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
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.
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
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
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
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