In a large steel mill, prior to pouring the steel into a countinuous casting mac

Question

In a large steel mill, prior to pouring the steel into a countinuous casting machine to produce slabs, the steel is deoxidized using aluminum. Al will react with dissolved oxygen in the molten steel to form solid Al2O3 particles which will rise to the top of the molten steel pool held in a ladle (the oxide can be skimmed off or become part of the slag before the steel is cast). In a particular process, Al is added to the steel by feeding 3 strands of 10 mm diameter aluminum wire into the ladle. Assuming the weight % of aluminum added to the steel is 0.005% and the process needs to be completed in 5 seconds, calculate the speed (m/s) at which the aluminum wire must be fed into a 30-ton bath of steel in the ladle.

If someone could please explain to solution to this problem and give a step by step procedure, that would be great! I am completely lost.

Explanation / Answer

Forget about first 2-3 lines of the question, aluminium is used in steel in ratio of 0.005%.

Now find the mass of aluminium used= 0.005% of 30 ton= 0.0015 ton =1.5kg

Lets calculate length of aluminium used in 1 second,Let it be L,

then its speed of use will be L m/s   and Mass used in 1 seconds= 1.5/5=0.3kg

Volume used in 1 sec = 3*pi*(0.005)*(0.005)L

mass=volume * density

0.3kg=    3*pi*(0.005m)*(0.005m)L   * 8,050kg/m3........i have used density of steel as it was not given in question

0.3=1.9L

L=0.158 m

speed =0.158 m/s

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