Fluid Mechanics
NAME_
Homework 08, 2016
There are 9 problems on this exam for a total of 185 points.
By signing below I agree to abide by the following honor code:
As a member of the Northwestern community, I will not take unfair advantage of any other me
Instructions for Lab 2
Remember: Do not let the pump run dry. Be sure that the pump is completely covered in water at all times.
This means that the outlet of the Tygon tube must run back to the water container.
Things you will need: All the handed out pa
The ideal gas law
We will not cover the ideal gas law in very much detail in this course. The reasons are that:
1) presumably, you have worked with the law already quite a bit in chemistry and in thermodynamics,
2) we want to devote most of our time in th
Topic 19: Review of Kinematics
Please memorize this derivation so that you never need to memorize any of these equations ever
again.
Yes, you need to memorize the quadratic formula.
a=a
Z
v=
a dt = at + v0
can be written as:
t=
v v0
a
Z
x=
1
v dt = at2 +
1. Consider the vector field V and the scalar function
If it is possible, find the quantities requested below. If it is not possible to find the quantity, write not possible
xV
V
V
2V
2
x
V
(V )V
2. Consider the vector field V and the scalar function .
Pascals law and pressure variation in a fluid at rest
1. Circle true or false. The pressure at any point in a moving, inviscid fluid is the same in all directions, as
long as that fluid is contained in a single continuous volume.
2. Using the equation P2
Incompressible, single fluids
1. Find the pressure in the fish tank as a function of z. Assume = constant
1A. Express your answer in absolute pressure
1B. Express your answer in gage pressure
1C. Suppose you take the fish tank and set it on a shelf six fe
Stacked incompresible fluids
1. Find the pressure in the fish tank as a function of z. Assume 1 and 2 are constants
1A. Express your answer in gage pressure
1B. Express your answer in absolute pressure
1C. Suppose you take the fish tank and set it on a sh
Manometers
Remember that for this class, all manometer problems will contain only
incompressible fluids.
1. What is the specific weight A of the fluid in pipe A?
The manometer is open to the atmosphere. Your answer may include some or all
of the following
Topic 02 Basic properties of fluids
1. Gaining some physical intuition for orders of magnitude and the properties of our amazing planet.
There are FOUR NUMBERS you must memorize for this course.
For this first problem, the FOUR numbers that you need to me
Topic 18. Buoyancy and Stability
Hint: Students often lose points on exams because they do not indicate whether is fluid or object. We hate to
take points off for this, but often times we cannot tell which one you meant, and we cant give you credit.
When
Instructions for Lab 1
Remember: Do not let the pump run dry. Be sure that the pump is completely covered in water at all times.
This means that the outlet of the Tygon tube must run back to the water container.
Things you will need: The handed out parts:
Instructions for Lab 3
Remember: Do not let the pump run dry. Be sure that the pump is completely covered in water at all times.
This means that the outlet of the Tygon tube must run back to the water container.
Things you will need: All the handed out pa
4
Exam 5, Spring 2008
page 7
Problem 5 (20 points)
In class we discussed the use of a Venturi meter to
measure the velocity of a fluid flow. Here is a
"Venturi Pump," which consists of a constricted
circular tube connected to a vertical pipe as shown.
The
Fluid Mechanics
Problem Set 1
1. Complete the homework problems on the worksheet on the Del Operator
Answers posted separately
2. Complete the homework problems on the worksheet on Double Integrals
Answers posted separately
3. Think about derivatives and
Extra problems on buoyancy
Problem 1:
A cylindrical slab of ice (density 900kg/m3) of circular cross section (radius R=2.0m) and
height H=20cm floats in sea water (density 1030kg/m3).
(a) A group of N=50 penguins (mass m=5.0kg each) decides this is a good
Solutions to problem 0 and Problem 17 will not be posted, they are just problems for you to
think about.
Problem 19 does not exist.
1. Find the pressure in the fish tank as a function of z.
Assume = constant
a) In gauge pressure, 0 so:
b) In
ME 241/ BME 270
Worksheet on the operator (called del or nabla)
Adapted from Introduction to Electrodynamics by David J. Griffiths, Prentice Hall, 1981
Part One: The definition of the operator
All of differential vector calculus flows from the operator.
ME 241/BME 270
Worksheet on Double Integrals
Part 1: Cartesian coordinates
Problem 1: Write a double integral to find the area of the rectangle between x1 and x2, and y1
and y2.
Problem 2: The surface density of people in a rectangular room varies as: p(x
Fluid Mechanics
NAME_
Homework 08, 2016
There are 9 problems on this exam for a total of 185 points.
By signing below I agree to abide by the following honor code:
As a member of the Northwestern community, I will not take unfair advantage of any other me
Fluid Mechanics
NAME_
Homework 6, Spring 2016
There are 6 problems on this exam for a total of 111 points.
By signing below I agree to abide by the following honor code:
As a member of the Northwestern community, I will not take unfair advantage of any ot
Topic 18. Buoyancy and Stability
Hint: Students often lose points on exams because they do not indicate whether is fluid or object. We hate to
take points off for this, but often times we cannot tell which one you meant, and we cant give you credit.
When