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

1.50. CHAPTER 1, PROBLEM 50
51
1.50 Chapter 1, Problem 50
Problem: What pressure change, p, starting from atmospheric pressure, is required to cause a 1%
change in density for helium, mercury and water? Assume the process is isothermal, and express your
a

AME 309: Midterm Exam #1 Study Guide_Spr2015
Exam Format
Exam time: 90 minutes allowed.
Number of questions: three (3), in a similar style to homework problems
The midterm exam will be open book to the extent of lecture notes, your
personal notes, homewo

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

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

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

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

Problem 1.
Solution: (a) First, note that the floats total volume is
2
2
V = 2 R3 + R2 R = 2 R3
3
3
Spherical Caps
Cylinder
To solve, we must balance all of the forces acting on the float. There are three forces acting, viz., the
weight of the float, Fw ,

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

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

498
CHAPTER 4. KINEMATICS
4.14 Chapter 4, Problem 14
Problem: For cylindrical coordinates, the acceleration in two-dimensional flow is
ar
a
ur u ur u2
ur
=
+ ur
+
t
r
r
r
u
u u u ur u
=
+ ur
+
+
t
r
r
r
Find the acceleration vector for the following

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

11.32. CHAPTER 11, PROBLEM 32
41
11.32 Chapter 11, Problem 32
Problem: A two-dimensional potential flow has streamfunction (r, ) = Jr4 sin 4
where J is a constant of dimensions 1/(L2 T ).
(a) Determine the velocity components ur (r, ) and u (r, ).
(b) Det

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

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

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

1.30. CHAPTER 1, PROBLEM 30
31
1.30 Chapter 1, Problem 30
Problem: Find the effective molecular weight of air, where the units of molecular weight are
slug/(slug-mole).
Solution: The perfect-gas constant for air is R = 1716 ftlb/(slugo R) and the universa

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

294
CHAPTER 2. DIMENSIONAL ANALYSIS
2.106 Chapter 2, Problem 106
Problem: Furry animals shake themselves vigorously to shed water when they are wet. In order to study
the process experimentally, a researcher is conducting experiments to determine the shak

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

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

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

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

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

5.72. 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 ,

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

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