MAE 101A, Homework 8 Solution
Problem 7.2
The dimensional equation is given by
A
4y
2y
+ EI 4 = 0
2
t
x
(1)
Nondimensionalize lengths by L and time by 1/. Denoting the dimensionless variables by stars, we have
y
L
x
x =
L
t = t
y =
(2)
(3)
(4)
Therefore,
MAE 101A, Homework 5 Solution
Problem 6.2
The acceleration of a particle is given by
a=
V
DV
=
+ (V
Dt
t
+v
V
x
y
= (Ax + By)
+ (Bx Ay)
[(Ax + By) + (Bx Ay)
i
j]
x
y
= [(Ax + By)A + (Bx Ay)B] + [(Ax + By)B + (Bx Ay)(A)]
i
j
)V =
u
= (A + B )x + (A + B )
MAE 101A: Introductory Fluid Mechanics Winter 2009 FINAL EXAM Professor Alison Marsden Thursday 19th, 2009. Short answers: 1. (6pt) State in words the physical meaning for a) the gradient of a scalar eld and c) the curl of a vector eld v. 2. (2pt) State i
MAE 101A
Winter 2014
HOMEWORK # 8
D. MILLER
2/24/14
Due: Thurs, 3/6/14, by 5pm at 380 EBU II, or earlier in class. NO late homework accepted!
Read: Chapter 7  all sections.
Exam # 4 : Friday, 3/7/13 ; the closed book exam will cover HW 6 & 7 material in
MAE 101A
WINTER 2014
FLUID MECHANICS
D. MILLER
1/6/14
TEXT: Introduction to Fluid Mechanics by Fox, McDonald, Pritchard; Wiley, 8th ed ; Chap 17 (selected topics from
each chapter will be assigned).
LECTURES (2M,W,F): Mon: 1010:50 in 212 CH and Mon, Wed
MAE 101A: Introductory Fluid Mechanics Homework 6 Due Friday March 12, 5:00 PM
Problem 1 The y component of velocity in a steady incompressible ow eld in the xy plane is v= 2xy (x2 + y 2 )2
Show that the simplest expression for the x component of velocity
Chapter 8 Potential Flow and Computational Fluid Dynamics
8.1 Prove that the streamlines (r, ) in polar coordinates, from Eq. (8.10), are orthogonal to the potential lines (r, ). Solution: The streamline slope is represented by
dr r d
streamlin
Cylindrical wave pattern produced in a ripple tank. When not modified by the noslip condition at solid surfaces, waves are nearly inviscid and well represented by the potential theory of
this chapter. (Courtesy of Dr. E. R. Degginger/ColorPic Inc.)

v
MAE 101A:Introductory Fluid Mechanics Homework 5 Due Monday March 1, 5:00 PM
Problem 1 Air enters a duct, of diameter D = 25 mm, through a wellrounded inlet with uniform speed, U1 = 0.870 m . At a downstream section where L = 2.25 m, the fully s develope
Table tennis ball suspended by an air jet. The control volume momentum principle, studied in this chapter, requires a force to change the direction of a flow. The jet flow deflects around the ball, and the force is the balls weight. (Courtesy of Paul Silv
MAE 101A:Introductory Fluid Mechanics Homework 4 Due Monday February 15, 5:00 PM
Problem 1 A reducer in a piping system is shown. The internal volume of the reducer is 0.2m3 and its mass is 25 kg. Evaluate the total force that must be provided by surround
The turbulent wake behind a bluff body immersed in a stream flow is a subject of the present chapter. This is a digitized video image showing the distribution of tracerdye concentration in the wake of the body. Compare with Fig. 5.2a of the text, which i
MAE 101A Winter 2014 HW #4
Due: Friday, February 7 (beginning of class)
Note:
Submit problems in following order:
H4.1, H4.2, 4.127
Text Problems:
4.127
Handout Problems:
H4.1 A horizonal water jet from a stationary nozzle impinges normally on a vertical
MAE 101A: Introductory Fluid Mechanics Homework 2 Due Friday January 22, 5:00 PM
Problem 1 The manometer shown in gure 1 contains water and kerosene. With both tubes open to the atmosphere, the freesurface elevations dier by H0 = 20.0 mm. Determine the e
fo/ Uri {'69 El
MAE 101A  Homework Assignments and Solutions
o HWI (Due Fri. 1(17114 at beginning of class*):
Textbook problems:
1.6, 1.29, 2.37, 2.41 (include shear stress prole), 2.44, 2.64 Problem 1.6
1.6 A spherical tank of inside diameter in t
MAE 101A Winter 2014 HW #7
Due: Friday, February 28 (beginning of class)
Submit problems in following order:
H7.1, H7.2, H7.3, 6.30, 6.44, 6.56, 6.58, 6.69
Text Problems:
6.30, 6.44, 6.56, 6.58, 6.69
Handout Problems:
H7.1 Recall the class demonstration o
gamer.
MAE 101A Winter 2014 HW #4
Due: Friday, February 7 (beginning of class)
Note:
Submit problems in following order: H4.1, H412, 4.127
Text Problems:
4.127
Handout Problems:
H41 A horizonal water jet from a stationary nozzle impinges normally
MAE 101A Winter 2014 HW #3
Due: Friday, January 31 (beginning of class)
Note:
Do problems in following order:
2.15, 4.25, H3.1, 4.79, 4.84, 4.109, H3.2
Submit problems in following order:
H3.1, H3.2, 4.109, 2.15, 4.25, 4.79, 4.84
Text Problems:
2.15, 4.25
S01 MHOV)
MAE 101A Winter 2014 HW #3
Due: Friday, January 31 (beginning of class)
Note:
Do problems in following order:
Submit problems in following order:
12,15,425, H3.1, 4.79, 4.84, 4.109, H32
H3.1, H32, 4.109, 2.15, 4.25, 4.79, 4.84
Text P
EXAMPLE 2.13
The coffee cup in Example 2.12 is removed from the drag ra tated about its central axis until a rigidbody mode occurs. F will cause the coffee to just reach the lip of the cup and (b) th condition.
MAE 101A: Introductory Fluid Solution Mecha
MAE 101A Spring 2014  HW #6
(Due Friday 2/21/14 beginning of class)
H6.1 Consider steady, fully developed, incompressible ow between two innite horizontal parallel
plates separated by gap width d (the origin of the x y coordinate system is located on the
An illustration of a mass balance with a deforming control volume has already been given in Example 3.2. The controlvolume mass relations, Eq. (3.20) or (3.21), are fundamental to all fluidflow analyses. They involve only velocity and density. Vector dir
MAE 101 A
WINTER 2009
MIDTERM #1
PROBLEM 1 (25 points)
A twodimensional unsteady ﬂow is given by the velocity field 17 = ui+ v}+ WE,
where u: x(l+ 3t), 12 =2y, w=0.
a) Find the equation of the time varying streamline passing through the point
(1,1) at so
MAE 101A: Introductory Fluid Mechanics
Winter 2009
MIDTERM EXAM #1 ‘
meessoi' Alison Maxsden
January 29th. 2009.
Short answers:
1. (Suit) If the velocity vector v has commonents (it. v. w), write down the material derivative of the density p.
to
_ {apt} S
2f24r’2009
MAE 101 A
WINTER 2009
Professor Juan C. Lasheras
Midterm #2
PROBLEM 1. EXTRA CREDIT (10 points)
Consider a steady flow of water through a device shOWn in ﬁgure. The three cross
sectional areas are equal A.= A2= A3=A. The volumetric ﬂow rate in
MAE101A  HW2 SOLUTION
Problem 1
Problem 3.23
[2]
Problem 2
Problem 3.27
[2]
Problem 3
Problem 3.33
[3]
s = L/he = L/(SG h) = 5/SG
Problem 4
Problem 3.51
!"#
$
Given: Find:
,./)01$.($23)4.05$46$(.0$789:9;098/
h H$%$&'$()$ A R$%$*+$()$ y B FA y z x
Sol