2.26. CHAPTER 2, PROBLEM 26
153
2.26 Chapter 2, Problem 26
Problem: For laminar flow, Newton postulated that the shear stress is a function of viscosity, , and
velocity gradient, du/dy. Verify that the Buckingham Theorem implies that there are no dimensio

3.70. CHAPTER 3, PROBLEM 70
405
3.70 Chapter 3, Problem 70
Problem: Determine the force on gate AB if the upper layer of fluid has density 1 = and the lower
layer has density 2 = 4. The gate is rectangular and has width 2H out of the page. Express your
an

MAE103
Midterm 1 Solution
Question:
1. Dynamic viscosity is the ration of shear stress to velocity gradient. In this figure, fluid A has a
higher dynamic viscosity than fluid B since the slope of the lines associated with it is higher than
that of B.
The

660
CHAPTER 6. CONTROL-VOLUME METHOD
6.16 Chapter 6, Problem 16
Problem: A cylindrical tank of diameter D is supplied with an incompressible fluid of density by a
pipe of diameter d and velocity U . Fluid leaves the tank through another horizontal pipe of

6.44. CHAPTER 6, PROBLEM 44
699
6.44 Chapter 6, Problem 44
Problem: A two-dimensional channel of width H has a slot of width h as shown. Fluid is injected
through the slot at an angle to the horizontal. The fluid is incompressible with density and body
fo

892
CHAPTER 6. CONTROL-VOLUME METHOD
6.132 Chapter 6, Problem 132
Problem: Captain Janeways shuttle is returning to the Voyager when the Borg turn on their tractor
beam. To counter the beams effect, i.e., to continue moving on the same course with velocit

722
CHAPTER 6. CONTROL-VOLUME METHOD
6.56 Chapter 6, Problem 56
Problem: A water jet of cross-sectional area A with velocity Uj and density causes a cart to move at
a constant velocity U = 1 Uj . Use a Galilean transformation and a stationary control volu

7.22. CHAPTER 7, PROBLEM 22
931
7.22 Chapter 7, Problem 22
Problem: A laser is used to energize the steady flow of air through a channel of height H and width 5H
out of the page. Pressure is constant and equal to 1 atm throughout the channel. The design o

970
CHAPTER 7. ENERGY PRINCIPLE
7.52 Chapter 7, Problem 52
1
Problem: For a hydroelectric plant the head loss between Points 1 and 2 is hL = 10 H. The mass-flow
rate through the turbine is m. The kinetic-energy correction factor, , is 1.06 throughout the

8.6. CHAPTER 8, PROBLEM 6
1089
8.6 Chapter 8, Problem 6
Problem: Pressure, p, and density, , for seawater are related by p/pa ( + 1)(/a )7 ,
where pa and a are surface values, and = 3000 is a dimensionless constant. If pa = 1 atm
and a = 1030 kg/m3 , what

INFORMATION SHEET
Mechanical & Aerospace Engineering MAE 103
Elementary Fluid Mechanics
Fall, 2016
Class Hours:
o Regular lectures: Tu, Th 4:00PM to 5:50PM, MS 5200
o Recitation Sections:
Discussion 1A, F, 8:00AM to 9:50AM, Pub Aff 2214
Dis

8.34. CHAPTER 8, PROBLEM 34
1121
8.34 Chapter 8, Problem 34
Problem: Superman is traveling faster than a speeding bullet. In fact, he is traveling at 5 times the speed
of sound in the ambient atmosphere (temperature 20o C at 1 atm). Estimate the maximum t

8.24. CHAPTER 8, PROBLEM 24
1109
8.24 Chapter 8, Problem 24
Problem: The ratio of the total density to the static density of a gas is t / = 5.02. The Mach number
is M = 2.4 and the flow is isentropic.
(a) Assuming the gas is one of those listed in Table A

8.60. CHAPTER 8, PROBLEM 60
1151
8.60 Chapter 8, Problem 60
Problem: A wind tunnel is designed to have Mach number M = 2.5, static pressure p = 2.5 psi, and
static temperature T = 100o F in the test section. Determine the required area ratio of the nozzle

MAE 103 Final Exam Information
Fall 2016
Audrey Pool ONeal, Ph.D.
Final Exam Logistics
Final exam date: 12/07/16
Final exam time: 8:00AM11:00AM
Final exam location: Young Hall CS 24
You may bring one page of 8.5 x 11 hand-written notes
(front and back)jus

MAE 103 Elementary Fluid Mechanics
Fall 2016 Exam 1 SOLUTIONS
1) (20 points) A clean glass tube is to be selected in the design of a manometer to measure the
pressure of kerosene. The Specific Gravity (SG) of kerosene = 0.82 and the surface tension
of ker

Name:_
UID: _
MAE 103 Elementary Fluid Mechanics
Fall 2016 Exam 2
11/08/16SOLUTIONS
1) You will be allotted 1 hour 50 minutes to complete this exam
2) Write your name and UID on this front cover sheet
3) Write your name at the top of every sheet
4) Be sur

1.110. CHAPTER 1, PROBLEM 110
123
1.110 Chapter 1, Problem 110
Problem: Using the pipe-flow solution, we can analyze laminar flow of blood in the aorta.
(a) Show that, for a given pressure difference, the volume-flow rate, Q, increases as R4 , where
R
Q 2

1.94. CHAPTER 1, PROBLEM 94
99
1.94 Chapter 1, Problem 94
Problem: Measurements show that the shear stress for Couette flow is = 0.18 lb/ft2 . The plateseparation distance is h = 2 in and the velocity is U = 12 ft/sec.
(a) What is the viscosity of the flu

534
CHAPTER 4. KINEMATICS
4.66 Chapter 4, Problem 66
Problem: Spectre thugs, pursued by Agent 007, are vacating Spectre headquarters. The number of
thugs per unit volume near the exit is n, the exit area is A and the thugs are moving at velocity v
as they

512
CHAPTER 4. KINEMATICS
4.44 Chapter 4, Problem 44
Problem: Consider the flowfield whose velocity is given by u = Cy i + Cx j, where C is a constant of
dimensions 1/T . Derive an equation defining the streamlines for this flow. Sketch a few streamlines

4.40. CHAPTER 4, PROBLEM 40
507
4.40 Chapter 4, Problem 40
Problem: The velocity for a low-speed flow is u = 2U xy/h2 iU y 2 /h2 j, where U and h are constants.
Compute the circulation, = C u ds, on the rectangular contour shown. Verify that your result i

3.76. CHAPTER 3, PROBLEM 76
411
3.76 Chapter 3, Problem 76
Problem: Determine depth h as a function of H such that the net force in the x direction vanishes on
gate AB separating two liquids of density 1 and 2 . For this value of h, what is the vertical f

492
CHAPTER 4. KINEMATICS
4.28 Chapter 4, Problem 28
Problem: Assuming U , A and are constants, compute the vorticity for the following velocity vectors.
(a) u = A(y i x j)
(b) u = A(x i y j 2z k)
(c) u = U 1 ez/ (i + j)
Solution: (a) Since the velocity i

422
CHAPTER 3. EFFECTS OF GRAVITY ON PRESSURE
3.86 Chapter 3, Problem 86
Problem: Compute the depth, , at which the cube shown below will float in the two-liquid reservoir.
The density of the cube is c = 1.75.
.
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.
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.

486
CHAPTER 4. KINEMATICS
4.22 Chapter 4, Problem 22
Problem: In cylindrical coordinates, the rate of change of the position vector, r, is given by
dr
d
dr
d
=
(rer ) =
er + r e
dt
dt
dt
dt
The velocity vector for rigid-body rotation is u = r e , where is

4.8. CHAPTER 4, PROBLEM 8
471
4.8 Chapter 4, Problem 8
Problem: The velocity for a steady, two-dimensional, incompressible flow is u = (y x)(i + j),
where is a constant of dimensions 1/T . Compute the acceleration vector, a.
Solution: Since the given velo

3.56. CHAPTER 3, PROBLEM 56
385
3.56 Chapter 3, Problem 56
Problem: A rectangular gate with negligible weight and constant width 3 H out of the page pivots
4
about a hinge as shown. The gate is connected by a cable and pulley to a concrete sphere of densi

402
CHAPTER 3. EFFECTS OF GRAVITY ON PRESSURE
3.68 Chapter 3, Problem 68
Problem: A swimming pool has a set of (n 1) steps at one end. Each step has a horizontal and
vertical length of h/n, where h is the total depth. The width of the steps out of the pag