In a particular mold design, the down sprue has an area of Cross section of $$6.45\,\,c{m^2}$$ where the pouring basin leads into the sprue. The sprue is $$20$$ $$cm$$ long. The required metal flow rate at the top section of the sprue is $$820$$ $$c{m^3}/s.$$ Determine the pouring height necessary above the sprue top. Also determine the area of $$C.S$$ of sprue at its bottom to avoid the aspiration of liquid molten metal.

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.

An aluminium cube of $$10$$ $$cm$$ side has to be cast along with a cylindrical riser of height equal to its diameter. The riser is not insulated on any surface. If the volume shrinkage of aluminium during solidification is $$6\% $$, calculate shrinkage volume of cube on solidification and minimum size of the riser so that it can provide the shrinkage volume.