# Streamlined section - using equations to find the dimensions

## Homework Statement

I need to find the values of thickness (t), mean diameter (D) and mean length (L) that will give the minimum area for the streamlined section, given that it's moment of inertia is 5.42 in^4.

## Homework Equations

(the I's and A's after all K's here are meant to be subscripts, but they didn't appear properly...)
I = K$$_{I}$$tD$$^{3}$$
K$$_{I}$$ = 0.290R+0.054

A = K$$_{A}$$tD
K$$_{A}$$ = 1.875R+0.992

R = L/D

## The Attempt at a Solution

Substitute K$$_{I}$$, K$$_{A}$$, R into both equations.

I thought I'd try using a matlab script (attached) to run through the different values of L,D,t but I don't know how to deal with 3D equations. Also, somewhere along the way I need to use the I = 5.42, but I don't know how to use that piece of information. So instead I solved the I equation for t using that I, and substituted that into the A equation. Then, making sure that t can't be greater than or equal to D/2 (since physically, that'd mean that the thickness is bigger than the radius which is obviously ridiculous). There's also a consideration that the formulae may or may not apply when the thickness to total length ratio is greater than 1/10, so I put that in there at the end but it didn't improve things. I ran the script and did a surface plot of the area, but I don't think I'm getting a sensible plot.

After that, I'm not quite sure how I'd find my values of t, D, and L... But as a first step, getting my solution in the right form would be the priority. It'd be great if anyone could help me out.

#### Attachments

• try3.m
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