HW1.2

Homework 1 Problem 2

//Main focus: This problem depends heavily upon integration. You must also know the definition of flow and the definition of a velocity profile//. //This problem is a conservation of mass problem.//

Qin = Qout Qout = Qtop + Qright

=> Qtop = Qin-Qright

Q=vA Area in this problem is related to b & d.

First, set up a coordinate system. This is a good idea to do in problem in which you need to integrate. It helps you visualize what is going on in the problem better as well as shed some light on ideas that you would not otherwise consider.

Qin = ∫∫Uo•da = Uo*bd Qright = ∫∫u•da

Integrate the Qright term with respect to the width first (I called this z, the width into the page), then integrate Qright with respect to y.**

You should end up with this:

Qtop = Uobd-5/8Uobd

Answer: Qtop = 3/8Uobd


 * Important note: Problem sets will often use "u" to demarcate a velocity profile, use this to your advantage. Most of the time you need to integrate this.
 * Note: You will need to change the "Nu" term to the y/d format when integrating to get the correct answer