Light impurities in the molten metal are prevented from reaching the mold cavity by providing a

The pouring basin in a sand mold is $$200$$ $$mm$$ diameter $$100$$ $$mm$$ height. The mould cavity is a cube of $$125$$ $$mm$$ side and must be filled in $$25$$ seconds. The maximum velocity must ensure laminar flow into the mould cavity and in the gates of circular cross-section. Design the sprue to avoid aspiration effects.

Assume
(a) constant temperature,
(b) no loss in the velocity head and
(c) diameter of gate $$=8$$ times diameter at the sprue base.

Properties of the molten metal are $$\gamma = 0.9\,\,m{m^2}$$ per second, $$\rho = 700\,\,kg/{m^3},$$ & $${C_p} = 33.6\,\,J/mol$$-$$K.$$ The diameter of sprue to avoid aspiration effect.

A wire of $$0.1mm$$ diameter is drawn from a rod of $$15mm$$ diameter dies giving reductions of $$20\% $$, $$40\% $$ and $$80\% $$ are available. For minimum error in the final size, the number of stages and reduction at each stage respectively would be