MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 1.03
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Oil Spills may occur in ports where oil tankers are loaded. The density of oil, is le
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 1
Distributed:
Due:
Monday, February 13, 2006
Tuesday, February 21, 2006
Reading Assignment: Hibbeler Sections 1.3, 1.4, 1.
MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 1.07
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
air, Pa
h
water reservoir R
R F
Bearing, O
Given h, R, g , and the water density , de
MASSACHUSETTS
INSTITUTE TECHNOLOGY
OF
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 9
Distributed:
Due:
Wednesday, May 1,2006
Wednesday, May 8,2006
Reading Assignment: By Wed May 3: Hibbeler, sections 12.1,
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 8
Distributed: Wednesday, April 19, 2006
Due:
Monday, April 24, 2006
NO LATE HOMEWORK WILL BE ACCEPTED!
1) Reading Assignme
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 2
Distributed:
Due:
Tuesday, February 21, 2006
Monday, February 27, 2006
Reading Assignment: Hibbeler Sections 3.1, 3.2, 3.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 3
Distributed:
Due:
Tuesday, February 27, 2006
Monday, March 6, 2006
Reading Assignment: Hibbeler Sections 10.6 (+examples
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.001Mechanics and Materials I Spring, 2006
Problem Set 5
Distributed: Due:
Wednesday, March 22, 2006 Monday, April 3, 2006
Reading Assignment. Hibbeler: review Section 8.1 + read
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 10
Distributed:
Due:
Monday, May 8, 2006
Friday, May 12, 2006 Please place in collection bin in 1307
Due to the concomitan
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 6
Distributed:
Due:
Wednesday, April 5 ,2006
Wednesday, April 12 ,2006
Reading Assignment. Hibbeler: sections 6.1, 6.2, 6.3
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Mechanical Engineering
2.001Mechanics and Materials I
Spring, 2006
Problem Set 7
Distributed: Wednesday, April 12, 2006
Due:
Wednesday, April 19, 2006
Reading Assignment: Hibbeler: sections 6.5, 6.6, 7.
18.335 Practice Midterm 1. (5 points) Let A be real symmetric and positive semidenite, i.e. xT Ax 0 for all x = 0. Show that if the diagonal of A is zero, then A is zero. 2. (5 points) Show that if Y= then F (Y ) = 2n + Z 3. Let
2. F
IZ 0I
a1
c T = 1
b1
2.25 ADVANCED FLUID MECHANICS QUIZ 1 TUESDAY, OCTOBER 6, 2003, 7:009:00 P.M.
OPEN QUIZ WHEN TOLD AT 7:00 PM
THERE ARE TWO PROBLEMS
2.25 Advanced Fluid Mechanics Quiz 1, 2003 PROBLEM 1 An inventor has proposed an inexpensive, expendable device for measuri
18.335 Problem Set 1 Solutions
Problem 1: Gaussian elimination
The inner loop of LU, the loop over rows, subtracts from each row a dierent multiple of the pivot row. But this is exactly a rank1 update U U xy T , where x is the columnvector of multiplier
18.335 Problem Set 2
Due Friday, 1 October 2010.
Problem 1: Floatingpoint
(a) Trefethen, probem 13.2. (For part c, you can use Matlab, which employs IEEE double precision by default.) (b) A generalization of Trefethen, problem 14.2: given a function g (x
MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 1.00
This problem is from 2.25 Advanced Fluid Mechanics by Ain Sonin
Rate of change of properties measured by a probe moving through the earths atmosphere plus some things abou
MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Particle Kinematics
Lagrangian and Eulerian Frames  Material Derivatives The Eulerian velocity eld (u,v ) of a steady twodimensional uniform ow with velocity U in the xdirection pas
MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Change of Volume/Area, ATP
Consider a twodimensional steady ow in a domain described by an Eulerian velocity eld V = (u(x, y ), v (x, y ). Find an expression for the instantaneous rela
MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 1.13
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Accelerometer
It is a proposed to use the type of system shown in the sketch as an ac
MIT Department of Mechanical Engineering
2.25 Advanced Fluid Mechanics
Problem 1.05
This problem is from Advanced Fluid Mechanics Problems by A.H. Shapiro and A.A. Sonin
Cylinder with gas trapped
The sketch shows an inverted cylinder in which gas is trapp