Drag of a Disk in Laminar Flow and Flat-Plate Theory

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Presentation transcript:

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

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

Sketch Side view Top View

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

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

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

Calculations con’t Next we find the drag coefficient which is based on the Reynolds number, this is an approximation given in Eq. 7.27 of the book

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

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

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.

Questions ?