to use the principal of superposition.
(2%)
b. Plot the shear force and bending moment diagrams and identify the maximum shear force
and bending moment.
(2%)
c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x.
(1%)
Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the…
Chapter 2 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 2 - Define shear stress as it applies to a moving...Ch. 2 - Define velocity gradient.Ch. 2 - State the mathematical definition for dynamic...Ch. 2 - Which would have the greater dynamic viscosity, a...Ch. 2 - State the standard units for dynamic viscosity in...Ch. 2 - State the standard units for dynamic viscosity in...Ch. 2 - State the equivalent units for poise in terms of...Ch. 2 - Why are the units of poise and centipoise...Ch. 2 - State the mathematical definition for kinematic...Ch. 2 - State the standard units for kinematic viscosity...
Ch. 2 - State the standard units for kinematic viscosity...Ch. 2 - State the equivalent units for stoke in terms of...Ch. 2 - Why are the units of stoke and centistoke...Ch. 2 - Define a Newtonian fluid.Ch. 2 - Define a non-Newtonian fluid.Ch. 2 - Give five examples of Newtonian fluids.Ch. 2 - Give four examples of the types of fluids that are...Ch. 2 - Appendix D iS gives dynamic viscosity for a...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D iS gives dynamic viscosity for a...Ch. 2 - Appendix D iS gives dynamic viscosity for a...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - Appendix D gives dynamic viscosity for a variety...Ch. 2 - If you want to choose a fluid that exhibits a...Ch. 2 - Which type of viscosity measurement method uses...Ch. 2 - In the rotating-drum viscometer, describe how the...Ch. 2 - In the rotating-drum viscometer, describe how the...Ch. 2 - What measurements must be taken to determine...Ch. 2 - Define the term terminal velocity as it applies to...Ch. 2 - What measurements must be taken to determine...Ch. 2 - Describe the basic features of the Saybolt...Ch. 2 - Are the results of the Saybolt viscometer tests...Ch. 2 - Does the Saybolt viscometer produce data related...Ch. 2 - Which type of viscometer is prescribed by SAE for...Ch. 2 - Describe the difference between an SAE 20 oil and...Ch. 2 - What grades of SAE oil are suitable for...Ch. 2 - What grades of SAE oil are suitable for...Ch. 2 - If you were asked to check the viscosity of an oil...Ch. 2 - If you were asked to check the viscosity of an oil...Ch. 2 - Prob. 2.53PPCh. 2 - The viscosity of a lubricating oil is given as 500...Ch. 2 - Using the data from Table 2.5. report the minimum,...Ch. 2 - Convert a dynamic viscosity measurement of 4500 cP...Ch. 2 - Convert a kinematic viscosity measurement of 5.6...Ch. 2 - The viscosity of an oil is given as 80 SUS at...Ch. 2 - Convert a viscosity measurement of 6.5x103 Pa.s...Ch. 2 - An oil container indicates that it has a viscosity...Ch. 2 - In a falling-ball viscometer, a steel ball 1.6 mm...Ch. 2 - A capillary tube viscometer similar to that shown...Ch. 2 - In a falling-ball viscometer, a steel ball with a...Ch. 2 - A capillary type viscometer similar to that shown...Ch. 2 - A fluid has a kinematic viscosity of 15.0 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 55.3 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 188 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 244 mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 153mm2/s at...Ch. 2 - A fluid has a kinematic viscosity of 205mm2/s at...Ch. 2 - An oil is tested using a Saybolt viscometer and...Ch. 2 - An oil is tested using a Saybolt viscometer and...Ch. 2 - Prob. 2.73PPCh. 2 - Prob. 2.74PPCh. 2 - An oil is tested using a Saybolt viscometer and...Ch. 2 - Prob. 2.76PPCh. 2 - Convert all of the kinematic viscosity data in...Ch. 2 - Use a spreadsheet to display the values of...
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