AME331Exam1
Fall2010
Prof.JesseLittle
10/4/10
1. (30 points) Water flows down a pipe that is inclined 30o as show below. Find the pressure
wn
difference,p=pApB,ifL=1.5mandh=15cm.SGHg= 13.55
2. (45 points) A static thrust stand for testing a jet engine is

9/30/2010
AME 331
Introduction to Fluid Mechanics
Chapter 5: Differential Analysis of Fluid
Motion
Prof. Jesse Little
University of Arizona
10/1/10
1
Lecture Preview and Assignments
Today
Chapter 5.3 (skipped 5.2)
Read Chapter 5.3 for next time
We wil

Quiz 1
Two containers with the same depth c hold
water (w) as sketched, where a=2b.
1
b
a
P1
a
2
b
P2
Calculate the water weight ratio: W2/W1
Calculate the pressure ratio: P2g/P1g
1.
W1=wabc ; W2=wbac
2.
P1g=wgb ; P2g=wga=2wgb
P2
P1
=
Pa + 2wgb
Pa + wgb

Quiz 2
1. Express mathematically the conservation of
mass law in integral form, and explain the
physical interpretation of each term.
2. In general, which energy is conserved?
3. State the Bernoulli Eq. for steady, incomp.
flow with no energy source/sink.

AME 331 Introduction to Fluid Mechanics
Fall 2013
Aug 26, 2013 - Dec 11, 2013
Class Meetings:
Tuesday & Thursday, 08:00-09:15 am, AME S202
Course Description:
Fundamentals of fluid mechanics covering properties of fluids, fluid
statics, dynamics of incomp

AME 331 Exam 2
Fall 2010
Prof. Jesse Little
11/5/10
. This represents a solution to the
1. (30 points) A velocity field is given by:
Navier-Stokes equation for a fluid with constant density, =1.2 kg/m3, and constant
viscosity, =2x10-5 N*s/m2. Body forces

Quiz 5
1. Define the proper Reynolds number for the
laminar-to-turbulent flow transition on a flatplate boundary layer with no pressure gradient.
2. What is the transition Reynolds number from
laminar to turbulent flow in a flat-plate
boundary layer with

1/11/2013
AME 331
Introduction to Fluid Mechanics
Lecture 1
Chapter 1: Introduction
Prof. Jesse Little
University of Arizona
1/11/13
1
Course Structure
Lectures posted by midnight on the day before
lecture
Lecture examples posted after lecture
D2L used

9. Boundary Layers
The concept of a boundary layer is due to
Prandtl. Many viscous flows can be analyzed by
dividing the flow into two regions, one close to
the solid boundaries, the other covering the rest
of the flow.
Only in the thin region adjacent to

Problem 2.44
Given:
Ice skater and skate geometry
Find:
[Difficulty: 2]
Deceleration of skater
yx =
y
Solution:
Governing equation:
du
yx =
dy
Fx = M ax
du
dy
V = 20 ft/s
h
x
L
Assumptions: Laminar flow
The given data is
W = 100 lbf
V = 20
5 lbf s
=

Problem 2.37
[Difficulty: 2]
Given:
Sutherland equation
Find:
Corresponding equation for kinematic viscosity
1
Solution:
=
b T
2
1+
Governing equation:
S
p = R T
Sutherland equation
Ideal gas equation
T
Assumptions: Sutherland equation is valid; air is an

Problem 2.38
Given:
Sutherland equation with SI units
Find:
[Difficulty: 2]
Corresponding equation in BG units
1
Solution:
=
b T
2
1+
Governing equation:
S
Sutherland equation
T
Assumption: Sutherland equation is valid
The given data is
6
b = 1.458 10
kg

Problem 2.36
[Difficulty: 4]
Given:
Velocity field
Find:
Coordinates of particle at t = 2 s that was at (2,1) at t = 0; coordinates of particle at t = 3 s that was at (2,1) at t = 2 s;
plot pathline and streakline through point (2,1) and compare with stre

Problem 2.35
[Difficulty: 4]
Given:
Velocity field
Find:
Coordinates of particle at t = 2 s that was at (1,2) at t = 0; coordinates of particle at t = 3 s that was at (1,2) at t = 2 s;
plot pathline and streakline through point (1,2) and compare with stre

Problem 2.34
[Difficulty: 3]
Given:
Velocity field
Find:
Equation for streamline through point (2.5); coordinates of particle at t = 2 s that was at (0,4) at t = 0; coordinates of
particle at t = 3 s that was at (1,4.25) at t = 1 s; compare pathline, stre

Problem 2.33
[Difficulty: 3]
Given:
Velocity field
Find:
Equation for streamline through point (1.1); coordinates of particle at t = 5 s and t = 10 s that was at (1,1) at t = 0;
compare pathline, streamline, streakline
Solution:
Governing equations:
v
For

Problem 2.25
[Difficulty: 3]
Given:
Flow field
Find:
Pathline for particle starting at (3,1); Streamlines through same point at t = 1, 2, and 3 s
Solution:
dx
For particle paths
Separating variables and integrating
dy
= u = a x t
dx
x
an
d
= a t dt
dt
or

Problem 2.26
[Difficulty: 4]
Given:
Velocity field
Find:
Plot streamlines that are at origin at various times and pathlines that left origin at these times
Solution:
v
For streamlines
u
=
dy
dx
v 0 sin t
=
u0
v 0 sin t
So, separating variables (t=const)

Problem 2.27
Given:
Velocity field
Find:
[Difficulty: 5]
Plot streakline for first second of flow
Solution:
Following the discussion leading up to Eq. 2.10, we first find equations for the pathlines in form
(
x p( t) = x t , x 0 , y 0 , t0
)
and
(
y p( t)

Problem 2.28
[Difficulty: 4]
Given:
Velocity field
Find:
Plot of streakline for t = 0 to 3 s at point (1,1); compare to streamlines through same point at the instants t = 0, 1
and 2 s
Solution:
Governing equations:
For pathlines
up =
dx
vp =
dt
dy
v
For s

Problem 2.29
[Difficulty: 4]
Given:
Velocity field
Find:
Plot of streakline for t = 0 to 3 s at point (1,1); compare to streamlines through same point at the instants t = 0, 1
and 2 s
Solution:
Governing equations:
For pathlines
up =
dx
vp =
dt
dy
v
For s

Problem 2.30
[Difficulty: 4]
Given:
Velocity field
Find:
Plot of pathline for t = 0 to 3 s for particle that started at point (1,2) at t = 0; compare to streakline through same
point at the instant t = 3
Solution:
Governing equations:
up =
For pathlines
d

Problem 2.31
[Difficulty: 4]
Given:
2D velocity field
Find:
Streamlines passing through (6,6); Coordinates of particle starting at (1,4); that pathlines, streamlines and
streaklines coincide
Solution:
v
For streamlines
u
=
a y
Integrating
3
dy
dx
b
=
2
a

Problem 2.32
Solution
Pathlines:
t
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
3.80
4.00
[Difficulty: 3]
The particle starting at t = 3 s follows the particle starting at t = 2 s;
The particle starting at

Problem 2.40
[Difficulty: 2]
Given:
Velocity distribution between flat plates
Find:
Shear stress on upper plate; Sketch stress distribution
Solution:
Basic equation
du
yx =
dy
yx =
At the upper surface
Hence
y=
du
=
dy
d
dy
u max 1
2
2 y = u 4 2 y = 8