ENGR 2122-03: Fundamentals of Fluid Mechanics
Fall Semester 2016
Course Instructor:
Office:
Email:
Dr. Ahmed S. El-Gendy
SSE 1073
[email protected]
Organization
The course consists of a lecture and one three-hour lab
Lecture Time:
Mondays and Thu
ENGR 261/2122 Fundamentals of Fluid Mechanics
Assignment # 5
Out: November 29, 2016
Due: December 8, 2016
Q.1 A water jet of diameter 25 mm and speed v =
20 m/s is filling a tank. The tank has a mass
of 25 kg and contains 30 liters of water at the
instant
The American University in Cairo
ENGR 2122-03 Fundamentals of Fluid Mechanics
Assignment # 1
Out: September 8, 2016
Due: September 22, 2016
1. A 25 mm diameter steel cylinder falls under its own weight at a uniform rate
of 0.1 m/s inside a tube of slightl
ENGR 2122-03 Fundamentals of Fluid Mechanics
Assignment # 6
Out: December 8, 2016
Due: December 15, 2016
Question 1
(A)Determine the type of flow in a 305 mm diameter pipe when
1. Water flows at average velocity of 1.0 m/sec and = 1.13 x 10-6 m2/sec.
2. G
ENGR 2122-03 Fundamentals of Fluid Mechanics
Assignment # 4
Out: November 7, 2016
Due: November 17, 2016
1. A tank has a hole in the bottom with a crosssectional area of 0.0025 m2 and an inlet line on
the side with a cross-sectional area of 0.0025 m2,
as
Review Problems
Set 1
Problems Provided by Dr. Hatem Elayat
Fall 2011
Dr. Ahmed M. Tolba
E-mail: [email protected]
Problem 1
How much money today is equivalent to
$10,000 in 12 years, with interest at 10%
compounded annually?
Problem 1
Solution:
F=$10,00
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
When referring to an interest, we always said
that it was x% compounded annually or x%
annual compound interest.
Practically all engineering economic analyses
incorporate annual compounding.
In per
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
The Future Worth of a uniform series is
calculated using the formula:
n
F = A
(1+i) - 1
i
OR
F=A(FA, i% ,n)
Where (FA, i%, n) is referred to as the
uniform series future worth factor.
Example: If L
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
Assessment:
Assignments
Quizzes
Project
First Midterm
Second Midterm
Final Exam(Comprehensive)
10%
10%
10%
20%
20%
30%
Most Important Dates:
March 1st - Midterm 1
April 19th Midterm 2
Other Importa
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
Solving the present worth or future worth
equivalent by treating each cash flow
individually can be time consuming.
Many Cash Flow Series are well-behaved
allowing the use of short-cuts.
Three exam
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
F=P(1+i)
n
We use this formula to determine values of F
when given values of P, i, and n.
If we want to determine the value of P when
given values of F, i, n, what should we do?
P=
F
n
(1+i(
OR
-n
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
Simple Interest is seldom used in real life
because it has an opportunity cost.
If you deposit your money in a bank account
that pays simple interest you are losing the
opportunity to gain interest
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
There is a mathematical relationship between the
present value of a single sum and its future value
in considering the time value of money.
When moving money forward on the time scale,
we are calcu
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
Occurs when the size of a cash flow
increases(decreases) by a fixed percent from n-1
A (1+j)
one time period to the next.
1
A1(1+j)
A1
0
1
P
A1(1+j)
2
A1(1+j)
n-2
2
3
n-1
End of Period
n
If j denot
Spring 2017
Dr. Ahmed M. Tolba
E-mail: [email protected]
Cash Flow Diagrams (CFDs) are used to
analyze cash flows that occur over several
time periods.
A CFD is constructed using a segmented
horizontal line as a time scale, with vertical
arrows indicatin
Abstract:
In this report I am going to discuss my experience gained through the training
session I took at Hakim Egypt Company for plastic and pipes industry. Through the
following lines not only my technical experience will be stated but I will also shed
1.6. Mul(ple Random Variables
Hatem Elayat
Mechanical Engineering Department AUC
Dr. Hatem Elayat, AUC
1
Joint Probability Distribu(ons
Vector random variables
Two Discrete random variables
Joint probability
1.4. Probability Distribu1ons
Hatem Elayat
Mechanical Engineering Department AUC
Dr. Hatem Elayat, AUC
2
References
Probability, Random Variables, and Stochas1c
Processes, Fourth Edi1on, Athanasios Papoulis &
S
1.7. Further Topics on Random
Variables & Expecta<on
Hatem Elayat
Mechanical Engineering Department AUC
Dr. Hatem Elayat, AUC
0
Topics
Expected value of RV
Variance of a RV
Sum of a random number of RV
1.3. Random Variables
Hatem Elayat
Mechanical Engineering Department AUC
Dr. Hatem Elayat, AUC
Outline
No>on of a random variable (RV)
Basic concepts
Deni>on of a Random variable
Examples of random variables
The cumula
1.8. Bivariate Normal & Jointly
Normal Random Variables
Hatem Elayat
Mechanical Engineering Department AUC
Bivariate Normal Distribu;on
The probability density func;on of a bivariate normal distribu;on is
f X ,Y (x,
1.2. Conditional Probability
Hatem Elayat
Mechanical Engineering Department AUC
Dr. Hatem Elayat, AUC
Outline
Conditional probability
Properties of conditional probability
Multiplication rule
Total probability theorem & Bayes rule
Independence
Conditional
Review Set 7: One Function of Two Random Variables
Hatem Elayat
Given two random variables X and Y and a function g(x,y), we form a new random
variable Z as
Z = g(X,Y) (examples of g(X,Y) can be Z=X+Y, Z = X/Y, or any function)
Given the joint pdf f XY (x
Review Set 6: Jointly Gaussian Random Variables
By
Hatem Elayat
Case 1: if X and Y are both independent Gaussian random variables
X ~ N ( X , X2 ) and Y~ N (Y , Y2 ) , we want to find the joint pdf of X and Y.
1 x
y
X
Y
[(
) +(
) ]
1
2 X
Y
f X,Y (x, y) =
Review Set 5: Expectations, Variance, Covariance, and Correlation
By
Hatem Elayat
Expectation
A. The following is true for any random variables (whether they are independent or not)
E[X+Y] = E[X]+E[Y]
E[aX+bY] = a E[X] + b E[Y]
E[a1 X1 + a2 X 2 + .an X n
Review set 4: Multiple Random Variables
Hatem Elayat
Problem 1:
The discrete random variables X and Y have joint p X,Y (u, v) given by
4
0
1/12
1/6
3
1/6
1/12
0
-1
1/12
1/6
1/12
v u->
0
1
3
1/12
1/12
0
5
a)Find PX Y (u 3)
the marginal of y is PY (-1) = 2(