1.
PETE2060ComputinginPetroleumEngineering
Homework1
Duedate09142010
Note.Pleasedonotforgettoimprovethelayoutofthespreadsheets.
Problem (Excel) Devise a test to demonstrate the validity of the following common
trigonometric formulae. What values of A and B should be used to test these functions
thoroughly?
(a) Sin( A B) Sin( A)Cos( B) Cos( A) Sin( B)
(b) Sin 2 ( A) 1 2 1 2 Cos (2 A)
Note. In excel, Sin 2 ( A) should be entered as =(sin(A))^2. This causes sin(A) to be evaluated
first and then
Problem 2. (Excel) A fairly common shape for a dry-solids storage bin (such as cements or
proppants) is a cylindrical silo with a conical section at the base where the product is removed.
R
hcon
To calculate the volume of the contents, you use the formula for a cone, as long as the height of
the product, h, is less than the height of the conical section hcon:
1
V r 2 h
3
if h< hcon
Here, rh is the radius at height h and can be calculated from h by trigonometry.
If the height of the storage is greater than the height of the conical section, the equation for a
cylinder be must added to the volume of the cone:
1
V R 2 hcon R 2 (h hcon )
3
if h> hcon
If the height of the conical section is 3m, the radius of the cylindrical section is 2m, and the total
height of the storage bin is 10m.
(a) For a series of h values between 0 and 10 m (at least for 15 different heights), calculate rh
values and bin volume in the excel sheet.
(b) Plot the volume vs. height data.
Problem 3. (Excel) Using Excel built-in functions calculate the values of Sine and Cosine
functions of angles 0, 5, 10, 15, , 355, 360 degrees. Plot the calculated values for sine and
cosine versus angles in one graph (hint: in the first column, you will put angles in degrees, in
second column you will calculate the angles of the first column in radians, in the third and fourth
column you will calculate sine and cosine respectively).
Problem 4. Write an algorithm (Pseudocode and flowchart) to calculate the summation of
numbers from 1 to 100.
Problem 5. Write an algorithm (Pseudocode and flowchart) to calculate the summation of even
numbers from 1 to 100.