EML 5060 Analysis in Mechanical Engineering 9/19/03
Closed book Van Dommelen 9:15-10:05 pm

Show all reasoning and intermediate results leading to your answer, or credit will be lost. ``My calculator says so'' is not acceptable. One book of mathematical tables, such as Schaum's Mathematical Handbook, may be used, as well as a calculator, and a single handwritten letter-size formula sheet.

1.

The contour of a wall in an inviscid flow satisfies the equation

This can be solved for y as

Be careful though, the only occurring values for the in the first expression are those in between and . Find the extends, intercepts, asymptotes, maxima and minima, and symmetries of this curve and based on those, draw the curve as accurately as possible. Solution.

2.

A flat solar power panel works best if it is directed towards the sun. Use an x,y,z-coordinate system with the y-axis along the ground pointing north, the x-axis pointing east, and the z-axis straight up. Assume that the sun is in the northeast, and at an inclination angle of 45 degrees above the ground. Also that the center of the solar panel is 5 meter above the ground on the z-axis. Find the equation for the plane of the solar panel in terms of the given coordinate system.

Solution.

3.

If the dimensional errors in a batch of manufactured parts follow a normal probability distribution, then the amount of parts that exceed the acceptable tolerance can be computed using the so called error function . This function is defined as

Use a Taylor series to evaluate erf(0.5) to an error of less than 0.001 using only the following keys on your calculator: . Do not evaluate more terms than needed.

Solution.