1. Drag of a Disk in Laminar Flow and Flat-Plate Theory
Submitted by:
Jeffrey Fontenot

2. Given
A disk of nominal thickness is submerged parallel to the flow in a fluid of constant velocity of U

3. Sketch
Side view
Top View

4. Assumptions Steady laminar flow fully developed
no slip boundary conditions
constant temperature
constant viscosity
constant position of disk
constant velocity
smooth surfaces
disk thickness is negligible

5. Find
An approximate equation to find the drag on a disk in a parallel constant laminar flow

6. Calculations We start by finding the Reynolds number U is the velocity
D is the diameter

7. Calculations con’t
Next we find the drag coefficient which is based on the Reynolds number, this is an approximation given in Eq of the book

8. Calculations con’t
The next step is to find the drag of one side and is given as

9. We can apply this equation to any dimensions or fluids
Calculations con’t
This can be expanded to find the total drag of the disk in the following equation
We can apply this equation to any dimensions or fluids

10. Biomed Application
This type of equation could be applied to anything that would be inserted into the cardio-vascular system. Some examples consist of stints, needles, or pacemaker leads.

11. Questions ?