484
CHAPTER 4. KINEMATICS
4.20 Chapter 4, Problem 20
Problem: For flow near the stagnation point of a cylinder, the velocity is u = (4U/D) (x i y j),
where D is the cylinders diameter and U is the speed of the incident flow. Determine the Lagrangian
descr

3.8. CHAPTER 3, PROBLEM 8
347
3.8 Chapter 3, Problem 8
Problem: James Bond has just thrown Blofeld into a vat of mercury. If Blofeld,
chained to a piece of Plutonium, sinks to a depth of 9 ft, will he have to worry about
the bends as he floats back to the

11.52. CHAPTER 11, PROBLEM 52
77
11.52 Chapter 11, Problem 52
Problem: In a hurricane, the wind is blowing with velocity U = 50 m/sec, freestream
pressure p = 101 kPa and density = 1.20 kg/m3 past a quonset hut, which is a half
cylinder of radius R = 4 m

AME 309 SPRING 2007
TEST 1
NAME
.I.D\~+Of'>
;
Problem 1
A cylindrical shaft having an outside diameter o f I8 mm turns at 20 revolutions per
second inside stationary cylindrical bearing 60 mm long. A thin film of oil. 0.2 mm thick
fills the concentric ann

1.6. CHAPTER 1, PROBLEM 6
7
1.6 Chapter 1, Problem 6
Problem: Aviation pioneer Amelia Earhart weighed 118 lbs and stood 5 feet 8 inches
tall. What was Earharts mass in slugs? Determine her mass and height in kg and m,
respectively.
Solution: First, denoti

4.60. CHAPTER 4, PROBLEM 60
553
4.60 Chapter 4, Problem 60
Problem: The velocity vector is u = U y 2 z/h3 j U yz 2 /h3 k for an incompressible
flow, where U and h are constant velocity and length scales, respectively. Compute the
mass flux, m, and momentu

5.58. CHAPTER 5, PROBLEM 58
623
5.58 Chapter 5, Problem 58
Problem: The figure depicts incompressible flow through a pipe and nozzle that emits a vertical jet.
The flow is steady, irrotational, has density and the only body force is gravity. What is the v

5.48. CHAPTER 5, PROBLEM 48
613
5.48 Chapter 5, Problem 48
Problem: Determine the maximum pressure on your hand when you hold it out the window of your
automobile on a day when the ambient pressure is 1 atm and the temperature is 68o F. Assuming the
condi

4.16. CHAPTER 4, PROBLEM 16
501
4.16 Chapter 4, Problem 16
Problem: Consider a flow for which the velocity vector is u = U (ay i + j), where U
and a are characteristic velocity and inverse length scales, respectively. Determine the
Lagrangian description

11.58. CHAPTER 11, PROBLEM 58
89
11.58 Chapter 11, Problem 58
Problem: The Flettner-Rotor ship was designed with two rotating cylinders of height
H acting as sails. The cylinders have diameter D and rotate with angular velocity .
The ship moves with veloc

440
CHAPTER 3. EFFECTS OF GRAVITY ON PRESSURE
3.100 Chapter 3, Problem 100
Problem: A rectangular gate of height 2h and width h out of the page separates two liquids of densities
and as shown. A cube-shaped air balloon of side and negligible weight is at

4.14. CHAPTER 4, PROBLEM 14
477
4.14 Chapter 4, Problem 14
Problem: The velocity vector for a flow is u = f (y, z ) i + h(z, t) k, where f (y, z ) and h(z, t) are
arbitrary functions of dimensions L/T . What is the acceleration vector, a?
Solution: The ac

522
CHAPTER 4. KINEMATICS
4.54 Chapter 4, Problem 54
Problem: For unsteady flow near the stagnation point of an accelerating body, the velocity is given by
u = F (t) [x i y j], where F (t) denotes dF/dt.
(a) Derive an equation for the instantaneous stream

420
CHAPTER 3. EFFECTS OF GRAVITY ON PRESSURE
3.84 Chapter 3, Problem 84
Problem: You have invited your wifes family for Christmas dinner. Your mother-in-law, who has
been misled by two generations of late-night talk-show hosts, hates fruit cake and has j

538
CHAPTER 4. KINEMATICS
4.70 Chapter 4, Problem 70
Problem: A mountain community is connected to a large city in the valley by a single highway. The
rate at which autos enter the highway from the communitys single on-ramp is non . There is one off
ramp

502
CHAPTER 4. KINEMATICS
4.36 Chapter 4, Problem 36
Problem: In cylindrical coordinates for two-dimensional flow, the vorticity is given by
=
1
ur
(ru )
k
r r
Compute the vorticity for the following velocity vectors, where U and R are constants.
(a) u

504
CHAPTER 4. KINEMATICS
4.38 Chapter 4, Problem 38
Problem: For stagnation-point flow, the velocity is u = Ax i Ay j, where A is a constant. Compute
the circulation, = C u ds, on the rectangular contour shown. Verify that your result is consistent
with

5.20. CHAPTER 5, PROBLEM 20
575
5.20 Chapter 5, Problem 20
Problem: The y component of the velocity vector for a two-dimensional, incompressible, irrotational
flow is v (x, y ) = U (y/h 1), where U and h are constant velocity and length scales, respective

5.4. CHAPTER 5, PROBLEM 4
559
5.4 Chapter 5, Problem 4
Problem: In a one-dimensional, compressible flow, the density decreases exponentially from b to a ,
i.e., = a (a b ) et/ , where is a constant time scale. If the velocity at x = 0 is u(0, t) = uo ,
wh

604
CHAPTER 5. MASS AND MOMENTUM PRINCIPLES
5.42 Chapter 5, Problem 42
Problem: A cylinder moves at constant speed U through glycerin at 68o F. The difference between
the pressure at the front stagnation point on the cylinder and at Point P in the wake of

594
CHAPTER 5. MASS AND MOMENTUM PRINCIPLES
5.34 Chapter 5, Problem 34
Problem: A small car containing an incompressible fluid of density is rolling down an inclined plane.
Show that the free surface is planar and determine the angle it makes with the hor

5.72. CHAPTER 5, PROBLEM 72
637
5.72 Chapter 5, Problem 72
Problem: Consider a poorly designed Pitot-static tube with a single static-pressure hole at the top of
the tube as shown. If the tube radius is r, develop a formula for the true velocity, Utrue ,

4.82. CHAPTER 4, PROBLEM 82
553
4.82 Chapter 4, Problem 82
Problem: The two-dimensional Laplacian of the velocity vector, u, is defined by
2 u =
2u 2u
+2
x2
y
By direct substitution, verify the following identity in Cartesian coordinates for two-dimensio

532
CHAPTER 4. KINEMATICS
4.64 Chapter 4, Problem 64
Problem: The velocity vector is u = (U/h3 )(y 2 z j yz 2 k) for an incompressible flow of density ,
where U and h are constant velocity and length scales, respectively. Compute the mass flux, m, and
mom

Problem 1.
Solution: To begin our solution, we note that the distance the fluid rises in a capillary tube, h, is
h =
P
cos
gA
where P is the perimeter of the tube and A is its cross-sectional area. For a square tube with side s, we
have
4
P
P = 4s
and
A

368
CHAPTER 3. EFFECTS OF GRAVITY ON PRESSURE
3.42 Chapter 3, Problem 42
Problem: Use the parallel-axis theorem to compute the centroid location, z , area, A, and moment of
inertia about the centroid, I , for the diamond-shaped geometry shown.
.
.
.
.
.
.

2.8. CHAPTER 2, PROBLEM 8
135
2.8 Chapter 2, Problem 8
Problem: The empirical Ostwald de Waele formula, is an approximation for non-Newtonian fluids
given by
n
du
=K
dy
where is shear stress, u is velocity, y is distance normal to the flow direction and

1.112. CHAPTER 1, PROBLEM 112
125
1.112 Chapter 1, Problem 112
Problem: Water is flowing very slowly through a drain pipe of diameter D = 5 cm and length
L = 120 m. The pressure difference between inlet and outlet is (p1 p2 ) = 0.04 kPa, and the temperatu

1.100. CHAPTER 1, PROBLEM 100
107
1.100 Chapter 1, Problem 100
Problem: A cube of density and side s slides down an inclined plane coated with a thin lubricating
film of thickness h and viscosity . Its terminal velocity is U . Assume the Couette-flow solu

Thermodynamics
What is it?
A theory is the more impressive the greater the simplicity of its premises, the more
different kinds of things it relates, and the more extended its area of applicability.
Therefore the deep impression classical thermodynamics h

Basic definitions and other boring, but
essential stuff
Boundary
An infinitely thin demarcation between two regions.
A boundary point separates a line into 2 linear
regions
A boundary line separates a plane into 2 planar
regions
A boundary plane separates

Properties of a pure, simple,
compressible substance
Pure substance
Chemically homogeneous with a fixed chemical
composition (no reactions allowed).
Atoms of a single element; or
Molecules of a single compound (two or more
chemically combined elements)