Engr5011: Dimensionless Variables and ODE Recipes - Engineering Assignment Help

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For this problem provide the summary of your answers below, and attach the worked derivation and matlab code behind this sheet, as described in the header on this page.

1. Derive the -groups (as shown in class) that G.I. Taylor used for estimating of the detonation energy of the Alamogordo nuclear test.

2. Use matlab to do the least-square Öt of the data (on next page) to Önd the detonation energy (I know we did this in class, but if you already are accustomed to matlab, it will be straightforward. On the other hand, if you are new to matlab, it will be instructive!). Provide a summary of the answer here.

3. Suppose G.I.Taylor was given faulty information about the details of the Ölm, so that data distances were in "yards" instead of "meters" (and note that 1 yard = 0.9144 meters). In this situation, what is the detonation energy? (Hint, you do not need to redo the least-squares Öt.)

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Again, do your derivation on attached sheets as needed, and summarize your results on this page. The sun heats the surface of the earth with a solar-radiation áux in a cyclical fashion q 00 sun sin(! t): (Here, the units of ! is [1/sec], and the units of heat áux q 00 sun are [watts/m2 ].) The thermal conductivity of the soil k has units [watts/(m-oC)],and the thermal di§usivity of the soil a has units [m2 /sec].

1. Using q 00 sun ; !; k; and a, Önd the characteristic penetration depth a (in [m])of the sunís energy into the surface of the earth.

2. Using q 00 sun ; !; k; and a, Önd the characteristic temperature magnitude T (in [oC]), due to the sunís cyclical heating, in this surface region.

Your task in this problem is to put the governing equations in dimensionless form (only). I am not looking for the solution the resulting system of equations. A rocket is launched from rest and the governing equations are (at least while there is still fuel):

1. What is your dimensionless mass?

2. What is your dimensionless time?

3. What is your dimensionless height?

4. What is the coupled system of di§erential equations in your dimensionless variables?

5. After the fuel runs out, what are the governing equation

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